# Senior Honors Theses

**Robert Kwark, '17 ***Berry-Phase Interference in the Ni4 Single-Molecule Magnet*Faculty Advisor: Professor Jonathan R. Friedman

**David Lane, '17***Developing a Quantum Toolbox: Experiments with a Single-Atom Harmonic Oscillator and Prospects for Probing Molecular Ions*Faculty Advisor: Professor David Hanneke

**Edward Kleiner, '16***Quantum Control of Be ^{+} Ions*

Faculty Advisor: Professor David Hanneke

**Ji Hoon Lee, '16***Geometry of the Kepler Problem and the Kepler-Lorentz Duality*

Faculty Advisor: Professor Kannan Jagannathan

**Wonjae Lee, '16***Exotic Synthetic Electromagnetic Fields in Shankar Skyrmions*

Faculty Advisor: Professor David Hall

**Daniel Ang, '15***In Search of New Geometries for Probing Spin-Spin Interactions*

Faculty Advisor: Professor Larry Hunter

**Andrei Horia Gheorghe, '15***Topological Excitations in Spinor Bose-Einstein Condensates*Faculty Advisor: Professor David Hall

**Owen Marschall, '15***Anomalies in Quantum Mechanics*Faculty Advisor: Professor William Loinaz

**Julian Ricardo, '15***Optimizing a Polarization-Sensitive Resonance Energy Transfer Assay for Observing Microtubule Nucleation*Faculty Advisor: Professor Keisuke Hasegawa

**Sarah Vickery, '15***Meron Pairs: A Topological Defect in Bose-Einstein Condensates*Faculty Advisor: Professor David Hall

**Changyun Yoo, '15***Towards Landau-Zener-Stueckelberg Interferometry on Single-Molecule Magnets*

Faculty Advisor: Professor Jonathan Friedman

**Jiajun Shi, '15E***Radiofrequency Synthesis System for Laser Modulation* Faculty Advisor: Professor David Hanneke

**Shah Saad Alam, '14***High Resolution Laser Spectroscopy of the B(0)-X(0) Cycling Transition of Diatomic Thallium Fluoride* Faculty Advisor: Professor Larry Hunter

**Andre Antunes de Sa, '14***Constructing an Optical Phase-Locked Loop for Partial-Transfer Imaging of Bose-Einstein Condensates* Faculty Advisor: Professor David Hall

**Phyo Kyaw, '14***Constructing An Ultra-High Vacuum Chamber and a Radio Frequency Helical Resonator for Trapping Ions* Faculty Advisor: Professor David Hanneke

**Andrew Mowry, '14***Refining the Spectroscopic Techniques for the Characterization of Single Molecule Magnets* Faculty Advisor: Professor Jonathan Friedman

**Chu Teng, '14E***Frequency Control and Stabilization of a Laser System* Faculty Advisor: Professor David Hanneke

**Spencer Adams, '13***Towards an Examination of the Sweet Spot Principle in Cr _{{7}}Mn, a Single Molecule Magnet Qubit*

Faculty Advisor: Professor Jonathan Friedman

**Nicholas Bern, '13***AC Magnetic Noise Cancellation For The Purpose of Creating Dirac Monopoles in a Spinor Condensate*Faculty Advisor: Professor David Hall

**Celia Ou, '13***Third Harmonic Conversion*Faculty Advisor: Professor David Hanneke

**Shenglan Qiao, '13***Constructing a Linear Paul Trap System for Measuring the Time-variation of Electron-Proton Mass Ratio*

Faculty Advisor: Professor David Hanneke

**Nathan Thomas, '13**

Applications of Stimulated Raman Scattering in Bose-Einstein Condensates

Faculty Advisor: Professor David Hall

**Neha Wadia, '13***Measurements of Branching Ratios for the B(0) - X(v) Transition in Thallium Fluoride to Determine its Potential for Laser Cooling*

Faculty Advisor: Professor Larry Hunter

**Aftaab Dewan, '12***Neutrino Scattering as Probe for High-Energy Physics*Faculty Advisors: Professors Kannan Jagannathan and William Loinaz

**Saugat Kandel, '12***Seeking a Dirac Monopole in a Spinor Condensate*Faculty Advisor: Professor David S. Hall

**Emine Altuntas, '11***Real-Time Dynamics of Co-Rotating Vortex Pairs in Bose-Einstein Condensates*

Faculty Advisor: Professor David S. Hall

**Andrew Eddins, '11***Direct Observation of Superradiance in Fe _{8} Single-Molecule Magnets*

Faculty Advisor: Professor Jonathan R. Friedman

**Andrew Greenspon, '11***A Measurement of the Lifetime and Franck-Condon Factors for the B(0) State of TlF to Determine its Potential for Laser Cooling*

Faculty Advisor: Professor Larry R. Hunter

**Thomas Langin, '11***Generation of Counter-Circulating Vortex Lines in a Bose-Einstein Condensate*

Faculty Advisor: Professor David S. Hall

**Thomas McClintock, '11***The Contribution from Low-Mass X-Ray Binaries to the Positron Annihilation in the Galactic Disk*

Faculty Advisor: Professor Fulvio Melia

**Kathryn McKinnon, '11***Decaying Dark Matter as a Possible Resolution to the Cusp Problem in Large-Scale Structure*

Faculty Advisor: Professor Fulvio Melia

**Rachel S. Ruskin, '10***A Quantitative Analysis of Voltage-Gated Potassium Ion Channel Transitions*

Faculty Advisor: Professor William A. Loinaz

**Vikyath Deviprasad Rao, '10***Searching for interference of flux-tunneling paths in the microwave-driven single Cooper-pair transistor*

Faculty Advisor: Professor Jonathan R. Friedman

**Daniel V. Freilich, '10***Real-Time Experimental Visualization of Bose-Einstein Condensates with One and Two Vortices*

Faculty Advisor: Professor David S. Hall

**Dean U. Udom, '10***Improving the Experimental Precision of a Solid-State Electron EDM Search*

Faculty Advisor: Professor Larry R. Hunter

**Dylan Bianchi, '09**

*Characterizing a Crossed-Beam Optical Dipole Trap for Ultra-cold*

^{ 87}Rb AtomsFaculty Advisor: Professor David Hall

The construction in our laboratory of a crossed-beam optical dipole trap in 2006 opened up many exciting experimental possibilities. The purely optical potential permits us to study ^{87}Rb Bose-Einstein condensates in any spin state and with tunable interactions. The crossed-beam trap also solves the long-standing problem of confining condensates with quantized vorticity. Studies of the interplay between these three phenomena are expected to yield new insights into the behavior of quantum fluids. To precisely describe these phenomena, the optical potential in which our condensates are confined must be quantitatively understood. In this thesis, we present several techniques for quantitatively characterizing this confining potential. We also discuss and diagnose several of our trap’s pathologies, and we describe procedures for efficiently aligning the trapping beams.

Faculty Advisor: Professor William Loinaz

Many theories of particle physics predict the appearance of new phenomena at energy scales at or above a TeV. This is no less true in the neutrino sector than anywhere else. We wished to test the statistical sensitivity of neutrino experiments at this scale, specifically beamline experiments firing on fixed target electrons.

We have, with the help of some outside software, successfully written a Mathematica based program that automates most of the calculation procedure for neutrino scattering. Our program takes a description of a particular interaction and calculates the differential cross section for that event at the tree level. The matrix element method of calculating the cross section from Feynman diagrams was our basis for these calculations.

The program then uses the cross section and certain user defined beam parameters to calculate the sensitivity of the event to statistical uncertainties in the vector and axial neutrino-electron coupling constants. This was done by assuming the Standard Model values to be correct and performing a regression analysis with our regression parameters (the deviation from the Standard Model coupling constants) set to zero in the pre defined dependent variables. The resulting uncertainty in the fit for those parameters then gives us a measure of how statistically limited the measurements taken by the experiment for that interaction are. By performing these calculations on a computer, we allowed for better adaptation of our procedure for processes not examined directly by us.

We performed this procedure for all possible events involving a neutrino or antineutrino of each of the three known flavors scattering off an electron. Our principal focus was on muon neutrinos, as those are the most likely to be used in future beamline experiments.

