# Browsing by Author "Gauthier, Daniel J"

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Item Open Access Bounding the outcome of a two-photon interference measurement using weak coherent states(OPTICS LETTERS, 2018-08-15) Aragoneses, Andrés; Islam, Nurul T; Eggleston, Michael; Lezama, Arturo; Kim, Jungsang; Gauthier, Daniel JItem Open Access Broadband chaos generated by an optoelectronic oscillator.(Phys Rev Lett, 2010-03-19) Callan, Kristine E; Illing, Lucas; Gao, Zheng; Gauthier, Daniel J; Schöll, EckehardWe study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.Item Open Access Bunching-induced optical nonlinearity and instability in cold atoms [Invited].(Opt Express, 2011-11-07) Greenberg, Joel A; Schmittberger, Bonnie L; Gauthier, Daniel JWe report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(⁵) = 7.6 × 10⁻¹⁵ (m/V)⁴, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/10⁵), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.Item Open Access Cavity-free photon blockade induced by many-body bound states.(Physical review letters, 2011-11) Zheng, Huaixiu; Gauthier, Daniel J; Baranger, Harold UThe manipulation of individual, mobile quanta is a key goal of quantum communication; to achieve this, nonlinear phenomena in open systems can play a critical role. We show theoretically that a variety of strong quantum nonlinear phenomena occur in a completely open one-dimensional waveguide coupled to an N-type four-level system. We focus on photon blockade and the creation of single-photon states in the absence of a cavity. Many-body bound states appear due to the strong photon-photon correlation mediated by the four-level system. These bound states cause photon blockade, which can generate a sub-Poissonian single-photon source.Item Open Access Collective light-matter interactions via emergent order in cold atoms(2012) Greenberg, JoelCollective behavior in many-body systems, where the dynamics of an individual element depend on the state of the entire ensemble, play an important role in both basic science research and applied technologies. Over the last twenty years, studies of such effects in cold atomic vapors have lead to breakthroughs in areas such as quantum information science and atomic and condensed matter physics. Nevertheless, in order to generate photon-mediated atom-atom coupling strengths that are large enough to produce collective behavior, these studies employ techniques that intrinsically limit their applicability. In this thesis, I describe a novel nonlinear optical process that enables me to overcome these limitations and realize a new regime of collective light-matter interaction.

My experiment involves an anisotropic cloud of cold rubidium atoms illuminated by a pair of counterpropagating optical (pump) fields propagating at an angle to the trap's long axis. When the pump beam intensities exceed a threshold value, a collective instability occurs in which new beams of light are generated spontaneously and counterpropagate along the trap's long axis. In order to understand the physical mechanism responsible for this behavior, I study first the system's nonlinear optical response when driven below the instability threshold. I find that the incident optical fields produce an optical lattice that causes the atoms to become spatially organized on the sub-wavelength length scale. This organization corresponds to the formation of an atomic density grating, which effectively couples the involved fields to one another and enables the transfer of energy between them. The loading of atoms into this grating is enhanced by my choice of field polarizations, which simultaneously results in cooling of the atoms from T~30 μK to T~3 μK via the Sisyphus effect. As a result, I observe a fifth-order nonlinear susceptibility χ^{(5)}=1.9x10^-12 (m/V)^4 that is 7 orders of magnitude larger than previously observed. In addition, because of the unique scaling of the resulting nonlinear response with material parameters, the magnitude of the nonlinearity can be large for small pump intensities (\ie, below the resonant electronic saturation intensity 1.6 mW/cm^2) while simultaneously suffering little linear absorption. I confirm my interpretation of the nonlinearity by developing a theoretical model that agrees quantitatively with my experimental observations with no free parameters.

