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Articles 31 - 60 of 72
Full-Text Articles in Quantum Physics
Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar
Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar
Pomona Faculty Publications and Research
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.
Asymmetric Architecture For Heralded Single-Photon Sources, Luca Mazzarella, Francesco Ticozzi, Alexander V. Sergienko, Giuseppe Vallone, Paolo Villoresi
Asymmetric Architecture For Heralded Single-Photon Sources, Luca Mazzarella, Francesco Ticozzi, Alexander V. Sergienko, Giuseppe Vallone, Paolo Villoresi
Dartmouth Scholarship
Single-photon sources represent a fundamental building block for optical implementations of quantum information tasks ranging from basic tests of quantum physics to quantum communication and high-resolution quantum measurement. In this paper, in order to compare the effectiveness of different designs, we introduce a single-photon source performance index, based on the maximum probability of generating a single photon that still guarantees a given signal-to-noise ratio. We then investigate the performance of a multiplexed system based on asymmetric configuration of multiple heralded single-photon sources. The performance and scalability comparison with both currently existing multiple-source architectures and faint laser configurations reveals an advantage …
Multiband S -Wave Topological Superconductors: Role Of Dimensionality And Magnetic Field Response, Shusa Deng, Gerardo Ortiz, Lorenza Viola
Multiband S -Wave Topological Superconductors: Role Of Dimensionality And Magnetic Field Response, Shusa Deng, Gerardo Ortiz, Lorenza Viola
Dartmouth Scholarship
We further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced earlier [Deng, Viola, and Ortiz, Phys. Rev. Lett. 108, 036803 (2012)]. Provided that a sign reversal between the two superconducting pairing gaps is realized, the topological phase diagram can be determined exactly (within mean field) in one and two dimensions as well as in three dimensions upon restricting to the excitation spectrum of time-reversal-invariant momentum modes. We show how, in the presence of time-reversal symmetry, Z2 invariants that distinguish between trivial and nontrivial quantum phases can be constructed by considering only one of the Kramers’ sectors …
Review Of Computing With Quantum Cats: From Colossus To Qubits And Schrödinger’S Killer App: Race To Build The World’S First Quantum Computer, Matthew S. Leifer
Review Of Computing With Quantum Cats: From Colossus To Qubits And Schrödinger’S Killer App: Race To Build The World’S First Quantum Computer, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
Book reviews of Computing With Quantum Cats: From Colossus To Qubits by John Gribbin and Schrödinger’s Killer App: Race To Build The World’s First Quantum Computer by John Dowling.
Automated Synthesis Of Dynamically Corrected Quantum Gates, Kaveh Khodjasteh, Hendrik Bluhm, Lorenza Viola
Automated Synthesis Of Dynamically Corrected Quantum Gates, Kaveh Khodjasteh, Hendrik Bluhm, Lorenza Viola
Dartmouth Scholarship
Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the …
Nanomechanical Resonator Coupled Linearly Via Its Momentum To A Quantum Point Contact, Latchezar L. Benatov, Miles P. Blencowe
Nanomechanical Resonator Coupled Linearly Via Its Momentum To A Quantum Point Contact, Latchezar L. Benatov, Miles P. Blencowe
Dartmouth Scholarship
We use a Born-Markov approximated master equation approach to study the symmetrized-in-frequency current noise spectrum and the oscillator steady state of a nanoelectromechanical system where a nanoscale resonator is coupled linearly via its momentum to a quantum point contact (QPC). Our current noise spectra exhibit clear signatures of the quantum correlations between the QPC current and the back-action force on the oscillator at a value of the relative tunneling phase (η=−π/2) where such correlations are expected to be maximized. We also show that the steady state of the oscillator obeys a classical Fokker-Planck equation, but can experience thermomechanical noise squeezing …
Majorana Modes In Time-Reversal Invariant S -Wave Topological Superconductors, Shusa Deng, Lorenza Viola, Gerardo Ortiz
Majorana Modes In Time-Reversal Invariant S -Wave Topological Superconductors, Shusa Deng, Lorenza Viola, Gerardo Ortiz
Dartmouth Scholarship
We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the s-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.