*Using Repeated Landau-Zener Transitions to Factor Integers in a Superconducting Qubit*

Faculty Advisor: Professor Jonathan Friedman

In 1994, Peter Shor demonstrated that quantum computers can efficiently factor large integers, a problem believed to be computationally difficult on classical computers. Despite the excitement created over this discovery, to date scientists have managed to factor only the number 15 using Shor's algorithm. The goal of this thesis is to explore an end-around method of factoring integers that is fundamentally different than that of Shor.

We consider a superconducting flux qubit as our two level system (though it can be extended to other implementations). The two lowest energy levels of this qubit have an energy splitting at the flux degeneracy point resulting in an avoided crossing. By initializing the qubit in its ground state and applying a harmonic driving flux, we can induce repeated Landau-Zener transitions into the excited state as the qubit passes the avoided crossing. This process is analogous to Mach-Zehnder interferometry and results in diffraction. If the drive frequency is a factor of the flux detuning (in appropriate units), then repeated the Landau-Zener transitions will yield constructive interference. As it stands, however, this method is a factor tester and not a factorizer. We are exploring different entanglement schemes that might allow us to test multiple factors simultaneously and produce the desired speedup.

**Adam Kaufman, '09**

Radiofrequency Dressing of Atomic Feshbach Resonances

Faculty Advisor: Professor David Hall

A Feshbach resonance occurs when the energy of the free scattering state of two colliding atoms becomes degenerate with a molecular bound state supported by the interatomic potential. These resonances can be observed by adjusting an external magnetic field, which changes the relative energy of the atomic and molecular systems. In our system, when the field is tuned to the Feshbach resonance the atoms are lost due to molecular decay. This thesis addresses three interspecies Feshbach Resonances in ^{87}Rb near 9 G. Theoretically, the introduction of a radiofrequency drive couples the resonances and leads to a series of avoided crossings between the various internal states. This greatly modifies the loss profile as a function of magnetic field. We experimentally observe at least two avoided crossings using a Landau-Zener technique, and present a precise measurement of the three Feshbach resonances.

*Lattice Simulations of the φ4 Theory and Related Systems*

Faculty Advisor: Professor William Loinaz

Lattice models are a big industry in physics, spanning multiple fields from polymer science to quantum field theory. The primary mode of their investigation is through Monte Carlo simulation: sampling some of the many possible states of the model using a computer, in the hope of obtaining an accurate picture of the entire system. In my work, I perform a sequence of such simulations, using models of increasing complexity, most of which are instances of the so-called classical N-vector model. I begin with random walks, including the self-avoiding variety; move on to the Ising model of the ferromagnet; and finally focus on a discretized φ^{4} quantum field theory. Despite being closely related, some of these models are much more tractable than others. For instance, properties of the non-reversing random walk or the two dimensional Ising model can be derived exactly, while the self-avoiding random walk and the three dimensional Ising model appear insoluble. I quote or derive analytical results where these are obtainable and use them as a check on my simulations.

The final objective of my work is a precise determination of the φ^{4 }critical line in two and three dimensions, necessary to make inferences about the theory’s critical coupling, a quantity of interest from a QFT perspective. Certain quantities characterizing the model, such as specific heat or magnetic susceptibility, diverge at the phase transition and can therefore serve as its indicators. Unfortunately, the phase transition line I am interested in is the one of the infinite lattice, while my simulations are, of course, performed on finite lattices. To overcome this difficulty, I resort to a number of finite size scaling techniques borrowed from the study of classical systems, such as the Ising model. If time permits, I may also apply and discuss renormalization group methods, another large family of techniques from statistical physics.

*An Investigation of Precursors in Fluid Surface Waves*Faculty Advisor: Arthur Zajonc

My research concerns wave phenomena called precursors that are an interesting consequence of dispersion (the dependence of wave velocity on frequency). Precursors manifest themselves as characteristic wave patterns that precede---and sometimes follow---a signal as it travels through a medium. By detecting the fastest precursor, one can therefore receive a signal before the original signal technically arrives.

Precursors theoretically occur in any medium that supports wave motion, but they can be extraordinarily difficult to detect in the case of some electromagnetic waves. My research, which combines both experimental and theoretical work, is limited to the case of fluid surface waves, which is by far the easiest place to observe precursors. The experimental portion involves creating impulses in a tank of water and recording the resulting waveforms using non-disruptive methods at different distances of propagation for different depths of water. The theoretical portion is concerned with how this data should be analyzed to determine whether or not precursors are present. Traditionally this task takes an indirect approach, since closed-form solutions to the equations that model precursor behavior only exist for very idealized and unrealistic cases, water waves not among them. To help bridge the gap between theory and experiment, I am investigating the application of numerical techniques to the problem with the aim of simulating a complete precursor waveform using only first principles and a few limited assumptions specific to my apparatus. By comparing this directly with my experimental data, I hope to elucidate the main theoretical issues in my analysis.

*Interference of Flux Tunneling Paths in a Superconducting Qubit *Faculty Advisor: Professor Jonathan Friedman

Interference crops up in diverse areas of physics. In quantum mechanics, it is fundamental. The interference between paths governs the dynamics of a quantum system. In this thesis, I investigate interference between two tunneling paths taken by quantized units of magnetic flux. The system I investigate is a superconducting flux qubit cooled to ~10 mK in a dilution refrigerator. In this system, a large number of cooper pairs occupy the same quantum state, acting in concert as a single quantum system. Two Josephson junctions in series are the key nonlinear elements of this superconducting circuit. These junctions are insulating gaps that weakly couple the separated superconductors. The supercurrent passing through the qubit is dependent on the phase difference across the two Josephson junctions. When a single flux quantum tunnels across the qubit through this gap, the phase “slips” by 2*pi*. Because there are two gaps, there are two possible paths the flux quantum may take, and the possibility for destructive interference. For certain parameters, the phase will only slip by multiples of 4*pi*. Evidence of this phenomenon can be observed by applying electromagnetic radiation and measuring the I-V characteristics of the qubit. This will produce Shapiro steps, where the voltage is allowed only quantized values depending on the bias current. The *n*^{th} step corresponds to the phase slipping by (2*pi*)*n* during each cycle of the radiation. If only 4*pi* phase shifts occur, the voltage difference measured between consecutive steps will double. I hope to observe this doubling of Shapiro step voltage in the qubit, and attribute it to interference that prohibits the tunneling of single flux quanta, but allows pairs.

_{12}-tBuAc. The core of this molecule has an arrangement of twelve Manganese magnetic ions giving the molecule a total (giant) spin of 10. This SMM has a large uniaxial anisotropy between the m=+10 and m=-10 eigenstates of the S

_{z }spin operator. The spin can reverse direction by rotating from up (m=+10) to down (m=-10) if it has enough thermal activity to “climb” over the anisotropy barrier. But at low enough temperatures this classical relaxation behavior will be suppressed in favor of a semi-classical phenomenon called thermally assisted tunneling of magnetization. In particular, this research investigates the longitudinal- and transverse-field dependences of the magnetic relaxation rate for Mn

_{12}-tBuAc. We interpret our results as evidence that the dominant levels for thermally assisted resonant tunneling change abruptly as the applied transverse field is increased.

**Michael Goldman, '08**

Spinor BECs Through Landau-Zener Transitions

Faculty Advisor: Professor David Hall

The recent construction of a cross-beam optical dipole trap has opened to our laboratory the possibility of conducting experiments involving Bose-Einstein condensates of $\Rb$ atoms in any of the quantum states of the ground state F=1 hyperfine manifold. At Amherst, the final phase of Bose-Einstein condensation is conducted in magnetic confinement, resulting in BECs composed entirely of atoms in a magnetically trappable state. Using a Landau-Zener transition, atoms can be transferred from this one state into any of three states in the F=1 hyperfine manifold.

By precisely controlling the parameters of the Landau-Zener transition, we can choose to create a BEC in a balanced superposition of all three states or to transfer the entire population of atoms from the magnetically trappable state to a magnetically untrappable one. Exercising the first option results in the formation of a spinor condensate, a multiple-component condensate with the orientation of the atomic spins as a degree of freedom. This allows us to observe the coevolution of vortices in the three component condensates. We can also study the spatial separation of the condensates in order to diagnose the presence of stray magnetic field gradients that may be inherent in our apparatus.