The collective instability therefore corresponds to the situation where the cold vapor transitions spontaneously from a spatially-homogeneous state to an ordered one. This emergent organization leads to the simultaneous emission of new optical fields in a process that one can interpret either in terms of mirrorless parametric self-oscillation or superradiance. By mapping out the phase diagram for this transition, I find that the instability can occur for pump intensities as low as 1 mW/cm^2, which is approximately 50 times smaller than previous observations of similar phenomena. The intensity of the emitted light can be up to 20% of the pump beam intensity and depends superlinearly on the number of atoms, which is a clear signature of collective behavior. In addition, the generated light demonstrates temporal correlations between the counterpropagating modes of up to 0.987 and is nearly coherent over several hundred μs. The most significant attributes of the light, though, are that it consists of multiple transverse spatial modes and persists in steady-state. This result represents the first observation of such dynamics, which have been shown theoretically to lead to a rich array of new phenomena and possible applications.

Item Open Access Decoy-state quantum key distribution with nonclassical light generated in a one-dimensional waveguide.(Optics letters, 2013-03) Zheng, Huaixiu; Gauthier, Daniel J; Baranger, Harold UWe investigate a decoy-state quantum key distribution (QKD) scheme with a sub-Poissonian single-photon source, which is generated on demand by scattering a coherent state off a two-level system in a one-dimensional waveguide. We show that, compared to coherent state decoy-state QKD, there is a two-fold increase of the key generation rate. Furthermore, the performance is shown to be robust against both parameter variations and loss effects of the system.Item Open Access Efficient Entangled Biphoton Production and Manipulation for Quantum Applications(2015) Guilbert, HannahThe creation and manipulation of biphotons is important for many applications in quantum optics and quantum information. Topics that benefit from efficient biphoton sources range from the most fundamental quantum science experiments to the highly applied fields of quantum communication and quantum computation. Biphoton sources have long been hailed as one of the leading methods for creating entangled photon pairs for tests of Bell's inequality, creating heralded photon pairs that are used in on-demand single-photon sources and heralded measurement techniques, and for quantum communication protocols to name a few. Specifically for quantum communication, biphoton sources are commonly used for cutting edge quantum key distribution (QKD) protocols.

In the first part of the thesis, I focus on realizing an efficient biphoton source that produces high yield photon pairs.

More specifically, I develop an optimized biphoton source using the nonlinear optical process of spontaneous parametric down-conversion in a second-order nonlinear crystal. I develop a formalism for predicting the two important metrics of a biphoton source: the heralding efficiency and joint count rate. I show how, from a large parameter space, one can tailor the phase matching of the nonlinear interaction to create a high quality biphoton source that produces both high heralding efficiency and high joint count rate. I achieve heralding efficiencies of 86$\pm$5$\%$ and joint count rates of 2.58$\pm$0.6 kHz per mW pump power. I show that using a collinear nondegenerate geometry allows for heralding efficiencies of up to 99.7$\%$ assuming no loss in the system. I verify the theoretical model with experimental results and find good agreement.

In the second part of the thesis I turn to manipulating the single photons born from the biphoton source for applications in creating single-photon spectrometers and time-frequency QKD systems. The security of QKD is only guaranteed if the two parties have access to a set of states called mutually unbiased states. I create a set of these states in time and their conjugate states in the frequency basis and show that I can manipulate single photon correlations in time and frequency so that an eavesdropper can be detected if she localizes a photon to a 1 ns time interval.

Additionally, in these experiments, I stretch a single photon wavepacket of 5-ps-width to a wavepacket of 8.3-ns-width and subsequently recompress it to at least the resolution of the detectors ($\sim$ 300 ps). This demonstrates a stretch factor of >1600 for a single-photon pulse using a group velocity dispersive material. To my knowledge, this is the largest reported stretch factor for a single-photon wavepacket produced by a biphoton source. The ability to stretch and recompress a single photon by this amount has applications in creating high-resolution, high-efficiency, single-photon spectrometers as well as advancing time-frequency QKD systems and other temporal pulse shaping applications.

Item Open Access Fast, Nondestructive Quantum-state Readout of a Single, Trapped, Neutral Atom(2018) Shea, Margaret EileenExperimental systems that trap single, neutral atoms have recently emerged as a promising platform for experiments in a range of disciplines such as quantum information science, quantum simulation and fundamental light-atom interaction. In this thesis, I build such a system and use it to trap and study a single, neutral atom of 87Rb. I confront and overcome several experimental challenges while designing and building the system. For example, I develop a MOT of unusual geometry with which to load the single-atom trap and also a detection scheme that robustly detects the trapped atom nondestructively, that is, without pushing it out of the trap. The result of this design and construction process is a system that stably traps a single atom in an optical dipole trap. I achieve trap lifetimes of over 1 minute in the absence of near-resonant laser light.

