A geometric journey toward genuine multipartite entanglement

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2024.This thesis focuses on the challenge of characterizing multipartite entanglement. While the study of bipartite entanglement is well-documented in scientific literature, recognizing that entanglement can involve more than two parties—i.e. three or more parties—is crucial, as multipartite entanglement enables the completion of more complicated tasks in quantum information science. Previous discussions on entanglement, especially within scenarios such as information scrambling, primarily concentrated on bipartite entanglement, thus overlooking the rich landscape of multipartite entanglement. By involving more parties, multipartite entanglement exhibits a larger degree of nonlocality, significantly deepening our insights into the dynamical properties of quantum many-body systems, going far beyond what has been revealed through bipartite entanglement. Despite its long-recognized importance, a proper quantification of multipartite entanglement, along with the understanding of the “genuine multipartite entanglement” criterion, continues to pose substantial challenges. The work in this thesis reveals an unexpected connection between multipartite entanglement and the geometry of simplices. Specifically, we demonstrate that every three-qubit state can be associated with a triangle, with its area measuring the genuine tripartite entanglement within that state. Similarly, every four-qubit state can be associated with a tetrahedron, with its volume measuring the genuine quadripartite entanglement within that state. With these results, we embark on a geometric journey toward addressing the quantification problem of genuine multipartite entanglement, offering new perspectives on the complexity of even larger quantum many-body systems

Soliton solutions for high-bandwidth optical pulse storage and retrieval

Thesis (Ph. D.)--University of Rochester. Dept. of Physics and Astronomy, 2013.Quantum-optical information processing in material systems requires on-demand manipulation and precision control techniques. Previous implementations of optical pulse control have mostly been limited to weak, narrowband probe fields, often using a modified form of Electromagnetically Induced Transparency (EIT). We propose optical pulse control in a contrasting regime with high-bandwidth optical pulses, enabling higher clock-rates and on-demand fast pulse switching. Our novel solutions exploit the coherent interaction between short, strong pulses and resonant media (such as a cloud of ultra-cold atoms) to store, manipulate, and retrieve high-bandwidth optical pulse information. The evolution equations that model such short pulse propagation are inherently nonlinear and they govern both amplitudes and phases of the propagating field and the dielectric medium. They cannot be modeled by population rate equations or simplified with steady-state assumptions. Nonlinear evolution equations do not yield solutions easily and using them to characterize the physics at hand typically requires complementary analytical and numerical approaches. We take both approaches here, using analytical methods and our own numerical integration code. For uniform and infinitely extended media we generate novel three-pulse soliton solutions: robust, nonlinear waves with the unique property of preserving their shape under interaction (or "collision"). This important property enables one high-bandwidth soliton to push another from one location in an atomic cloud to another, predictably and nondestructively. We then also probe the practical utility of our specialized infinite-extent solutions by numerically solving the same nonlinear evolution equations for a variety of initial pulse shapes and strengths. Our numerical simulations confirm that our novel soliton solutions provide appropriate control parameters, including pulse storage locations and pulse sequencing, even in finite media under non-idealized initial conditions. Combining our numerical and analytic results, we propose a scheme to manipulate high-bandwidth optical information and achieve on-demand, high-fidelity retrieval

Theory of strong-field atomic ionization for elliptical or circular polarization

Thesis (Ph. D.)--University of Rochester. Dept. of Physics and Astronomy, 2013.Interaction between intense laser fields (with intensities on the order of 1 PW/cm2) and gas-phase atoms or molecules has led to many new physical phenomena, such as multiphoton ionization, above-threshold ionization, nonsequential double ionization, high harmonic generation, attosecond pulse generation, coherent X-ray generation, etc. These phenomena have been of interest from the perspectives of both fundamental physics and potential applications. The first step of all these strong-field phenomena is atomic ionization. Therefore understanding atomic ionization is the basis of understanding all strong-field phenomena. Extensive work has been done on atomic ionization, but mainly with linearly polarized laser fields. Little attention has been paid to elliptical or circular polarization, for two reasons. First, many of the above-mentioned strong-field processes can only be generated or maximized with linear polarization. Second, elliptical or circular polarization is very difficult to deal with, especially theoretically. In this dissertation, we will be focusing on atomic ionization with elliptical or circular polarization. The first question: why would one bother to study elliptical or circular polarization? The answer is that elliptical or circular polarization is able to reveal important ionization information that is not accessible with linear polarization. For example, at what time during a pulse was an electron emitted? Surprisingly, this obvious question cannot be answered with linear polarization, but it can be answered with elliptical or circular polarization. Atomic ionization with elliptical or circular polarization will be studied systematically, mainly using a classical ensemble method. Our study covers a range of ionization channels, including single ionization, double ionization, and triple ionization. We will explain how to decode new ionization information from experimentally measurable ion momentum distributions. We will also resolve a couple of interesting puzzles with elliptical or circular polarization. For example, is recollision, which has been accepted as playing a central role in initiating many strong-field phenomena with linear polarization, possible under elliptical or circular polarization? For another example, can the two electrons emitted sequentially in a double ionization event be viewed as independent