Exercising the second option enables us to explore various Feshbach resonances, none of which are accessible from the magnetically trapped state. We will explore both a low-field interspecies Feshbach resonance and intraspecies resonances at higher magnetic fields. The latter will enable us to observe vortex behavior around a Feshbach resonance and hopefully will also yield such phenomena as soliton formation and condensate collapse.

*Measuring the Swarm Expansion Rate of B. subtilis: Does Chemotaxis Play a Role in Swarm Expansion?*Faculty Advisor: Nicholas Darnton

Swarming is a rapid and coordinated form of motility of *B. subtilis* on wet and nutritious surfaces. Some possible driving and limiting factors governing swarming are chemotaxis (the bacteria’s tendency to move up a nutrient gradient), population growth pressure, and wetness or hardness of the agar surface. The plausibility of chemotaxis in swarming is probed by modeling nutrient diffusion and consumption by bacteria in one dimension. Swarm expansion was measured under various initial nutrients configurations, such as different initial nutrients concentration and different depths of agar gel. No significant difference in expansion rates was observed. Diffusion coefficient tests were performed to provide counter evidence to the common belief that limited diffusion of nutrients causes *B. subtilis* swarming to fail to swarm at high agar concentration. Taken together, these results suggests that nutrient gradients are not an important factor in the initiation or propagation of bacterial swarming.

*A Search for Local Lorentz Violation*

Faculty Advisor: Professor Larry Hunter

General Relativity (GR) and the Standard Model (SM) have successfully withstood the scrutiny of generations of prominent experimentalists. However, the twenty adjustable dimensionless parameters of the SM and the innate incompatibility between GR and SM suggest possible limits to their validity. Our experiment probes GR and SM by testing the Local Lorentz Symmetry, the bedrock on which both theories are built.

The experiment consists of two atomic clocks (Cs and Hg) mounted on a rotating table. We lock the magnetic field to a Cs clock and search for a sinusoidal variation of the Hg precession frequency in phase with the sidereal day. The experiment is sensitive to any differential energy coupling between the absolute direction and the atoms’ spin. The sensitivity of an earlier experiment was limited by drifts in the apparatus over the long integration times. A rotating table was constructed to reduce the consequences of any long-term drifts in the apparatus. We have made several improvements to the experimental apparatus. 1) The Cs laser collimator has been redesigned and reconstructed. 2) A new Cs signal detection circuit has been constructed. 3) The acoustic isolation of Cs laser has been improved by lining its containing box with SorbothaneÒ. 4) Current modulation has allowed an increase in the lock frequency of the Cs laser from 2 kHz to ~30kHz, resulting in better laser frequency stability. 5) Braces have been added to improve the rigidity of the apparatus support structure. 6) The Hg laser intensity stability has been improved through adjustment of the doubling cavity. We are continuing to characterize and eliminate the instability of both Cs and Hg laser systems. We hope to attain <0.001° point to point variation in our data. A day’s measurement with such an improvement will enable us to set the upper limit on the neutron energy coupling at 4.5´10^{-32}GeV, a factor of two improvement over the current limit of 1.1´10^{-31}GeV.

*Votices in an optically trapped Bose-Einstein Condensate*Faculty Advisor: Professor David Hall

The crossed-beam optical dipole trap

^{1}constructed in 2006 by Daniel Guest

^{2}has opened up avenues of research in Bose-Einstein condensation (BEC) unavailable with the magnetic or magneto-optical hybrid traps in use elsewhere. The optical trap liberates the condensate's spin degree of freedom, permitting experiments on spinor condensates. Furthermore, the high degree of cylindrical symmetry and tight trapping in all three dimensions afforded by the cross-beam configuration permitted the first

^{3}observation of sustained rotation in an all-optically confined condensate. These two results suggest a third possibility: studying the exchange of angular momentum between the condensate's macroscopic rotation, manifested in vortex cores, and its intrinsic spin state. In this thesis, I will discuss our progress in refining and characterizing the trap and meeting the stringent conditions required for trapping vortices. I will also present the results of our further exploration of vortex dynamics in spinor condensates.

^{1}C. S. Adams, H. J. Lee, N. Davidson, M. Kasevich, and S. Chu. Evaporative Coolingin a Crossed Dipole Trap. *Physical Review Letters*, **74**:3577-3580, May 1995.

^{2}D. Guest. *A Cross-Beam Far Off-Resonance Optical Trap for Bose-Einstein Conden**sates**. *Undergraduate thesis, Amherst College, 2006.

^{3}*Ibid.*

**Jesse Rasowsky, '08**

*Quantifying Entanglement**Faculty Advisor: Professor Kannan Jagannathan*

* *

**Kyle Virgien, '08**

*Minimizing Systematic Effects in a Solid-State Electron Electric Dipole Moment Measurement*

Faculty Advisor: Professor Larry Hunter

The idea of symmetry, that we can use the outcome of one event to describe another similar event, is essential to the study of physics. Many physical laws are derived directly from the assumption of the existence of certain symmetries—the laws of conservation of energy and momentum, for example, require the symmetries of time and space translation—but we have no justification in assuming that such symmetries are true besides the simple fact that the system of physics that we obtain from them seems to do a good job of describing the world that we observe. Symmetries seem intuitively obvious to us, but they are not as universally true as we might think they are. A few instances where symmetries are disobeyed have been observed, and there are certainly more remaining to be discovered. The ultimate goal of the work described in this thesis is to observe a breakdown of some of the symmetries that physicists have long considered to be true. The laws of the standard model of physics would fail to explain this observation, and they would have to evolve in order to account for it.

*Refining Limits on the Electron EDM Using Polycrystalline GdIG*

Faculty Advisor: Professor Larry Hunter

Symmetry finds many pleasing forms in nature, from the facial and body symmetries of animals to complex geometric shapes that reflect over various planes. Indeed, the world is so replete with symmetries that we expect them; to see a tree with branches only on its left side would be puzzling. However, if one imagines seeing next to it a tree without branches on its right side, the situation is less distressing. In this way, we casually assume symmetry in the world despite the complexity it entails. Symmetry finds beautiful forms in the laws of physics. While they are consequences of the fundamental, dynamical equations, discrete symmetries also serve as guiding principles. By associating them with conservation laws, we further appreciate that symmetries are more than amusing observations: they are underlying principles. The three fundamental, discrete symmetries are charge, parity, and time, and these are conserved in most of known physics. Our experiment examines predicted violations of the last two in the electron. Many theories predict a non-zero value of the electron electric dipole moment (eEDM) in an effort to explain other observed symmetry violations. Such an EDM, if measured, would itself indicate a violation of both parity and time-reversal symmetries. We test for a non-zero value of the electron electric dipole moment (eEDM) by magnetically polarizing a polycrystalline sample of gadolinium iron garnet (GdIG). The electrons’ spin axes should align parallel or anti-parallel to the field, bringing their EDMs into alignment and creating an effective surface charge. This “charge” will manifest as a potential difference that can be measured directly. Our current limit is 1.1 x 10-24 e-cm, which is nearly a factor of 200 better than any previous solid-state experiment to measure the eEDM. The accuracy of our experiment is limited by an unexpectedly large, magnetically symmetric effect that we seek to eliminate. Current results indicate that it is a surface effect due to the bonding of electrodes onto the sample.

*A Cross-Beam Far Off-Resonance Optical Trap for ^{87}Rb Bose-Einstein Condensates*

Faculty Advisor: Professor David Hall

*Simulating the Polarization Properties of VCSELs with Optical Feedback*

Faculty Advisor: Professor Robert Hilborn

Vertical-cavity surface-emitting lasers (VCSELs) are a new type of semiconductor laser that are emerging as an economical alternative to conventional edge-emitting lasers. Anisotropies within these lasers, such as birefringence and preferential gain, cause their optical output to favor one of two orthogonal linear polarizations; however, other optical outputs such as elliptical polarization and polarization coexistence are possible under some circumstances. When using these lasers in real systems, optical feedback (from a fiber-optic cable or CD) is almost unavoidable. Numerical simulations suggest that under optical feedback conditions, VCSELs lose their polarization stability and descend into chaotic behavior. These complex dynamics, however, are extremely sensitive to the relaxation rates of the system. In addition, recent work at Mount Holyoke College suggests that short cavity lengths can heavily influence the threshold current of these lasers. My thesis will focus on two separate investigations. In the first, I will develop a model to simulate the polarization dynamics of VCSELs in short external cavities, to complement the work that has been done at Mount Holyoke. In the second, I will investigate how VCSELs react to optical feedback under low-temperature conditions, from both a theoretical and experimental perspective.

