Quantum Physics Commons^™

A Method For Achieving Analytic Formulas For Three Body Integrals Consisting Of Powers And Exponentials In All Three Interparticle Hyllerass Coordinates, Chris M. Keating

Dissertations and Theses

After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function f(kr₁) (such as a spherical Bessel function) in addition to …

Device-Independent Quantum Key Distribution With Generalized Two-Mode Schrödinger Cat States, Curtis J. Broadbent, Kevin Marshall, Christian Weedbrook, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show how weak nonlinearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrödinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that, over any distance in this channel, the quantum bit error rate is identically zero, in principle, and …

Qubit Measurement Error From Coupling With A Detuned Neighbor In Circuit Qed, Mostafa Khezri, Justin Dressel, Alexander N. Korotkov

Mathematics, Physics, and Computer Science Faculty Articles and Research

In modern circuit QED architectures, superconducting transmon qubits are measured via the state-dependent phase and amplitude shift of a microwave field leaking from a coupled resonator. Determining this shift requires integrating the field quadratures for a nonzero duration, which can permit unwanted concurrent evolution. Here we investigate such dynamical degradation of the measurement fidelity caused by a detuned neighboring qubit. We find that in realistic parameter regimes, where the qubit ensemble-dephasing rate is slower than the qubit-qubit detuning, the joint qubit-qubit eigenstates are better discriminated by measurement than the bare states. Furthermore, we show that when the resonator leaks much …

Hohenberg-Kohn Theorems In Electrostatic And Uniform Magnetostatic Fields, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle …

Hohenberg-Kohn Theorems In Electrostatic And Uniform Magnetostatic Fields, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle …

Can The Wave Function In Configuration Space Be Replaced By Single-Particle Wave Functions In Physical Space?, Travis Norsen, Damiano Marian, Xavier Oriols

Physics: Faculty Publications

The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated – replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation …

Optimal Measurements Tasks And Their Physical Realizations, Vadim Yerokhin

Dissertations, Theses, and Capstone Projects

This thesis reflects works previously published by the author and materials hitherto unpublished on the subject of quantum information theory. Particularly, results in optimal discrimination, cloning, and separation of quantum states, and their relationships, are discussed.

Our interest lies in the scenario where we are given one of two quantum states prepared with a known a-priori probability. We are given full information about the states and are assigned the task of performing an optimal measurement on the incoming state. Given that none of these tasks is in general possible to perform perfectly we must choose a figure of merit to …

Effective Microscopic Models For Sympathetic Cooling Of Atomic Gases, Roberto Onofrio, Bala Sundaram

Dartmouth Scholarship

Thermalization of a system in the presence of a heat bath has been the subject of many theoretical investigations especially in the framework of solid-state physics. In this setting, the presence of a large bandwidth for the frequency distribution of the harmonic oscillators schematizing the heat bath is crucial, as emphasized in the Caldeira-Leggett model. By contrast, ultracold gases in atomic traps oscillate at well-defined frequencies and therefore seem to lie outside the Caldeira-Leggett paradigm. We introduce interaction Hamiltonians which allow us to adapt the model to an atomic physics framework. The intrinsic nonlinearity of these models differentiates them from …

Bulk Equations Of Motion From Cft Correlators, Daniel N. Kabat, Gilad Lifschytz

Publications and Research

ToO (1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the …

Thermodynamic Effects Of A Local Bell State Projection Interaction In A One-Dimensional Dynamic Spin System, Nickolas H. Pilgram

Physics

No abstract provided.

Analyzing Major Challenges Of Wind And Solar Variability In Power Systems, Falko Ueckerdt, Robert Brecha, Gunnar Luderer

Physics Faculty Publications

Ambitious policy targets together with current and projected high growth rates indicate that future power systems will likely show substantially increased generation from renewable energy sources. A large share will come from the variable renewable energy (VRE) sources wind and solar photovoltaics (PV); however, integrating wind and solar causes challenges for existing power systems. In this paper we analyze three major integration challenges related to the structural matching of demand with the supply of wind and solar power: low capacity credit, reduced utilization of dispatchable plants, and over-produced generation. Based on residual load duration curves we define corresponding challenge variables …

Quantum Mechanics With A Quartic Dispersion Law, Joanna Ruhl

Graduate Masters Theses

Creation of three-dimensional matter waves, the three-dimensional analog of one-dimensional solitons, has been a goal of experimental physics for some time. A recent proposal has suggested that changing the dispersion law from quadratic to quartic for ultra cold atoms in a shaken lattice should allow for the creation of these objects. In this thesis, we develop the theoretical basis for quantum mechanics with a quartic dispersion law. The probability current functional is constructed from the corresponding time-dependent Schrödinger equation, and used to derive the junction conditions that connect the derivatives of the wavefunction on one side of a potential discontinuity …

Spin-Dependent Two-Color Kapitza-Dirac Effects, Scot Mcgregor, Wayne Cheng-Wei Huang, Herman Batelaan, Bradley Allan Shadwick

Department of Physics and Astronomy: Faculty Publications

In this paper we present an analysis of the spin behavior of electrons propagating through a laser field. We present an experimentally realizable scenario in which spin-dependent effects of the interaction between the laser and the electrons are dominant. The laser interaction strength and incident electron velocity are in the nonrelativistic domain. This analysis may thus lead to novel methods of creating and characterizing spin-polarized nonrelativistic femtosecond electron pulses.