Using qubits to reveal quantum signatures of an oscillator

Thesis (Ph. D.)--University of Rochester. Dept. of Physics and Astronomy, 2014.In this thesis, we seek to study the qubit-oscillator system with the aim to identify and quantify inherent quantum features of the oscillator. We show that the quantum signatures of the oscillator get imprinted on the dynamics of the joint system. The two key features which we explore are the quantized energy spectrum of the oscillator and the non-classicality of the oscillator’s wave function. To investigate the consequences of the oscillator’s discrete energy spectrum, we consider the qubit to be coupled to the oscillator through the Rabi Hamiltonian. Recent developments in fabrication technology have opened up the possibility to explore parameter regimes which were conventionally inaccessible. Motivated by these advancements, we investigate in this thesis a parameter space where the qubit frequency is much smaller than the oscillator frequency and the Rabi frequency is allowed to be an appreciable fraction of the bare frequency of the oscillator. We use the adiabatic approximation to understand the dynamics in this quasi-degenerate qubit regime. By deriving a dressed master equation, we systematically investigate the effects of the environment on the system dynamics. We develop a spectroscopic technique, using which one can probe the steady state response of the driven and damped system. The spectroscopic signal clearly reveals the quantized nature of the oscillator’s energy spectrum. We extend the adiabatic approximation, earlier developed only for the single qubit case, to a scenario where multiple qubits interact with the oscillator. Using the extended adiabatic approximation, we study the collapse and revival of multiqubit observables. We develop analytic expressions for the revival signals which are in good agreement with the numerically evaluated results. Within the quantum restriction imposed by Heisenberg’s uncertainty principle, the uncertainty in the position and momentum of an oscillator is minimum and shared equally when the oscillator is prepared in a coherent state. For this reason, coherent states and states which can be thought of as a statistical mixture of coherent states are categorized as classical; whereas states which are not valid coherent state mixtures are classified as non-classical. In this thesis, we propose a new non-classicality witness operation which does not require a tomography of the oscillator’s state. We show that by coupling a qubit longitudinally to the oscillator, one can infer about the non-classical nature of the initial state of the oscillator. Using a qubit observable, we derive a non-classicality witness inequality, a violation of which definitively indicates the non-classical nature of an oscillator’s state