*Exploring Spike Timing Dependent Plasticity in Neurons*

Faculty Advisor: Professor Robert Hilborn

Recent experiments indicate that the sign and magnitude of synaptic changes in neurons depend on the relative timing of pre- and post-synaptic action potentials. This form of synaptic plasticity is called spike-timing-dependent plasticity or STDP. The magnitude of STDP at a particular synapse can also depend on the strength of the synapse. For example, in certain systems strong synapses are strengthened less than weak synapses. Changing the strength dependence can lead to a range of distributions, characterized by differing degrees of stability and inter-synaptic competition. In this thesis I explore the consequences of various forms of STDP through computer simulations and through techniques from statistical mechanics, in particular, through the Fokker-Planck equation.

*Analyzing the Effects of Noise on Oscillatory Gene Networks*

Faculty Advisor: Professor Robert Hilborn

To function correctly, genetic networks depend upon a series of positive and negative regulatory proteins. For the type of genetic oscillator in which we are interested, this genetic network controls circadian rhythm: the means by which an organism regulates internal changes required at different times during a 24 hour period. This system can be modeled through two coupled differential equations describing the changes in the concentrations of a repressor protein and of an inactive complex formed from the binding of an activator and a repressor protein. We wish to explore the consequences of adding noise of varying amplitudes into our genetic oscillator system to mimic the fluctuations in protein concentrations and thermal fluctuations that occur in real cells. Preliminary results suggest that certain amplitudes of noise can stimulate regular oscillations in genetic oscillators that have otherwise settled into a steady state.

*Ground State Tunnel Splitting in Mn12 Acetate*

Faculty Advisor: Professor Jonathan Friedman

Molecular magnets stand between the realms of quantum and classical physics. At first glance they exhibit the trademark behaviors of macroscopic magnets, such as bi-stability and hysteresis. But when the temperature is low enough to suppress the classical behavior (i.e. thermal relaxation), unmistakable signatures of quantum behavior are revealed. For example, the magnetic moment of the molecule can tunnel through a classically forbidden energy region.

This quantum behavior is manifest because the individual ions in a molecular magnet are coupled together very strongly, and the entire molecule therefore behaves much like a single quantum entity (of spin 10). Despite the accuracy of such a quantum picture of the molecule, however, the large spin prevents much analytic progress from being made through a strictly quantum mechanical approach. Instead, one must use semi-classical methods to explain the quantum behavior.

The specific quantum effect that I will deal with in my thesis is the complete suppression of the tunneling rate between the ground states of Mn12-Acetate due to variations in the parameters of the system's Hamiltonian (with a fourth order perturbation that might be induced by mechanical pressure). This quenching effect has been understood in a similar situation (where the perturbation was given by a transverse magnetic field) to be the result of the interference between various tunneling paths. I will apply several semi-classical and approximate techniques which proved useful in the transverse field calculations in order to model the similar behavior of Mn12 under our Hamiltonian.

*Singular Potentials, Self-Adjointness, and Symmetries*

Faculty Advisor: Professor William Loinaz

The domain of a Hermitian operator H in quantum mechanics is a subset of the domain of its adjoint H

^{*}. When these domains are identical, H is said to be self-adjoint. It is sometimes possible to extend the domain of a non-self-adjoint H until it is self-adjoint. I will study the technique of choosing self-adjoint extensions, and its relation to renormalization theory, chiefly in the context of two problems in nonrelativistic quantum mechanics, the 2-D delta function potential and the inverse-square potential. A link between these problems is that both have classically scale-invariant potentials that acquire a scale upon quantization (which depends on the self-adjoint extension that is chosen); this feature is called "anomalous symmetry breaking" and is an important part of the symmetry structure of quantum mechanics. A related topic, which I will study if time permits, is modifying quantum mechanics so that it has an intrinsic scale built into it, and the consequences of this for symmetries and self-adjointness.

Symmetry has played an important role in the development of physics. One symmetry of particular interest is reflection symmetry, often referred to as parity (P) invariance. Although this symmetry is obeyed in much of physics, the weak interaction, responsible for nuclear beta decay, is know to violate parity.

My thesis deals with an analogous symmetry known as time reversal (T) invariance. Events viewed in reverse order, such as when a video tape is played backwards, often appear bizarre. Shattered crockery reassembles without a crack, and rivers flows uphill. However, in some sense the time-reversed universe is fundamentally the same as our own. Balls still bounce in the same way, and objects thrown in the air still follow parabolas. In fact, all the strange occurrences mentioned above are very unlikely to occur, but technically possible. In a fundamental sense, physical law is nearly completely T invariant.

At present, the only indication of fundamental T violation is the existence of certain decay modes of the neutral K and B mesons. Based on observations of these decays, some theories predict that the electron should have a nonzero electric dipole moment (EDM). To test these theories, we attempt to measure the electron EDM.

Using a magnetic field, we align the spins of electrons in polycrystalline GdIG. If the electron has a nonzero EDM, this should produce a voltage across the sample, which we measure using a sensitive voltage detector.

Recent work on the experiment has led to an improved upper limit on the electron EDM relative to past solid state measurements. In the process, a solid state effect has been observed, which seems to have been previously unknown. However, our limit remains a factor of 1000 larger than an existing limit derived from work on atomic thallium. Further improvements, and investigations into the solid state effect are planned, in the hope that these difficulties can be circumvented, leading to greatly improved sensitivity to the fundamental physics we originally set out to test.

*Topics in Bose-Einstein Condensation*

Faculty Advisor: Professor David Hall

Work in the summer of 2005 greatly improved our ability to measure the number of atoms present in a trapped cloud. This work included an upgrade to the system used to lock the frequency of our probe laser and implementation in our software of a more sophisticated model for calculating number, which takes saturation effects into account. With our improved ability to measure number, we set out to measure the rate at which atoms in the |f = 2, mf = 1> state are lost from the trap. In the other magnetically trappable states of Rubidium-87, namely the |1, -1> and |2, 2> states, trap losses are dominated by three body processes, but in the |2,1> state, two body losses dominate. Measuring this two body loss rate in condensates and in thermal clouds will allow us to test the prediction that collisions in a condensate are suppressed by a factor of n!, where n is the number of bodies involved in the collision. A factor of 6 reduction has been observed for three body losses in the |1,-1> state, but the factor of 2 reduction expected for two body collisions has not previously been observed. Additionally, we hope to measure two body losses near a Feshbach resonance, where elastic losses are greatly enhanced.

*Lattice Simulations of Nonperturbative Quantum Field Theories*

Faculty Advisor: Professor William Loinaz

The basic goal of elementary particle physics is to determine the nature of particles and their interactions. This is easier said than done. So far as physicists have been able to determine, particles and interactions are best described by quantum field theory, which combines quantum mechanics and special relativity. Quantum field theories are often studied perturbatively: the particles (such as photons and electrons) are first considered by themselves and then the interactions are added in, beginning with the strongest interactions and continuing with weaker ones until a point is reached at which adding additional interactions won't significantly affect the result and can be neglected.

This approach is not always valid, particularly when the system under consideration cannot be described by applying a small perturbation to a simpler, solvable system. For example, this is the case for low-energy quantum chromodynamics, collective phenomena such as solitons, and nonlinear quantum field theories in general. Performing numerical simulations on computers is an increasingly popular way to study such nonperturbative quantum field theories. This approach, lattice quantum field theory, has made major strides as computing power has increased in recent years.

For my thesis, I will carry out lattice simulations of some simple (but still nonlinear and nonperturbative) quantum field theories, such as phi^{4} theory and basic Yang-Mills theory. After some introductory work simulating statistical systems similar to these theories (such as the Ising, Potts and Heisenberg magnet models), I will pursue topics of original research, including the calculation of soliton masses in phi^{4} theory (in two and four dimensions) and Yang-Mills theory as well as the calculation of the critical coupling constant in four-dimensional phi^{4} theory.