In addition to the experimental apparatus, I develop a thorough rate-equation model to predict the population dynamics of the trapped atom's internal quantum state when probed by near-resonant light. This model gives unique insight into the influence of the atom's internal dynamics on the detected scattering rate. I use this model to predict several important experimental parameters and compare it to the experimental data. This allows me to characterize the parameters that govern how the atom interacts with near-resonant laser light and how that interaction affects the experimental data. For example, I perform an absolute calibration of the collection efficiency of the experimental system, a first for a single, neutral-atom trap.

Using these experimental and modeling tools, I investigate the scattering rate of an atom in the presence of near-resonant linearly-polarized laser light. This is of great interest to the field because it is used to measure the atom's internal quantum state, in a process known as quantum-state readout. Fast and accurate quantum-state readout is crucial to the success of many protocols in quantum information science and quantum simulation. Using the tools described here, I achieve quantum-state readout with an average fidelity of 97.6±0.2% using a linearly-polarized probe beam. The readout requires a measurement time of 160±20 μs, and the atom remains in the trap after the readout in 97.1±0.1% of the trials. I use linearly-polarized light instead of circularly-polarized light because it makes the readout less sensitive to the atom's occupation of a specific magnetic sublevel, and hence does not require sublevel-specific state preparation. It also allows for a more flexible experimental geometry. This is the fastest and highest-fidelity nondestructive readout of a single neutral atom performed with a linearly-polarized probe beam reported to date.

In addition, I identify a decay in the atom's scattering rate over the course of the readout time that limits the quantum-state readout fidelity. I investigate possible sources of this decay using the rate-equation model and a model of the readout protocol, and I conclude that it is likely caused by a combination of Raman transitions and heating. The heating is related to the near-resonant probe light and also to the optical dipole trap that holds the atom. I discuss ways that this decay can be avoided, but point out that these possible solutions result in longer readout times. This investigation has applications across a wide variety of experiments that require fast quantum-state readout.

Item Open Access FSBS resonances observed in a standard highly nonlinear fiber.(Opt Express, 2011-03-14) Wang, Jing; Zhu, Yunhui; Zhang, Rui; Gauthier, Daniel JForward stimulated Brillouin scattering (FSBS) is observed in a standard 2-km-long highly nonlinear fiber. The frequency of FSBS arising from multiple radially guided acoustic resonances is observed up to gigahertz frequencies. The tight confinement of the light and acoustic field enhances the interaction and results in a large gain coefficient of 34.7 W(-1) at a frequency of 933.8 MHz. We also find that the profile on the anti-Stokes side of the pump beam have lineshapes that are asymmetric, which we show is due to the interference between FSBS and the optical Kerr effect. The measured FSBS resonance linewidths are found to increase linearly with the acoustic frequency. Based on this scaling, we conclude that dominant contribution to the linewidth is from surface damping due to the fiber jacket and structural nonuniformities along the fiber.Item Open Access High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation.(Opt Express, 2011-01-17) Zhu, Yunhui; Lee, Myungjun; Neifeld, Mark A; Gauthier, Daniel JWe demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noisemodulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. In comparison with a previous slow-modulation method, eye-diagram and signal-to-noise ratio (SNR) analysis show that this broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR in the comparison.Item Open Access High-rate, high-dimensional quantum key distribution systems(2018) ISLAM, NURULThere is currently a great interest in using high-dimensional (dimension d>2) quantum states for various communication and computational tasks. High-dimensional quantum states provide an efficient and robust means of encoding information, where each photon can encode a maximum of log_2(d) bits of information. One application where this becomes a significant advantage is quantum key distribution (QKD), which is a communication technique that relies on the quantum nature of photonic states to share a classical secret key between two remote users in the presence of a powerful eavesdropper. High-dimensional QKD protocols are believed to overcome some of the practical challenges of the conventional qubit-based (d = 2) protocols, such as the long recovery time of the single-photon detectors, or the low error tolerance to quantum channel noise.