Response To Griffiths, Matthew S. Leifer
Response To Griffiths, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"First of all, I would like to thank Prof. Griffith for his comments. The exchange has reminded me of the series of letters that appeared in Physics Today following the publication of an article by Chandralekha Singh, Mario Belloni, and Wolfgang Christian on improving the teaching of undergraduate quantum mechanics (see http://ptonline.aip.org/ journals/doc/PHTOAD-ft/vol_60/iss_3/8_1.shtml). In those responses, both Griffiths and Travis Norsen argued that students’ understanding of quantum mechanics would be vastly improved if they were taught more about the foundations of quantum theory, and I wholeheartedly agree with that sentiment. The thing is, Griffiths argued vociferously that this should be …
Review Of The Mathematical Language Of Quantum Theory: From Uncertainty To Entanglement, Matthew S. Leifer
Review Of The Mathematical Language Of Quantum Theory: From Uncertainty To Entanglement, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A book review of The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement by Teiko Heinosaari and Mario Ziman.
Pbr, Epr, And All That Jazz, Matthew S. Leifer
Pbr, Epr, And All That Jazz, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. …
Review Of Elegance And Enigma: The Quantum Interviews, Matthew S. Leifer
Review Of Elegance And Enigma: The Quantum Interviews, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A review of Elegance and Enigma: The Quantum Interviews, edited by Maximilian Schlosshauer.
Experimental Characterization Of Coherent Magnetization Transport In A One-Dimensional Spin System, Chandrasekhar Ramanathan, Paola Cappellaro, Lorenza Viola, David G. Cory
Experimental Characterization Of Coherent Magnetization Transport In A One-Dimensional Spin System, Chandrasekhar Ramanathan, Paola Cappellaro, Lorenza Viola, David G. Cory
Dartmouth Scholarship
We experimentally characterize the non-equilibrium, room-temperature magnetization dynamics of a spin chain evolving under an effective double-quantum (DQ) Hamiltonian. We show that the Liouville space operators corresponding to the magnetization and the two-spin correlations evolve 90 degrees out of phase with each other, and drive the transport dynamics. For a nearest-neighbor-coupled N-spin chain, the dynamics are found to be restricted to a Liouville operator space whose dimension scales only as N2, leading to a slow growth of multi-spin correlations. Even though long-range couplings are present in the real system, we find excellent agreement between the analytical predictions …
The Quantum Dialectic, Logan Kelley
The Quantum Dialectic, Logan Kelley
Pitzer Senior Theses
A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …
Dynamical Critical Scaling And Effective Thermalization In Quantum Quenches: Role Of The Initial State, Shusa Deng, Gerardo Ortiz, Lorenza Viola
Dynamical Critical Scaling And Effective Thermalization In Quantum Quenches: Role Of The Initial State, Shusa Deng, Gerardo Ortiz, Lorenza Viola
Dartmouth Scholarship
We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous XY quantum spin chain in a transverse field, we characterize the nonequilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of …
The Trilinear Hamiltonian: A Zero-Dimensional Model Of Hawking Radiation From A Quantized Source, Paul D. Nation, Miles P. Blencowe
The Trilinear Hamiltonian: A Zero-Dimensional Model Of Hawking Radiation From A Quantized Source, Paul D. Nation, Miles P. Blencowe
Dartmouth Scholarship
We investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. We derive the conditions under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviations arise when the pump mode (black hole) has emitted nearly half of its initial energy into the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the …
Equilibrium States Of A Test Particle Coupled To Finite-Size Heat Baths, Qun Wei, S. Taylor Smith, Roberto Onofrio
Equilibrium States Of A Test Particle Coupled To Finite-Size Heat Baths, Qun Wei, S. Taylor Smith, Roberto Onofrio
Dartmouth Scholarship
We report on numerical simulations of the dynamics of a test particle coupled to competing Boltzmann heat baths of finite size. After discussing some features of the single bath case, we show that the presence of two heat baths further constrains the conditions necessary for the test particle to thermalize with the heat baths. We find that thermalization is a spectral property in which the oscillators of the bath with frequencies in the range of the test particle characteristic frequency determine its degree of thermalization. We also find an unexpected frequency shift of the test particle response with respect to …
Arbitrarily Accurate Dynamical Control In Open Quantum Systems, Kaveh Khodjasteh, Daniel A. Lidar, Lorenza Viola
Arbitrarily Accurate Dynamical Control In Open Quantum Systems, Kaveh Khodjasteh, Daniel A. Lidar, Lorenza Viola
Dartmouth Scholarship
We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems in such a way that decoherence is perturbatively compensated for to a desired (in principle arbitrarily high) level of accuracy, which depends only on the strength of the relevant errors and the achievable rate of control modulation. Our constructive and fully analytical solution employs concatenated dynamically corrected gates, and is applicable independently of detailed knowledge of the system-environment interactions and environment dynamics. Explicit implications for boosting quantum gate fidelities in realistic scenarios are addressed.