*A Test of Special Relativity - Pushing down the Limits on a Possible Violation of Local Lorentz Invariance*

Faculty Advisor: Professor Larry Hunter

We seek to measure a possible anisotropy in the laws of nature by looking for a variation in the relative precession frequencies of Cesium and Mercury with respect to the sidereal day. This experiment is a refinement of one done in 1995, which established the best limits at the time on certain parameters within the Kostolecky framework. Since then, these parameters have been overtaken by other experiments. The improvements include a rotating table, which allows us to control for long term drifts in relevant variables, and a solid state laser for the mercury magnetometer, which will decrease overall noise. These improvements should theoretically yield about two orders of magnitude improvement over the 1995 results. At this point, the experiment is fully constructed, but there is significant noise associated with the rotation of the table that will need to be eliminated to obtain the accuracy desired.

*Quantized Vortex Nucleation in a*

^{87}Rb Bose-Einstein CondensateFaculty Advisor: Professor David Hall

I will discuss two recent developments at the

^{87}Rb dilute gas Bose-Einstein condensation lab at Amherst College. In the summer and fall of 2004, the optical trapping system was upgraded to an elliptical beam trap, allowing increased lifetimes for optically trapped condensates. This led to the observation of a Feshbach resonance between the |1,1> and |2,-1> magnetic sub-states of

^{87}Rb. In the spring of 2005, quantized superfluid vortex lattices were nucleated in a condensate trapped in an oblate magnetic potential. I will talk about the construction of the elements that were necessary for the observation of these two phenomena, as well as our observations of their behavior. I will conclude by considering possible experiments that could tie together the seemingly disparate achievements of the past year.

*Life on a Merry-Go-Round: An Examination of Relativistic Rotating Reference Frames*

Faculty Advisor: Professor Kannan Jagannathan

When we measure the circumference and radius of a rapidly rotating disk in the inertial frame in which it is undergoing no translational motion, we find the ordinary relation C=2*pi*R. But in this frame the edge of the disk is moving in a direction parallel to itself, so this measurement must be of a length-contracted distance. The circumference in the rotating frame must therefore be greater than 2*pi times the radius, giving us a noneuclidean geometry in that frame. This is called Ehrenfest's paradox, and has troubled relativity almost since its inception.

The goal of my work is to provide a satisfactory explanation of the relativistic rotating reference frame. I will analyze the system with general relativity and also develop a computer-aided numeric method to visualize a set of points from the point of view of a rotating observer.

*An Observation of Sub-Poissonian Photoelectron Statistics*

Faculty Advisor: Professor Arthur Zajonc

A semi-classical treatment of the photoelectric effect and similar phenomena reveals that the rate of electron emission necessarily fluctuates due to two forms of noise - thermal noise and shot noise. The variance in a series of electron counts due to shot noise is simply the average number of counts ((DeltaN)

^{2}= <N>), making the statistics Poissonian. If the assumption is made that each emission is a statistically independent random event, these statistics may even be derived without recourse to a quantum theory of matter. The role of the semi-classical theory, then, is to justify the assumption.

A fully quantum analysis of this same phenomenon reveals that the electron emissions correlate directly with photon absorptions, revealing that the statistics observed are those of the incident light. The theory of Quantum Electrodynamics demonstrates that light can have sub-Poissonian statistics ((DeltaN)^{2} < <N>, where N now represents the photon number). Most notably, in number states of the electromagnetic field, there is no variance ((DeltaN)^{2} = 0). A measurement of the photocurrent induced by such an EM field will, then, reveal sub-Poissonian photoelectron statistics.

Certainly, QED provides an adequate description of the sub-Poissonian phenomenon; but, is it necessary to use this formulation to generate these results? Are there assumptions that, much as the description of shot noise in classical terms, would allow the description of sub-Poissonian statistics in semi-classical terms, relegating QED to the role of justifying these assumptions?

Our goal, then, is to observe both Poissonian and sub-Poissonian photoelectron statistics and to use the data from these observations to explore the constraints on any theory attempting to describe them.

*Spinning the Spins: Constructing a Rotating Apparatus to Set New Limits on Local Lorentz Invariance*

Faculty Advisor: Professor Larry Hunter

The experiment I am working on is a new version of an experiment done a decade ago, searching for a violation of Local Lorentz Invariance at very small atomic energy levels. Local Lorentz Invariance states that the laws of physics in one reference frame moving at a constant velocity will be the same as those in any other reference moving at a constant velocity. LLI is a postulate in Special Relativity and other modern physical theories, so high precision experiments such as this one are necessary to test the validity of these theories.

To test for violations in Local Lorentz Invariance, Cs and Hg atoms in a constant magnetic field are used. By looking for changes in the precession rates of the atomic spins when the spacial orientation of the apparatus is changed, a LLI violating energy shift can be observed. The spin of Cs is dependent on the electron and the spin of Hg is dependent on the neutron, so the experiment is testing for violations in two different particles. In the old setup of the experiment, the rotation of the Earth was used to change the direction of the experiment. By placing the apparatus on a rotating table, the time of direction will be cut from hours to minutes.

Currently, the apparatus is in the process of being moved onto the rotating table. In order to do this, an overhead structure is being suspended from the ceiling, both to hang a stationary magnetic shield from and to hold a bearing to support the rotating table on the top. Once the overhead structure is in place, all of the equipment which is now on a horizontal table will be moved onto the rotating table. Many thorns and snares lie along the path between the valley of the horizontal and the pinnacle of the vertical, but at some point in the future, new limits on Local Lorentz Invariance will be set.

*Exploring EPR and Non-Locality in Quantum Mechanics*

Faculty Advisor: Professor Arthur Zajonc

There are many classic thought experiments in Quantum Mechanics that display the seemingly paradoxical phenomena which underlie the foundation of the theory. One of these has come to be known as the EPR experiment, after the authors, Einstein, Podolsky, and Rosen, who first proposed it in a paper in 1935. The EPR paper was originally intended to show the incompleteness of quantum theory by explaining how the values of both quantities in an uncertainty pair, originally momentum and position, of a given particle could in principle be measured precisely without disturbing the particle at all. The proposed experiment took advantage of entangled states, in which two particles are correlated such that information about one can be obtained by making measurements on the other.

Bell used this experiment as the basis from which he derived his inequalities that hold for any local hidden variable theory under these circumstances. Bell's inequalities are violated for quantum mechanical theories, which means that they help us determine whether a local hidden variable theory can be used to explain the results of an EPR experiment, or whether we must appeal to quantum mechanics.

Our goal is to construct an apparatus that will allow us to perform EPR measurements and evaluate Bell's inequality simply and quickly using a laser diode and non-linear crystals to create photon pairs with entangled polarization states. Single-photon measurements can then be made on these photons using avalanche photodiodes. We should be able to quickly verify that our measurements violate Bell's inequalities, and thus demonstrate that the situation cannot be explained by any local hidden variable theory.

*An Investigation into Bohmian Mechanics*

Faculty Advisor: Professor Kannan Jagannathan

In 1952 David Bohm defied the Copenhagen interpretation of quantum mechanics by giving non-relativistic quantum mechanics a consistent ontology, and he did it using only classical concepts. Whereas Copenhagen said that electrons could be described as either a particle or a wave but not both, Bohm said that electrons are particles

*and*waves. Bohm explains the double slit experiment, for example, by attributing the interference pattern to guiding waves that determine where particles will hit the screen.

Bohm’s theory falls into the class of non-local hidden variable theories. I’m a local hidden variables kind of guy, but since these are difficult times for such theories, I decided to study Bohm’s theory instead. While its non-locality defies classical intuition, its hidden variables are just plain old position and momentum.

Bohm takes the Schrodinger equation as his starting point. He expresses the wave function as a real modulus multiplied by a complex phase and notices that the real and imaginary parts of the wave function yield two familiar equations. One is a continuity equation which describes how the absolute square of the wave function, R^{2}, evolves. The other is a classical energy equation with a new "quantum potential" term thrown in. The quantum potential, which is probably unmeasurable, is responsible for the strange behavior associated with quantum phenomena.

R^{2} gets interpreted as an ensemble density. If an experiment is done on particles initially distributed according to R^{2}, then Bohm’s theory makes the same predictions as the Copenhagen interpretation. My research is now focusing on what would happen if the initial position distribution of the particles is not equal to R^{2}. Future projects might include examinations into Bohm’s treatment of spin, measurement, and relativistic quantum mechanics. Questions concerning the ontology of the wave function might also be addressed.