In this thesis, I demonstrate experimentally and theoretically various novel QKD protocols implemented with high-dimensional quantum photonic states, where the information is encoded using the temporal and phase degrees of freedom. One challenging aspect of high-dimensional time-phase QKD protocols is that the measurement of the phase states requires intricate experimental setups, involving time-delay interferometers, fiber Bragg gratings, or a combination of electro-optic modulators and fiber Bragg gratings, among others. Here, I explore two different measurement schemes, one involving a tree of delay line interferometers, and the other using a quantum-controlled technique, where the measurement of the phase states is performed by interfering an incoming quantum state with another locally generated quantum state. Using the interferometric method (quantum-controlled) and a d = 4 (d = 8) encoding scheme, I achieve a secret key rate of 26.2 +/- 2.8 (16.6 +/- 1.0) Mbps at a 4 (3.2) dB channel loss. Overall, the secret key rates achieved in this thesis are a few folds improvement compared to the other state-of-the-art high-rate QKD systems.

Finally, I consider the possibility of an eavesdropper attacking the high-dimensional quantum states using a universal quantum cloning machine, where she uses weak coherent states of different mean photon numbers (decoy-state technique) to estimate the single-photon fidelity. I show that an eavesdropper can estimate the unknown quantum states in the channel with a degraded but optimal cloning fidelity. Specifically, I find that the upper bound of the cloning fidelity decreases from 0.834 +/- 0.003 at d= 2 to 0.639 +/- 0.003 at d = 6, thereby providing evidence for two conclusions. First, the decoy-state technique can be used to extract single-photon contribution from intricate weak coherent states based two-photon experiments. Second, high-dimensional quantum photonic states are more robust compared to the d = 2 quantum states.

Item Open Access Making Nuclear Magnetic Hyperpolarization Practical through Storage in Disconnected Eigenstates(2015) Claytor, Kevin E.There are two fundamental limitations in magnetic resonance: the poor signal amplitude and the short duration before the system return to equilibrium. Hyperpolarization methods solve the problem of signal amplitude, however, the duration of the hyperpolarized signal is still limited by the spin-lattice relaxation time, T1. Disconnected eigenstates provide a mechanism by which hyperpolarization can be stored for several times T1. This thesis contributes to the knowledge of these states in four important ways. First, the decay of hyperpolarized magnetization of gas is simulated in lung tissue with a contrast agent, yielding insights about the optimal field strength for imaging. Second, I show that it is possible to rapidly discover and characterize disconnected eigenstates by showing that they can be measured without synthesizing the isotopically labeled compound. Third, I extend the spin systems that can support disconnected eigenstates by expanding the theory to include spin-1 nuclei. Finally, I show that disconnected states with long lifetimes can be populated in conjunction with hyperpolarization techniques to simultaneously yield large signal amplitudes for long durations.

Applications of hyperpolarized spin order are likely to be in complex geophysical or biological structures. Understanding the effect of the inhomogeneous fields created when such structures are placed in a magnetic field on hyperpolarized spin order is a necessity to characterize the experimental signal. An example case of hyperpolarized 3He and 129Xe diffusing through lung tissue is examined. In particular a Monte Carlo simulation tool, combined with a magnetic field map of the inhomogeneous field created by mouse lung tissue, is used to determine the dephasing rate of hyperpolarized 3He and 129Xe in the presence of SuperParamagnetic Iron Oxide Nanoparticles (SPION). Contributions to the dephasing rate include the inhomogeneous field, the SPION magnetic field, and dephasing caused by collisions with the confining geometry. The sensitivity of either gas to SPION increases with increasing SPION concentration and decreasing field strength.