Limits to resolution in spectral analysis of pulses

Thesis (Ph. D.)--University of Rochester. College of Engineering and Applied Science. Institute of Optics, 1987. This thesis was digitized by the Institute of Optics in 2014 and was determined to have lapsed into the public domain. If you are the author and have questions about the digitization of your work, please contact Kari Brick, Graduate Program Coordinator for the Institute of Optics, at [email protected]. Other contact information for the Institute is available at http://www.optics.rochester.eduIt has traditionally been one of the main endeavors of spectroscopists to develope measurement techniques yielding even greater spectral resolution. In atomic and molecular spectroscopy, for example, a variety of linear and nonlinear techniques now exist which allow one to overcome spectral distortion due to Doppler broadening, collisional broadening, and even the broadening due to natural linewidths. In that same spirit, we present a study of the ability of three conventional optical spectrometers - the diffraction grating, the Fabry-Perot, and the prism - to resolve the Fourier energy spectra of pulses, that is, signals that are time limited. We have developed new techniques for overcoming the distortion of pulse spectra due to spectrometer bandwidth. These techniques employ the use of prior knowledge of a finite bound on the maximum possible length of the input pulse. We show that when the time-dependent output intensity of a spectrometer is measured, prior knowledge of maximum pulse length can make it possible to violate the classical uncertainty principle which relates the degree of spectral resolution one obtains to the duration of the spectral analysis. In such cases where the uncertainty principle is violated, spectral resolution can be enhanced by using a time-delayed observation technique similar to that employed in subnatural linewidth spectroscopy. When the total output energy of a spectrometer is recorded, spectral distortion is of the convolution type. In this case we determine the conditions under which prior knowledge of the maximum pulse length can make it theoretically possible to resolve the pulse's Fourier spectrum perfectly by deconvolving the spectrometer's frequency profile function from the measured spectrum. Although deconvolution removes error due to spectrometer bandwidth, it can also magnify random noise present in the measured spectrum. We have found that an analytic expression can be derived for the ratio of the maximum possible error in the measured spectrum (due to spectrometer blurring plus random noise) to that in the deconvolved spectrum (due to magnified random noise only). Numerical simulations of the measurement and deconvolution of noisy pulse spectra are presented to demonstrate the usefulness of that error ratio in predicting when deconvolution is most worthwhile

Theory of multipartite entanglement for X-states

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2015.More than a century after the seminal work of Schmidt and with all the enthusiasm that have surrounded entanglement ever since the controversial EPR paper, it remains an open challenge to determine whether a given state possesses entanglement or not. The problem is even more difficult if one considers the entanglement among more than two parties, i.e. multipartite entanglement. In the following we first introduce the concept of multipartite entanglement and discuss what it means to quantify the entanglement of a given state. We then introduce a class of multiqubit states, called X-states, and find an algebraic formula for the multipartite entanglement of such states. We show that using this formula one can find a lower bound for the entanglement of any multiqubit state. We then explore the connection between the entanglement and purity in multiqubit states. In the fourth chapter, we introduce a geometrical measure of entanglement and quantify it for the set of GHZ-diagonal states. These are states that can be written as a convex sum of completely bit-flipped states. Using these results we can develop an upper and a lower bound for the entanglement of any density matrix. In the final chapter we survey some of the insights that can be developed using the results of the preceding chapters. We first explore the decay of entanglement in a decoherence scenario where each qubit is experiences decay through an amplitude damping channel, and finally we make a proposal to preserve and control multipartite entanglement through the phenomenon of collapse and revival

A Reexamination of early debates on the interpretation of quantum theory : Louis de Broglie to David Bohm

Thesis (Ph. D.)--University of Rochester. Depts. of History and Physics and Astronomy, 2011.The following dissertation reexamines the emergence and development of alternate formulations and interpretations of quantum theory from the 1920s to the early 1950s. Specifically, Louis de Broglie's alternate wave mechanical interpretation (1923 - 1927) and David Bohm's hidden variables program (1951 - 1952) are examined within their respective contexts of innovation. By presenting a more balanced and nuanced narrative of these 20th century physicists, and their work, subtleties within the scientific exchanges between those engaged in early quantum interpretational debates begin to emerge which can serve to dispel some of the myths that have persisted in the overall historical quantum narrative. While de Broglie and Bohm were ultimately interested in restoring determinism to quantum theory, their particular influences, arguments, methodologies, approaches, and receptions were unique to their respective historical periods and each physicist's position within the physics community. Combining a close reading of the two distinct programs of scientific innovation with a representative analysis of the historical context in which they worked allows us to reexamine de Broglie and Bohm in a new light. The following analysis serves to restore these two physicists' agency in carving out their particular places within the physics community and dispels simplistic myths of marginalization. It also sheds light on de Broglie and Bohm's important contributions to the early quantum mechanical interpretation debates, thereby restoring their importance within the larger historical quantum narrative. Some of the topics that will be addressed include the following: who they trained with; where they trained; what their primary influences were; what their motivations were for proposing their particular alternate interpretations; what their particular research programs consisted of; how these evolved; and how each was received within the particular physics community. In order to successfully reconstruct these quantum histories, various methods of analysis have been used, including close readings of published and unpublished scientific papers, personal and professional correspondence, and a meta-data analysis of aggregate biographical data that reveals new insights into the academic networks within their wider socio-political environments