*Experiments with Binary Bose-Einstein Condensates*

Faculty Advisor: Professor David Hall

My thesis will be an investigation of the properties of single and binary

^{87}Rb Bose-Einstein condensates. The addition of a microwave synthesizer, amplifier, and delivery horn over the summer has allowed us to produce cold thermal clouds or condensates in the |F=1,m

_{f}=-1> spin state and transfer them to the |2,1> state. With the aid of quickly reversible optical pumping we have also independently condensed |1,-1> and |2,2> condensates simultaneously in the same trap. Professor Hall and I will be investigating properties such as phase relations between binary condensates. What will be of particular interest will be the similarity or difference in phase measurements made between independently prepared and coherently prepared condensates. We may also be investigating: a) The two and three body density-dependent loss rates in single and binary condensates; and b) The time evolution of both mixture and superposition binary condensates.

*The Magic of Mn-12; a Quantum Disappearing Act*

Faculty Advisor: Professor Jonathan Friedman

The quantum mechanical catch-phrase "tunneling" describes those physical processes that, due to lack of sufficient energy, are prohibited in classical mechanics but are allowed within a quantum theory; one way to visualize this is to imagine a particle trapped inside of a deep well whose walls are so tall that the particle does not have the energy to climb over them, and yet it somehow manages to disappear through them and reappear on the outside just the same. Although most tunneling phenomena is confined to the atomic scale, this experiment will probe manifestations of spin tunneling on the macroscopic scale by performing AC susceptibility measurements on the molecular paramagnet Mn-12 (Manganese-12 Acetate) to determine its relaxation time as a function of applied transverse magnetic field. An AC susceptibility measurement is simply this: you apply an oscillating magnetic field to a paramagnet (in this case, Mn-12), then measure the extent to which its magnetic moment can align itself with the changing direction of the field. The time during which the moment can "comfortably" align itself with the field before it begins to lag is called the "relaxation time" of the paramagnet. Within our theoretical framework, shifts within this relaxation time can be associated with tunneling on a non-atomic, molecular level, and we can determine how different field strengths and applied angles help to induce the phenomenon.

*Constraints on the Higgs Sector Beyond the Standard Model*

Faculty Advisor: Professor William Loinaz

The Standard Model is a description of all known fundamental particles and their interactions via the strong, weak, and electromagnetic forces. However, the Standard Model Lagrangian doesn't explicitly give mass to the fundamental particles. They get their mass instead through the combined effects of spontaneous symmetry breaking and local gauge symmetry called the Higgs mechanism. However, this introduces another, as yet unobserved, particle, the Higgs boson.

There is some indirect experimental evidence of the Higgs which indicates that its mass is below 1TeV. However, if we take the Standard Model seriously as a quantum theory, the natural mass for the Higgs appears to be about 10^{16} TeV. This is called the Fine-Tuning Problem.

In this thesis, we study theoretical and phenomenological constraints on the Higgs sector in some theories beyond the Standard Model which show promise in resolving the fine-tuning problem.

*Searching for the Electron EDM Using a Solid State System*

Faculty Advisor: Professor Larry Hunter

Have you ever been seized with the uncontrollable urge to break a symmetry? In this experiment we are searching for the electron electric dipole moment, whose existence would imply a break down of time-reversal symmetry and other interesting physics. No one has ever observed an EDM of a fundamental particle, although experimenters have been looking since the 1950s, when E. M. Purcell and N. F. Ramsey first suggested the idea. Is a nonzero EDM just the pipedream of some quixotic experimentalist? It might be, but consider the following two points before jumping to conclusions. First, steadily improving limits on this quantity have eliminated many bogus physical theories attempting to explain CP violation. Second, there is nothing fundamental that forbids an elementary particle from possessing an EDM. We learned in the 1920s that certain particles have an intrinsic magnetic dipole moment, so perhaps they also have an EDM. To decide, we must put the question to experiment.

The principle of our experiment is to align the putative electron EDMs in a sample of gadolinium iron garnet (GdIG) and measure the voltage across it due to the electrical polarization. To align the EDMs we apply a magnetic field to the sample, since these must lie along the spin axis, the electron's only internal degree of freedom. GdIG is an ideal compound, since the gadolinium ions have a large enhancement factor, which is the constant of proportionality that relates the magnitude of the electron EDM to the magnitude of the atomic EDM. Moreover, GdIG's magnetic susceptibly is highly temperature dependent. This gives us a useful check on the experiment, since if we think we see a signal we should be able to change its size by tuning the temperature.

This year we've been using a small test sample to study nasty EDM-masking systematics in our apparatus. Right now we are just on the point of moving to the final sample, which is much larger and will give us more signal. We are presently rebuilding the apparatus to accommodate it.

*Measuring a Violation of Local Lorentz Invariance*

Faculty Advisor: Professor Larry Hunter

Symmetries abound in the universe, from atoms to snowflakes to orbits, and in the modern age physicists have used the correspondence between symmetries and conserved quantities to develop their theories for the natural world. The Standard Model incorporates various symmetries, among them Local Lorentz Invariance, the principle that the laws of physics are the same when measured in any inertial reference frame. But what if there is a more fundamental model for the universe in which Local Lorentz Invariance and other symmetries are not observed? The phenomena that violate Local Lorentz Invariance in this more fundamental model are usually suppressed, so only extremely precise experiments can look for them. Ours is one of those experiments.

We use gaseous cesium and mercury atoms shielded from the earth's magnetic field as magnetometers. We collect data on the relative phase angle between the atoms' spin vectors and an applied magnetic field, as a function of the orientation of our applied magnetic field with respect to the stars. This year we are working on two ways to improve our precision. One is making our frequency-quadrupling laser system more stable. The other is designing and assembling a new experimental setup. Our magnetic shields are presently horizontal and fixed to the earth, but in our next setup they will stand vertical and be fixed to a table that rotates a half turn. This will allow us to modulate the magnetic field direction every six minutes, rather than waiting twenty-four hours for the earth to rotate. With these improvements we hope to achieve high sensitivity to proposed particle interactions that would violate Local Lorentz Invariance, a symmetry bedrock upon which the Standard Model is built.

*Bose-Einstein Condensation of Rubidium 87 in a Dilute Gas*

Faculty Advisor: Professor David Hall

Bose-Einstein Condensates or BECs are an interesting state of matter, distinct from solid, liquid and gas. In a BEC, the atoms are cooled to a few billionths of a degree above absolute zero, where they behave collectively rather than as individuals. Consequently, the entire condensate can be treated as a single quantum object, which has led some to refer to condensates as "Super-atoms". This unique system affords us the chance to study the fundamental nature of matter in a new and unusual way.

This fall, after three years of hard work, BECs have finally been created at Amherst College. During the fall, the apparatus and procedure has been refined to quickly create very large condensates. Additions to the apparatus, such as optical tweezers and a microwave system, will enable us to study the properties of interacting two-component condenstates.

*GdIG Electron EDM*

Faculty Advisor: Professor Larry Hunter

The measurement of the electric dipole moment of the electron is of fundamental importance to much of physics. Currently, the upper limit stands at about 10

^{-27}e.cm. In this experiment, we hope to increase this limit by perhaps 3 orders of magnitude. We will be using Gadolinium atoms embedded in Gadolinium-Iron-Garnet (GdIG). The first step is to line up the magnetic moments of the valence electrons of the Gadolinium by applying a magnetic field. Any electric dipole moment of the electrons must be oriented in the same direction as the magnetic moment, thus the electric dipole moments of the valence electrons will be lined up by the applied magnetic field. Then we simply measure the macroscopic voltage produced by the superposition of all aligned electrons in the GdIG.

*An All-Optical Implementation of Quantum Computation*

Faculty Advisor: Professor Arthur Zajonc

Quantum computation is a rapidly developing field that exploits the power of the principles of quantum mechanics to solve problems more efficiently than classical computation. Quantum computers can be built which contain quantum circuits that carry and manipulate information that is stored in quantum states using quantum wires and quantum gates. The information is stored in qubits, which are analogous to bits in classical computers. Qubits have the states |0> and |1> as their computational basis states and can be any superposition of these basis states, a|0> + b|1>, provided that |a|

^{2}+ |b|

^{2}= 1. Using qubits and the principles of quantum mechanics it is possible to develop algorithms, which can solve problems such as factoring large numbers and quantum simulation. These quantum circuits can be realized physically in several ways including an all-optical implementation that uses simple optical devices such as beam splitters, phase shifters and non-linear Kerr media. Here the qubits represent modes of light where the state |0> contains no photons and the state |1> contains one photon. This thesis will focus on this all-optical implementation of quantum circuits and quantum computers. The quantum mechanical operations of these optical devices will be explained as well as the all-optical implementation of some quantum algorithms, including the Deutsch-Josza algorithm and the Grover search algorithm.