Damping And Decoherence Of A Nanomechanical Resonator Due To A Few Two-Level Systems, Laura G. Remus, Miles P. Blencowe, Yukihiro Tanaka
Damping And Decoherence Of A Nanomechanical Resonator Due To A Few Two-Level Systems, Laura G. Remus, Miles P. Blencowe, Yukihiro Tanaka
Dartmouth Scholarship
We consider a quantum model of a nanomechanical flexing beam resonator interacting with a bath comprising a few damped tunneling two-level systems. In contrast with a resonator interacting bilinearly with an ohmic free oscillator bath (modeling clamping loss, for example), the mechanical resonator damping is amplitude dependent, while the decoherence of quantum superpositions of mechanical position states depends only weakly on their spatial separation.
Dynamical Quantum Error Correction Of Unitary Operations With Bounded Controls, Kaveh Khodjasteh, Lorenza Viola
Dynamical Quantum Error Correction Of Unitary Operations With Bounded Controls, Kaveh Khodjasteh, Lorenza Viola
Dartmouth Scholarship
Dynamically corrected gates were recently introduced [K. Khodjasteh and L. Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence and pure dephasing on qubits. The effectiveness of dynamically corrected gates in an illustrative non-Markovian spin-bath setting is investigated numerically, …
Dynamically Error-Corrected Gates For Universal Quantum Computation, Kaveh Khodjasteh, Lorenza Viola
Dynamically Error-Corrected Gates For Universal Quantum Computation, Kaveh Khodjasteh, Lorenza Viola
Dartmouth Scholarship
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. Our results allow for a low-level err or correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls and may substantially reduce implementation requirements for fault-tolerant quantum computing architectures.
Dynamical Non-Ergodic Scaling In Continuous Finite-Order Quantum Phase Transitions, S. Deng, G. Ortiz, L. Viola
Dynamical Non-Ergodic Scaling In Continuous Finite-Order Quantum Phase Transitions, S. Deng, G. Ortiz, L. Viola
Dartmouth Scholarship
We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points (i.e., critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, …
Anomalies In Electrostatic Calibrations For The Measurement Of The Casimir Force In A Sphere-Plane Geometry, W. J. Kim, M. Brown-Hayes, D. A.R. Dalvit, J. H. Brownell, R. Onofrio
Anomalies In Electrostatic Calibrations For The Measurement Of The Casimir Force In A Sphere-Plane Geometry, W. J. Kim, M. Brown-Hayes, D. A.R. Dalvit, J. H. Brownell, R. Onofrio
Dartmouth Scholarship
We have performed precision electrostatic calibrations in the sphere-plane geometry, and observed anomalous behavior. Namely, the scaling exponent of the electrostatic signal with distance was found to be smaller than expected on the basis of the pure Coulombian contribution, and the residual potential found to be distance dependent. We argue that these findings affect the accuracy of the electrostatic calibrations and invite reanalysis of previous determinations of the Casimir force.