There are some general rules about what makes for a disconnected eigenstate (or singlet state) with a long lifetime. However, no systematic experimental study has been undertaken due to the cost and time-constraints of synthesizing the labeled species for study. I show that synthesis is not a barrier for characterizing the long-lived states. Instead the lifetimes may be determined by using the naturally occurring doubly-labeled isotopomer. I verified this method with two compounds, diphenyl acetylene (DPA) and diethyl oxylate (DEO). The former was determined to have a singlet lifetime TS = 251.40 ±3.16 s from the synthesized species, while the naturally occurring isotopomer yielded a lifetime TS = 202 ±55.30 s, both substantially longer than the spin-lattice relaxation time, T1 = 1.63 ±0.01s. In DEO, the lifetime from the disconnected eigenstate was determined to be TS = 14.62 ±0.76 s (synthesized), TS = 19.32 ±3.16 s (naturally occurring). This method is applied to a range of compounds ranging from simple four-spin systems, such as diacetylene (TS = 48.80 ±22.74 s, T1 = 18.66 ±1.16 s) to eight spin systems in dimethylmaleic anhydride (TS = 27.25 ±3.39 s, T1 = 9.38 ±0.43 s). Additionally, a family of compounds including naphthalene (TS = 4.37 ±0.34 s, T1 = 11.33 ±4.89 s), biphenyl (TS = 3.09 ±0.66 s, T1 = 4.69 ±0.10 s), and DPA show that the rotation of the phenyl rings and intermolecular dipole-dipole relaxation can be critical to the relaxation dynamics.

One particular method of accessing the disconnected eigenstate involves coupling a chemically equivalent spin-1/2 pair asymmetrically to an auxiliary spin-1/2 pair. I demonstrate that the disconnected state may still be accessed when the auxiliary nuclei are spin-1. This has two distinct advantages. When the auxiliary nuclei change from proton to deuterium, the couplings are reduced by a factor of ~6.5 which prevents the disconnected state from relaxing as rapidly back to equilibrium. This is demonstrated in diacetylene-d2 and DPA-d10, where the singlet lifetime was extended by a factor of ~1.7 via deuteration (TS,1H = 49 ±23 s, TS,2H = 83 ±30 s for diacetylene and TS,1H = 274 ±6.1 s, TS,2H = 479 ±83 s for DPA). Additionally, by reducing the coupling strength, deuteration allows additional structural moieties to be explored, such as RDC=CDR. One such structure is explored in trans-ethylene-d2, where the singlet character of the protons can be accessed by the reduced coupling to the deuterium. Additionally, this allows for a relatively strong deuterium-deuterium scalar coupling, requiring modification to the theory. This is carried out analytically, and implications for the relaxation properties are performed using a spin-dynamics numerical simulation. The lifetime of the disconnected state was determined to be TS = 30.2 ±12.3 s, compared to the T1 = 1.1 ±0.2 s at high concentration (270 mM), and increasing to TS = 117. ±9.80 s at low concentration (52 mM). The variation in long lifetime is attributed to intermolecular dipole-dipole relaxation.

Ultimately, the gains in lifetime from using disconnected eigenstates provide a means to the practical implementation of hyperpolarization in a wider range of experiments. A recent hyperpolarization method, Signal Amplification By Reversible Exchange in Shield Enables Alignment Transfer to Heteronuclei (SABRE-SHEATH) is shown to directly hyperpolarize long lived spin order in a diazirine containing molecule. Diazirine rings are three member N=N-C groups that can replace a methylene group and serve as a versatile MR and optical molecular tag. Hyperpolarization is accomplished by bubbling parahydrogen through a solution containing the diazirine and an iridium catalyst. Due to the chemical inequivalence of the 15N of the diazirine, hyperpolarization of longitudinal magnetization and singlet character could be observed by transfer to the high field spectrometer. Signal enhancements of over 14,000 were observed. The magnetic field strength required for buildup of magnetization and singlet character was derived and is in agreement with the experiment. The magnetization lifetime was observed to be T1 = 5.75 ±0.18 minutes and independent of field strength, while the lifetime of the singlet character was observed to be as long as TS = 30.1 ±13.4 minutes at low field (3 Gauss).

The combination of these experiments – understanding lifetimes in inhomogeneous magnetic fields that will be encountered in experiment, identification of disconnected eigenstates with long lifetimes via the naturally occurring isotopomer and extending these lifetimes even further with deuteration, and finally, the direct generation of long-lived hyperpolarized spin order – allows a measurement that required hyperpolarized spin order for the enhanced signal amplitude, to be carried out.