Experimental Design And Construction For Critical Velocity Measurement In Spin-Orbit Coupled Bose-Einstein Condensates, Ting-Wei Hsu, Yong P. Chen

The Summer Undergraduate Research Fellowship (SURF) Symposium

Quantum simulation using ultra-cold atoms, such as Bose-Einstein Condensates (BECs), offers a very flexible and well controlled environment to simulate physics in different systems. For example, to simulate the effects of spin orbit coupling (SOC) on electrons in solid state systems, we can make a SOC BEC which mimics the behavior of SOC electrons. The goal of this project is to see how the superfluid property of BECs change in the presence of SOC. In particular, we plan to measure the critical velocity of an 87Rb BEC with and without SOC by stirring it with a laser. This laser needs …

Device-Independent Relativistic Quantum Bit Commitment, Emily Adlam, Adrian Kent

Mathematics, Physics, and Computer Science Faculty Articles and Research

We examine the possibility of device-independent relativistic quantum bit commitment, introducing three relativistic quantum bit commitment schemes that offer device-independent security against hypothetical postquantum adversaries subject only to the no-signaling principle. We discuss the potential threat of location attacks, in which the behavior of untrusted devices used in relativistic quantum cryptography depends on their space-time location and show that our protocols are secure against both location attacks and memory attacks. The protocols are compared to a relativistic classical bit commitment scheme with similar features and we note some advantages for the quantum schemes.

Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova

Physics Faculty Publications

This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.

Comment On "Role Of Potentials In The Aharonov-Bohm Effect", Yakir Aharonov, Eliahu Cohen, Daniel Rohrlich

Mathematics, Physics, and Computer Science Faculty Articles and Research

Are the electromagnetic scalar and vector potentials dispensable? Vaidman [Phys. Rev. A 86, 040101(R) (2012)] has suggested that local interactions of gauge-invariant quantities, e.g., magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze six thought experiments that challenge this suggestion. All of them have explanations in terms of local interactions of gauge-dependent quantities, and, in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant formal description and that, in general, no local description can dispense with electromagnetic potentials.

Simulations Of The Angular Dependence Of The Dipole-Dipole Interaction, Jacob T. Paul, Matan Peleg

Physics and Astronomy Summer Fellows

In our project we ran computations on a supercomputer to simulate experiments performed on highly excited atoms at μK temperatures. At μK temperatures the atoms are moving slowly so there are essentially no collisions of the atoms on the time scales at which we perform our experiments. In the absence of collisions the atoms exchange energy through long range dipole-dipole interactions. This exchange depends on the distances between and relative orientation of the atoms. The angular dependence between two atoms has recently been studied experimentally¹ . We simulate experimentally accessible spatial arrangements to see if the effect of the …

Simulations Of The Angular Dependence Of The Dipole-Dipole Interaction, Matan Peleg, Jacob T. Paul

Physics and Astronomy Summer Fellows

We conducted simulations of Rydberg atoms in a magneto-optical trap using the supercomputer available on campus and the COMET supercomputer provided by the NSF. Our research focused on the angular dependence of the long range interaction between Rydberg atoms. We simulated randomly distributed atoms alligned with a magnetic and electric field. We compared the simulated interaction rates for different electric field directions.

Toward Quantum Analog Computing: Simulating Designer Atomic Systems, Veronica L. Sanford, Jacob L. Bigelow

Physics and Astronomy Summer Fellows

We use a magneto-optical trap to cool rubidium atoms to temperatures in the _µK range. On the _µs timescales of our experiment, the atoms are moving slowly enough that they appear stationary. We then excite them to a Rydberg state, where the outer electron is loosely bound. In these high energy states, the atoms can exchange energy with each other. Since the energy exchange depends on the separation and the relative orientation of the atoms, we can potentially control their interactions by controlling the spatial arrangements of the atoms. We model this system using simulations on a supercomputer …

Toward Analog Quantum Computing: Simulating Designer Atomic Systems, Jacob L. Bigelow, Veronica L. Sanford

Physics and Astronomy Summer Fellows

We use a magneto-optical trap to cool rubidium atoms to temperatures in the _µK range. On the _µs timescales of our experiment, the atoms are moving slowly enough that they appear stationary. We then excite them to a Rydberg state, where the outer electron is loosely bound. In these high energy states, the atoms can exchange energy with each other. Since the energy exchange depends on the separation and the relative orientation of the atoms, we can potentially control their interactions by controlling the spatial arrangements of the atoms. We model this system using simulations on a supercomputer …

Application Of Resurgence Theory To Approximate Inverse Square Potential In Quantum Mechanics, Jian Zhang Ms.