*Neurodynamics and Noise: Noise-Induced Periodicity in Coupled Neurons*

Neurons resond to stimuli by firing bursts of nerve impulses. Under close examination, real signals from bursting neurons display fluctuations from various noise sources. In some circumstances these fluctuations are necessary for the nervous system to function properly. When coupled neurons fire, for example, their impulses tend to become synchronized and subsequently more periodic than they would be if firing alone. Small amounts of noise seem to aid the synchronization and make the nerve impulses more periodic. Our goal is to illustrate how noise helps neruons synchronize and become more periodic by using concepts from nonlinear dynamics and methods such as graphical comparisons of nerve cell model behavior. More specifically, we are studying simple mathematical models of coupled bursting oscillators and extending these studies to the more complex Morris-Lecar model, which is a better representation of actual physiological conditions.

*The Search for Violations of Local Lorentz Invariance Using Hg and Cs Magnetometers*

Faculty Advisor: Professor Larry Hunter

*A Test of Relativity: Contractions, Clocks and Inner Perfection*

Faculty Advisor: Professor Arthur Zajonc

*The Search for the Cause of Tunneling in Molecular Magnets*

Faculty Advisor: Professor Jonathan Friedman

_{12}acetate (spin of 10), are anisotropic and bistable - the spin has two preferred directions, "up" and "down", corresponding to the lowest energy states. These two states occur when the spin is aligned with the crystal's longitudinal axis. The energy of this system can be modeled as a simple double-well potential, where the bottom of one well corresponds to the "up" state and the other well "down" and the barrier between them represents the anisotropy of the system. Two effects have been observed in Mn

_{12}that regulate a sample's relaxation rate - a characteristic rate at which the molecules can change the alignment of their spin-state. One is a classical effect caused by temperature: as temperature increases, random thermal fluctuations provide enough energy to excite the spin out of the ground state (and at "high" temperatures, over the anisotropy barrier causing the spin to realign in the opposite direction). The other effect is tunneling: a quantum mechanical process allowing particles without sufficient thermal energy to tunnel through the anisotropy barrier into the oppositely aligned spin state. It is not known what causes this effect to occur, however, analysis of the known part of the Hamiltonian for the system shows that an internal transverse magnetic field could cause spin-state tunneling.

We plan to study this by making AC susceptibility measurements of a sample of Mn _{12} acetate. These will allow us to determine the sample's relaxation rate. By varying the temperature (near a few degrees Kelvin) and the DC transverse magnetic field, we will test theories that predict how the relaxation rate depends on transverse magnetic field and attempt to find the specific states from which tunneling is occurring. This should allow us to determine the strength of the internal magnetic field required to cause the observed tunneling. Knowledge of the magnitude of the required field will facilitate the determination of the source of the tunneling-inducing field and will help answer the question, "What causes spin-state tunneling in Mn_{12} acetate?"

*Understanding Quantum Carpets*

Faculty Advisor: Professor William Loinaz

In analyzing these structures, I will first try to isolate the contributions of the spectrum from the particular eigenfunctions by studying various iso-spectral poentials. Also to be considered are the variations introduced by using different initial wavepackets in a single potential. Finally, I hope to study the connections between the carpets of algebraically related potentials, such as supersymmetric partner potentials.

*Magnetic Trapping and Evaporative Cooling for Bose-Einstein Condensation*

Faculty Advisor: Professor David Hall

^{87}Rb. The

^{87}Rb atoms are first collected, cooled and confined in a dual Magneto-Optic Trap (MOT) system. They are then loaded from the second MOT into a magnetic trap and evaporatively cooled until a sufficiently high phase-space density is achieved to realize Bose-Einstein Condensation.

Construction has already been completed on the first MOT, and begun on the second. My preliminary work will focus on designing and building a magnetic trap, and on optimizing the performance of the second MOT. I will then turn to generating an evaporation trajectory to cool the magnetically trapped atoms the rest of the way for Bose-Einstein Condensation.

*Monte Carlo Studies of Some Quantum Field Theories*

Faculty Advisor: Professor William Loinaz

^{4}theory and will study phase transition in several simple quantum field theories and/or statistical systems. The primary tool used to study these systems will be lattice Monte Carlo simulations, utilizing several Monte Carlo algorithms, such as Metropolis and cluster algorithms.

*Making the Coldest Stuff in the Universe: Vacuum Construction and Magneto-Optic Trapping for Bose-Einstein Condensate*

Faculty Advisor: Professor David Hall

^{-11}torr. With this initial step concluded, I have begun to design and construct the first Magneto-Optical trap (MOT) needed to drive the Rubidium atoms into their ground state energy level. These steps involve creating another saturation absorption set-up to lock the re-pump laser upon the F=1 transition, beam manipulation to achieve the proper size, strength and polarization of the incident lasers, and finally the winding of the necessary anti-Helmoltz coils.

*Exploring Chaos Using Neural Networks*

Faculty Advisor: Professor Robert Hilborn

Using neural networks, a computer modeling technique inspired by the human brain, we intend to model chaotic systems that have limited available data. The first task is to correlate the size of the neural network needed with the complexity of the chaotic system. We will then use the neural network to generate time series data for chaotic systems and use it, as well as the original data, to make quantitative statements about the system.

*Measuring One Dipole Moment and Looking for Another*

Faculty Advisor: Professor Larry Hunter

In this thesis I seek to measure the polarizibility of the a(1) state of PbO. The measurement is made using high-precision molecular spectroscopy in an effusive beam with laser excitation. Such an effort is directed toward the creation of a semi-empirical model of the structure of the PbO molecule in the a(1) state. This state of PbO has been identified as a prime candidate for a measurement of the electron Electric Dipole Moment (EDM). The semi-empirical model (and thus our measurement) is needed to set the sensitivity of the electron EDM measurement. The presence of a non-zero value for the electron EDM would have profound consequences for the foundations of theoretical physics as an indication of physics beyond the Standard Model."

*The Rotating Magnet Experiment: A Test of Relativity*

Faculty Advisor: Professor Larry Hunter

There has been much discussion concerning the voltage that should be measured across the faces of a rotating magnetic cylinder. A unique prediction of relativity is that magnetic dipoles appear to be electric dipoles in a moving reference frame. The application of this fact to the rotating cylindrical case, however, is not as simple as was originally believed. This experiment is designed to distinguish between two predictions that have been made for this voltage. The first prediction was made and tested by Wilson and Wilson in 1913. This experiment is now considered inconclusive due to an experimental flaw. The second prediction was made by Swift and Pellegrini in 1995 to solvewhat they saw as a problem of charge non-conservation in the Wilson's prediction. By correcting the experimental flaw in the Wilsons' experiment, this experiment will distinguish between the two predictions. These predictions differ by only 6%, so this experiment attempts to achieve uncertainty levels of 1% to make the data conclusive. Preliminary data suggests that such uncertainty levels will be possible. Currently statistical uncertainty levels have been reduced to this level and a through investigation of systematic errors is under way.

*Recent Seismicity and the State of Stress in the Adirondack Mountains, New York*

Faculty Advisor: Professor Joel Gordon

Regional seismographic networks in the northeastern United States and adjacent Canada have recorded more than 45 earthquakes in the Adirondack Mountains since 1990. Focal mechanism solutions have been determined for five of these earthquakes using P-wave first motion polarities and the computer program FOCMEC. The solutions all show thrust faulting with inferred P-axes oriented near horizontal, although there is significant variation in the P-axis trends. Only one mechanism shows good correlation with the pattern of northeast-southwest horizontal compression predicted by models based on plate tectonics and inferred from most other studied events in the Adirondack region. Possible explanations for the anomalous mechanisms include local perturbations of the stress field or reactivation of preexisting zones of weakness formed during an earlier stress regime.