Item Open Access Method to Sense Changes in Network Parameters with High-Speed, Nonlinear Dynamical Nodes(2013) Callan, KristineThe study of dynamics on networks has been a major focus of nonlinear science over the past decade. Inferring network properties from the nodal dynamics is both a challenging task and of growing importance for applied network science. A subset of this broad question is: How can one determine changes to the coupling strength between elements in a small network of chaotic oscillators just by measuring the dynamics of one of the elements (nodes) in the network? In this dissertation, I propose and report on an implementation of a method to simultaneously determine: (1) which link is affected and (2) by how much it is attenuated when the coupling strength along one of the links in a small network of dynamical nodes is changed. After proper calibration, realizing this method involves only measurements of the dynamical features of a single node.

Previous attempts to solve this problem focus mainly on synchronization-based approaches implemented in low-speed, homogeneous experimental systems. In contrast, the experimental apparatus I use to implement my method comprises two high-speed (ps-timescale), heterogeneous optoelectronic oscillators (OEOs). Each OEO constitutes a node, and a network is formed by mutually coupling two nodes. I find that the correlation properties of the chaotic dynamics generated by the nodes, which are heavily influenced by the propagation time delays in the network, change in a quantifiable way when the coupling strength along either the input or output link is attenuated. By monitoring multiple aspects of the correlation properties, which I call ``time delay signatures'' (TDSs), I find that the affected link can be determined for changes in coupling strength greater than 20% ± 10%. Due to the sensitivity with which the TDSs change, it is also feasible to determine approximately the time-varying coupling strength for large enough attenuations.

I also verify that the TDSs' sensitivity to changes in coupling strength are captured by a simple deterministic model that takes into account each OEO's nonlinearities, bandpass filtering, and time delays. I find qualitative agreement between my experimental observations and numerical simulations of the model and also use the model to explore the dependence of the TDS signature on the OEO heterogeneity. I find that making the time delays identical leads to larger changes in TDSs, which improves the precision with which the coupling strength can be determined. This also leads, however, to a decrease in the ability to determine which link has been attenuated, indicating that a balance must be struck between optimizing the network's ability to discern the new coupling strength and the affected link. To investigate the role of the nonlinearity, I again test my method numerically using the same delay-coupled topology, but with dynamics generated by a linear stochastic process. I find that sensing can be achieved in the absence of nonlinear effects, but that, with regards to determining which link is affected, the performance is optimized differently in the linear and nonlinear cases.

This method could be extended to design a low-profile intrusion detection system, where several OEOs are spread around a scene and wirelessly coupled via antennas. The ultra-wide-band signals emitted by the nodes (OEOs) can pass through building materials with little attenuation, but would be strongly attenuated by a person who enters the path between two nodes. Beyond practical applications, it also remains to be seen if TDSs could prove to be a simple way to analyze information flow in networks with chaotic dynamics and propagation delays between the nodes.

Item Open Access Multimode Atomic Pattern Formation via Enhanced Light-atom Interactions(2016) Schmittberger, Bonnie LeeThe nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.

Item Open Access Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.(Invest Ophthalmol Vis Sci, 2011-02-22) Hwang, Richard Y; Gauthier, Daniel J; Wallace, Dana; Afshari, Natalie APURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.Item Open Access Slow light with a swept-frequency source.(Opt Express, 2010-12-20) Zhang, Rui; Zhu, Yunhui; Wang, Jing; Gauthier, Daniel Jct: We introduce a new concept for stimulated-Brillouin-scattering-based slow light in optical fibers that is applicable for broadly-tunable frequency-swept sources. It allows slow light to be achieved, in principle, over the entire transparency window of the optical fiber. We demonstrate a slow light delay of 10 ns at 1.55 μm using a 10-m-long photonic crystal fiber with a source sweep rate of 400 MHz/μs and a pump power of 200 mW. We also show that there exists a maximal delay obtainable by this method, which is set by the SBS threshold, independent of sweep rate. For our fiber with optimum length, this maximum delay is ~38 ns, obtained for a pump power of 760 mW.Item Open Access Spatial Variation of Cardiac Restitution and the Onset of Alternans(2008-06-19) Dobrovolny, Hana MariaInstability in the propagation of nonlinear electro-chemical waves in the heart is responsible for life-threatening disease. This thesis describes an investigation of the effects of boundaries on cardiac wave propagation that arises from a site where an electrical stimulus is applied or from boundaries beyond which current does not flow. It is generally believed that the spatial scale for boundary effects is approximately equal to the passive length constant, lambda, of the tissue, the distance over which a a voltage pulse decays when it is below the threshold for wave generation. From the results of