Macalester Journal of Physics and Astronomy

Previous work concluded that the leading term of the energy spectrum of a quantum particle moving in an inverse-square law potential with regulated singularity is non-perturvative in nature. Trans-series and resurgence theory predicts the emergence of perturbative, and potentially logarithmic, corrections to the leading behavior. This talk relates an attempt to systematically calculate such corrections for the first time.

Static And Dynamical Properties Of Ferroelectrics And Related Material In Bulk And Nanostructure Forms, Zhigang Gui

Graduate Theses and Dissertations

Ferroelectrics (FE) and multiferroics (MFE) have attracted a lot of attentions due to their rich and novel properties. Studies towards FE and MFE are of both fundamental and technological importance. We use a first-principles-based effective Hamiltonian method, conventional ab-initio packages and linear-scale three-dimension fragment method to investigate several important issues about FE and MFE. Tuning the properties of FE and MFE films are essential for miniaturized device applications, which can be realized through epitaxial strain and growth direction. In this dissertation, we use the effective Hamiltonian method to study (i) BaTiO 3 films grown along the (110) pseudocubic direction on …

Shifting The Quantum-Classical Boundary: Theory And Experiment For Statistically Classical Optical Fields, Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly

Mathematics, Physics, and Computer Science Faculty Articles and Research

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger’s famous remark about it [Proc. Cambridge Philos. Soc. 31, 555 (1935)], prompts the examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments and report here values of the Bell parameter greater than ℬ=2.54. This is many standard deviations outside the limit ℬ=2 established by the Clauser–Horne–Shimony–Holt Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson …

How To Measure Magnetic Flux With A Single Position Measurement?, Eliahu Cohen, Lev Vaidman, Yakir Aharonov

Mathematics, Physics, and Computer Science Faculty Articles and Research

Current methods for measuring magnetic flux are based on performing many measurements over a large ensemble of electrons. We propose a novel method based on wave function "revival" for measuring the flux modulo using only a single electron. A preliminary analysis of the feasibility of the experiment is provided.

Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single …

Transition Orbits Of Walking Droplets, Joshua Parker

Physics

It was recently discovered that millimeter-sized droplets bouncing on the surface of an oscillating bath of the same fluid can couple with the surface waves it produces and begin walking across the fluid bath. These walkers have been shown to behave similarly to quantum particles; a few examples include single-particle diffraction, tunneling, and quantized orbits. Such behavior occurs because the drop and surface waves depend on each other to exist, making this the first and only known macroscopic pilot-wave system. In this paper, the quantized orbits between two identical drops are explored. By sending a perturbation to a pair of …

Mirror Buckling Transitions In Freestanding Graphene Membranes Induced Through Scanning Tunneling Microscopy, James Kevin Schoelz

Graduate Theses and Dissertations

Graphene has the ability to provide for a technological revolution. First isolated and characterized in 2004, this material shows promise in the field of flexible electronics. The electronic properties of graphene can be tuned by controlling the shape of the membrane. Of particular interest in this endeavor are the thermal ripples in graphene membranes. Years of theoretical work by such luminaries as Lev Landau, Rudolf Peierls, David Mermin and Herbert Wagner have established that 2D crystals should not be thermodynamically stable. Experimental research on thin films has supported this finding. Yet graphene exists, and freestanding graphene films have been grown …

Structure Of Local Quantum Operations And Classical Communication: Finite Versus Infinite Rounds, Scott M. Cohen

Physics Faculty Publications and Presentations

Every measurement that can be implemented by local quantum operations and classical communication (LOCC) using an infinite number of rounds is the limit of a sequence of measurements, where each measurement in the sequence requires only a finite number of rounds. This rather obvious and well-known fact is nonetheless of interest as it shows that these infinite-round measurements can be approximated arbitrarily closely simply by using more and more rounds of communication. Here we demonstrate the perhaps less obvious result that (at least) for bipartite systems, the reverse relationship also holds. Specifically, we show that every finite-round bipartite LOCC measurement …

Violating The Modified Helstrom Bound With Nonprojective Measurements, Justin Dressel, Todd A. Brun, Alexander N. Korotkov

Mathematics, Physics, and Computer Science Faculty Articles and Research

We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a nonguess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and nonguess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case.We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement.Notably, while the cost advantage …