*Uncertainty, Complementarity and Recent 'Which-Way' Experiments*

Faculty Advisor: Professor Arthur Zajonc

This thesis explores the principles of complementarity and uncertainty. The exclusive vehicle of this exploration is 'which-way' experiments. Recent experiments by Scully

*et al.*(thought) and Rempe

*et al.*(actual) have questioned the preeminence of uncertainty as the enforcement mechanism of complementarity. Their apparatuses gather which-way information without significantly affecting the center of mass spatial wave function of the experimented-on quantons. Complementarity is not violated, and the interference fringes are destroyed, but without any significant classical momentum spreading prescribed by the uncertainty relation. (Uncertainty is not violated, merely eschewed.)

Three recent theories address this matter of complementarity without the traditional uncertainty-relation enforcement. One by B.-G. Englert claims to state complementarity *quantitatively*, and *without* uncertainty. Two others look for and find new dynamical explanations for the loss of interference. Wiseman *et al.* find non-local momentum kicks; Luis *et al.* find classical phase kicks (these last two appear to be different statements of the same effect).

My thesis ends with a brief conclusion which reconciles the various theories and experience, albeit in a mostly qualitative way.

*High Resolution Spectroscopic Study of PbO Toward a Measurement of the Electron Electric Dipole Moment*

Faculty Advisor: Professor Larry Hunter

The a(1) state of PbO is a candidate system for use in a measurement of the electron electric dipole moment. In this thesis we report measurements of the hyperfine splitting (A = -8.07(13)GHz, isotope shifts (the field shift between

^{208}PbO and

^{206}PbO is found to be 0.71(24)GHz and the specific mass shift is -0.19(28)GHz, and the -doubling constant ( =.0001885(40)cm

^{-1}) in this state. The measurement of the -doubling constant is in good agreement with a previously measured value and is of higher precision. The other quantities, which will be used to calibrate the electric dipole moment measurement, are measured here for the first time. Background information on these measurements including an introduction to diatomic molecular spectra and a derivation of -doubling is given.

*Investigating the Milky Way: A Population Study of Carbon Stars in the Galactic Halo and Disk*

Faculty Advisor: Professor Arthur Zajonc

The 2MASS infrared all sky survey is the most detailed and complete near-infrared survey initiated to date. For galactic latitudes b > 20 degrees, search criteria based on the relative magnitudes of the J H and K

_{s}infrared bands (1.25, 1.65 and 2.17 microns, respectively) located 1000 possible carbon stars in the Galactic halo. J and K band spectra measured on the Kitt Peak 4-meter telescope during November, 1999 confirmed five of the thirteen reddest objects in this sample to be carbon stars. I have reclassified one of these objects, 2m J0649+7416, which previously had been misclassified as an M-star by Abranyam & Gigoyan (1995), as a C-N carbon star. We also classified the source 2m J0133+3038 as an L-dwarf of possible type L0-L4.

2MASS data were also used to search for carbon stars in the Galactic disk from 50 degrees <1<310 degrees. My preliminary analysis shows a much larger population of carbon stars than observed in previous surveys (Claussen et al 1987; Groenewegen et al 1991). I calculated scale heights and radii for the carbon stars within the Galactic disk. In the region of 50 degrees <1<80 degrees, I calculated the scale height as h _{z}= 350+/-50 pc, and a scale radius as h _{r}= 4.0+/-0.5 kpc. In the region of 160 degrees <1<190 degrees, I calculated h _{z}=400+/-100 and H _{r}=5.7+/-0.8 kpc; and in the region of 220 degrees <1<250 degrees, h _{z}=300+/-50 and h _{z}=4.0+/-0.5. These calculations indicate that the Galactic disk is not uniform as some Galactic evolution models propose, and suggest a larger vertical distribution at the edge of the disk than previously thought.

*Diode Laser Systems for Bose-Einstein Condensation*

Faculty Advisor: Professor David Hall

Bose-Einstein Condensation (BEC) is a macroscopic observation of quantum mechanical behavior. Populations of bosons, when cooled and condensed to high densities and extremely low temperatures, fall into a highly degenerate ground state where classical notions of distinguishability are lost. In an effort to explore some of the strange and unfamiliar properties of this system, the Hall lab seeks to Bose-condense

^{87}Rb using primarily optical techniques. My contribution to this project, and the subject of much of this thesis, is the construction of an external-feedback diode laser system for use in the first stages of trapping and cooling rubidium.

*Muonic Atoms and Effective Field Theory*

Faculty Advisors: Professors Barry Holstein and Kannan Jagannathan

Brian's thesis had two related aims: to give a pedagogical illustration of the power of Effective Field Theory techniques in a simple non-relativistic context, and to use that method to model muonic atoms. Effective Theories are a powerful and general way of parametrizing physics at very short distances or high energy scales where we have no specific reason to think that the current best theories are applicable. The method and the attitude that goes with it has dramatically altered our point of view towards renormalization in field theory, and in several other areas of physics. One no longer regards QED, or even the standard model, as the unique, true approximation at arbitrarily short distances to some underlying theory. Rather, one regards them as good enough descriptions at sufficiently large distances or small energies, to be supplemented by unknown physics at smaller distance scales. Thus, renormalizability of a theory, which had come to be regarded as a major virtue in recent decades, is no longer considered that important a feature. Instead, one develops a scheme for short-distance physics that is sufficiently general, somewhat analogous to the multipole expansion in classical electrodynamics, that it is capable of modeling any short-distance behavior by a sequence of phenomenological parameters. One obtains physical results to a desired order of approximation by including sufficiently many terms in such an expansion, and the unknown parameters are determined by as many experimental quantities. As in any such venture, the scheme is successful if its independent predictions are far more numerous than the number of input values.

Brian applied this scheme to model atoms in which an electron is replaced by a muon. Such systems have been studied both experimentally and theoretically for a long time. However, the application of the techniques of effective field theories, clarifies the physics behind the previous work and generalizes it to handle all different kinds of atoms.

*T-Odd, P-Even Interactions and Atomic EDM*

Faculty Advisors: David DeMille and Kannan Jagannathan

Margaret (Meg) Wessling's thesis focused on small violations of discrete symmetries, in particular inversion in time (T), and inversion in space (P). Her aim was to understand what the low energy experimental signatures might be of the most general interaction that is odd under T and even under P, given that CPT is a good symmetry. These results would be useful in motivating and understanding high-precision experiments in atoms that Professor DeMille is interesting in pursuing. T-even, P-odd interactions in atoms have been investigated for a long time, and more recently, tight limits are being set on elementary interactions that are odd under both symmetries in searches for atomic electric dipole moments (EDMs). However, it is possible that there is no elementary interaction that is both T- and P-violating leading to a non-zero EDM. If instead, there were an elementary interaction that is T-odd and P-even (TOPE), in conjunction with the orthodox P-odd, T-even (POTE) weak interaction, one would have in higher order, an effective violation of both discrete symmetries. This in turn would lead, generically, to a small atomic EDM. As the experimental upper bounds on EDMs get more stringent, it becomes important to explore such possibilities. Meg undertook a systematic exploration by setting up the most general Lorentz invariant, CPT symmetric, Lagrangian. She then took its non-relativistic limit to catalog the kinds of atomic interactions that would result. An inspection of these small new 'forces' is used to calculate the permanent dipole moments of various atomic states. The predictions, of course, are in terms of the parameters of the new interactions. By turning the comparison around, she is able to set upper bounds on these parameters using the current best experimental limits on EDMs. Meg's work was done in collaboration with Professor David DeMille of Yale University.

Attachment | Size |
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Langin.pdf | 3.78 MB |

Eddins Thesis Final.pdf | 30.58 MB |

Kandel thesis.pdf | 5.23 MB |

Qiao thesis | 7.75 MB |

Thomas thesis | 21.75 MB |

Chu Teng Thesis.pdf | 5.01 MB |

Phyo Kyaw Thesis | 15.85 MB |

Andrew Mowry.pdf | 5.43 MB |

Antunes.pdf | 17.44 MB |

Alam.pdf | 5.63 MB |

Wadia.pdf | 37.47 MB |

Yoo.pdf | 4.96 MB |

Ang_D.pdf | 8.26 MB |

Elizabeth West 08.pdf | 3.88 MB |

David Lane.pdf | 2.52 MB |

Robert Kwark.pdf | 24.04 MB |