*in vitro*experiments with bullfrog cardiac tissue and through numerical simulations, I find that boundaries affect wave propagation over a much larger spatial scale and that the spatial variation in some cardiac restitution properties is correlated statistically with the onset of alternans, a possible precursor to fibrillation in the human heart.An optical imaging system using novel illumination based on LEDs is used to determine the spatial dependence of action potential duration (APD) and the slope of the dynamic restitution curve S

_{DRC}, which describes the relationship between steady-state APD and diastolic interval. For tissue with nearly identical cells, I find that APD is longest near the stimulus and shortest near the physical boundary with significant changes (~100 ms) over a distance of ~10lambda. S_{DRC}decreases with distance from the stimulus at a constant rate (~0.1-1.5 /mm) over the surface of the tissue. Simulations using a two-variable cardiac model confirm that spatial patterns of APD and S_{DRC}can be induced by boundaries.Additional measurements with the simultaneous impalement of two microelectrodes are used to determine the spatial differences of other restitution properties. These studies indicate that APD and S

_{DRC}, as well as the slopes of the constant-BCL and S1S2 restitution curves, vary in space and that the spatial differences and onset of alternans at rapid pacing are correlated. If similar correlations are evident in humans, such measurements may identify patients who are susceptible to arrhythmias and allow for early treatment.Item Open Access Subwavelength Sensing Using Nonlinear Feedback in a Wave-Chaotic Cavity(2013) Cohen, Seth DanielTypical imaging systems rely on the interactions of matter with electromagnetic radiation, which can lead to scattered waves that are radiated away from the imaging area. The goal such an imaging device is to collect these radiated waves and focus them onto a measurement detector that is sensitive to the wave's properties such as wavelength (or color) and intensity. The detector's measurements of the scattered fields are then used to reconstruct spatial information about the original matter such as its shape or location. However, when a scattered wave is collected by the imaging device, it diffracts and inteferes with itself. The resulting interference pattern can blur spatial information of the reconstructed image. This leads to a so-called diffraction limit, which describes the minimum sizes of spatial features on a scatterer that can be resolved using conventional imaging techniques. The diffraction limit scales with the wavelength λ of the illuminating field, where the limit for conventional imaging with visible light is approximately 200 nm. Investigating subwavelength objects (< λ) requires more advanced measurement techniques, and improving the resolving capabilities of imaging devices continues to be an active area of research.

Here, I describe a new sensing technique for resolving the position of a subwavelength scatterer (< λ) with vastly subwavelength resolution (<< λ). My approach combines two separate fields of scientific inquiry: time-delayed nonlinear feedback and wave chaos. In typical time-delayed nonlinear feedback systems, the output of a nonlinear device is delayed and fed back to its input. In my experiment, the output of a radio-frequency (λ ~ 15 cm) nonlinear circuit is injected into a complex scattering environment known as a wave-chaotic cavity. Inside the cavity, the field interacts with a subwavelength dielectric object from all sides, and a portion of the scattered waves are coupled out of the cavity, amplified, and fed back to the input of the nonlinear circuit. The resulting closed-feedback loop generates its own radio-frequency illumination field (> 1 GHz), which contains multiple wavelengths and is sensitive to location of the scattering object. Using the dynamical changes in the illumination field, I demonstrate subwavelength position-sensing of the scatterer's location in the cavity with a one-dimensional resolution of ~λ/10,000 and a two-dimensional resolution of ~ λ/300.