Parameters Of Pseudorandom Quantum Circuits, Yaakov S. Weinstein, Winton G. Brown, Lorenza Viola
Parameters Of Pseudorandom Quantum Circuits, Yaakov S. Weinstein, Winton G. Brown, Lorenza Viola
Dartmouth Scholarship
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudorandom circuits, with the goal of identifying relevant tradeoffs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudorandom circuits and approximate t-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties …
Probing The Quantum Coherence Of A Nanomechanical Resonator Using A Superconducting Qubit: Ii. Implementation, M. P. Blencowe, A. D. Armour
Probing The Quantum Coherence Of A Nanomechanical Resonator Using A Superconducting Qubit: Ii. Implementation, M. P. Blencowe, A. D. Armour
Dartmouth Scholarship
We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper (Armour A D and Blencowe M P 2008 New. J. Phys. 10 095004). The implementation is based on the circuit quantum electrodynamics (QED) set-up, with the addition of a mechanical degree of freedom formed out of a suspended, doubly-clamped segment of the superconducting loop of a dc SQUID located directly opposite the centre conductor of a coplanar waveguide (CPW). The relative merits of two SQUID based qubit realizations are addressed, in particular a capacitively coupled charge qubit and inductively coupled …
Probing The Quantum Coherence Of A Nanomechanical Resonator Using A Superconducting Qubit: I. Echo Scheme, A. D. Armour, M. P. Blencowe
Probing The Quantum Coherence Of A Nanomechanical Resonator Using A Superconducting Qubit: I. Echo Scheme, A. D. Armour, M. P. Blencowe
Dartmouth Scholarship
We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximized and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states, this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows …
Quantum Analysis Of A Nonlinear Microwave Cavity-Embedded Dc Squid Displacement Detector, P. D. Nation, M. P. Blencowe, E. Buks
Quantum Analysis Of A Nonlinear Microwave Cavity-Embedded Dc Squid Displacement Detector, P. D. Nation, M. P. Blencowe, E. Buks
Dartmouth Scholarship
We carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear current-dependent inductance, inducing an external flux tunable nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive radiation pressure-type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, …
Advantages Of Randomization In Coherent Quantum Dynamical Control, Lea F. Santos, Lorenza Viola
Advantages Of Randomization In Coherent Quantum Dynamical Control, Lea F. Santos, Lorenza Viola
Dartmouth Scholarship
Control scenarios have been identified where the use of randomized design may substantially improve the performance of dynamical decoupling methods (Santos and Viola 2006 Phys. Rev. Lett. 97 150501). Here, by focusing on the suppression of internal unwanted interactions in closed quantum systems, we review and further elaborate on the advantages of randomization at long evolution times. By way of illustration, special emphasis is devoted to isolated Heisenberg chains of coupled spin-1/2 particles. In particular, for nearest-neighbor interactions, two types of decoupling cycles are contrasted: inefficient averaging, whereby the number of control actions increases exponentially with the system size, and …
Quantum Pseudorandomness From Cluster-State Quantum Computation, Winton G. Brown, Yaakov S. Weinstein, Lorenza Viola
Quantum Pseudorandomness From Cluster-State Quantum Computation, Winton G. Brown, Yaakov S. Weinstein, Lorenza Viola
Dartmouth Scholarship
We show how to efficiently generate pseudorandom states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudorandom algorithms in the cluster-state picture, we identify a strategy for optimizing pseudorandom circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs.
Shape Invariance And The Exactness Of Quantum Hamilton-Jacobi Formalism, Charles Cherqui, Yevgeny Binder, Asim Gangopadhyaya
Shape Invariance And The Exactness Of Quantum Hamilton-Jacobi Formalism, Charles Cherqui, Yevgeny Binder, Asim Gangopadhyaya
Physics: Faculty Publications and Other Works
Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr ̈odinger equation. It was recently shown that the shape invariance, which is an integrability condition in SUSYQM formalism, can be utilized to develop an iterative algorithm to determine the quantum momentum functions. In this paper, we show that shape invariance also suffices to determine the eigenvalues in Quantum Hamilton-Jacobi Theory.
The Development Of A Quantum Dot Solar Concentrator, Brenda Rowan
The Development Of A Quantum Dot Solar Concentrator, Brenda Rowan
Doctoral
The aim of this study was to investigate the feasibility of Quantum Dot Solar Concentrators (QDSCs). Quantum Dots offer the advantages of having broad absorption specr4a, tunable emission and improved stability. A range of Cadmium Selenide/|Zince Sulphide Quantum Dots were characterized in solution and composite form using time-resolved and steady state spectroscopie techniques and the stability of the composite samples was investigated over a 6 month period. A number of matrix materials were compared and the most suitable type for fabrication of QDSCs were identified. Techniques for fabrication and characterization of QDSCs were developed and a range of different QDSC …