This novel method demonstrates that the dynamical changes of a feedback oscillator can be exploited for resolving subwavelength spatial features. Unlike conventional imaging techniques, it uses a single scalar measurement of the scattered field and takes advantage of a complex scattering environment. Furthermore, this work demonstrates the first application of quasiperiodic dynamics (oscillations with incommensurate frequencies) from a nonlinear system. Using the key ingredients from my radio-frequency system, I extend my method to an experiment that uses optical frequencies (λ = 1550 nm) to demonstrate subwavelength sensing in two dimensions with a resolution of approximately 10 nm. Because this new sensing technique can be adapted to multiple experiments over vastly different length scales, it represents a potential platform for creating a new class subwavelength imaging devices.

Item Open Access Theory and Application of SBS-based Group Velocity Manipulation in Optical Fibers(2013) Zhu, YunhuiAll-optical devices have attracted many research interests due to their ultimately low heat dissipation compared to conventional devices based on electric-optical conversion. With recent advances in nonlinear optics, it is now possible to design the optical properties of a medium via all-optical nonlinear effects in a table-top device or even on a chip.

In this thesis, I realize all-optical control of the optical group velocity using the nonlinear process of stimulated Brillouin scattering (SBS) in optical fibers. The SBS-based techniques generally require very low pump power and offer a wide transparent window and a large tunable range. Moreover, my invention of the arbitrary SBS resonance tailoring technique enables engineering of the optical properties to optimize desired function performance,

which has made the SBS techniques particularly widely adapted for

various applications.

I demonstrate theoretically and experimentally how the all-optical

control of group velocity is achieved using SBS in optical fibers.

Particularly, I demonstrate that the frequency dependence of the

wavevector experienced by the signal beam can be tailored using

multi-line and broadband pump beams in the SBS process. Based on the theoretical framework, I engineer the spectral profile

to achieve two different application goals: a uniform low group velocity (slow light) within a broadband spectrum, and a group velocity with a linear dependence on the frequency detuning (group velocity dispersion or GVD).

In the broadband SBS slow light experiment, I develop a novel noise current modulation method that arbitrarily tailors the spectrum of a diode laser. Applying this method, I obtain a 5-GHz broadband SBS gain with optimized flat-topped profile, in comparison to the ~40 MHz natural linewidth of the SBS resonance. Based on the broadband SBS resonance, I build a 5-GHz optical buffer and use this optical buffer to delay a return-to-zero data sequence of rate 2.5 GHz (pulse width 200 ps). The fast noise modulation method significantly stabilizes the SBS gain and improves the signal fidelity. I obtain a tunable delay up to one pulse-width with a peak signal-to-noise ratio of 7. I also find that SBS slow light performance can be improved by avoiding competing nonlinear effects. A gain-bandwidth product of 344 dB.GHz is obtained in our system with a highly-nonlinear optical fiber.

Besides the slow light applications, I realize that group velocity dispersion is also optically controlled via the SBS process. In the very recent GVD experiment, I use a dual-line SBS resonance and obtain a tunable GVD parameter of 7.5 ns$^2$/m, which is 10$^9$ times larger than the value found in a single-mode fiber. The large GVD system is used to disperse an optical pulse with a pulse width of 28 ns, which is beyond the capability for current dispersion techniques working in the picosecond and sub picosecond region. The SBS-based all-optical control of GVD is also widely tunable and can

be applied to any wavelength within the transparent window of the

optical fiber. I expect many future extensions following this work

on the SBS-based all-optical GVD control using the readily developed SBS tailoring techniques.

Finally, I extend the basic theory of backwards SBS to describe the forward SBS observed in a highly nonlinear fiber, where asymmetric forward SBS resonances are observed at the gigahertz range. An especially large gain coefficient of 34.7 W$^{-1}$ is observed at the resonance frequency of 933.8 MHz. This is due to good overlap between the optical wave and the high order guided radial acoustic wave. The interplay from the competing process known as the Kerr effect is also accounted for in the theory.

Item Open Access Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.(Phys Rev E Stat Nonlin Soft Matter Phys, 2014-09) Rosin, David P; Rontani, Damien; Haynes, Nicholas D; Schöll, Eckehard; Gauthier, Daniel JWe study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.