Browsing by Subject "quant-ph"

Now showing 1 - 14 of 14
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    A Quantum Kinetic Monte Carlo Method for Quantum Many-body Spin Dynamics
    (2017-11-30) Cai, Z; Lu, J
    We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin dynamics, using different decomposition of the Hamiltonian. The effectiveness of the methods is tested for many-body spin systems up to 40 spins.
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    Bogoliubov corrections and trace norm convergence for the Hartree dynamics
    Mitrouskas, D; Petrat, S; Pickl, P
    We consider the dynamics of a large number N of nonrelativistic bosons in the mean field limit for a class of interaction potentials that includes Coulomb interaction. In order to describe the fluctuations around the mean field Hartree state, we introduce an auxiliary Hamiltonian on the N-particle space that is very similar to the one obtained from Bogoliubov theory. We show convergence of the auxiliary time evolution to the fully interacting dynamics in the norm of the N-particle space. This result allows us to prove several other results: convergence of reduced density matrices in trace norm with optimal rate, convergence in energy trace norm, and convergence to a time evolution obtained from the Bogoliubov Hamiltonian on Fock space with expected optimal rate. We thus extend and quantify several previous results, e.g., by providing the physically important convergence rates, including time-dependent external fields and singular interactions, and allowing for general initial states, e.g., those that are expected to be ground states of interacting systems.
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    Coherence distillation machines are impossible in quantum thermodynamics
    (Nature Communications, 2020-12) Marvian, Iman
    The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence a "coherence distillation machine", i.e. a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This question is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can we distill synchronized clocks in pure states, at a non-zero rate? In this paper we study quantities called "coherence cost" and "distillable coherence", which determine the rate of conversion of coherence in a standard pure state to general mixed states, and vice versa, in the context of quantum thermodynamics. We find that the coherence cost of any state (pure or mixed) is determined by its Quantum Fisher Information (QFI), thereby revealing a novel operational interpretation of this central quantity of quantum metrology. On the other hand, we show that, surprisingly, distillable coherence is zero for typical (full-rank) mixed states. Hence, we establish the impossibility of coherence distillation machines in quantum thermodynamics, which can be compared with the impossibility of perpetual motion machines or cloning machines. To establish this result, we introduce a new additive quantifier of coherence, called the "purity of coherence", and argue that its relation with QFI is analogous to the relation between the free and total energies in thermodynamics.
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    Driven-Dissipative Phase Transition in a Kerr Oscillator: From Semi-Classical PT Symmetry to Quantum Fluctuations.
    (Physical Review A, 2021-03-24) Zhang, Xin HH; Baranger, Harold U
    We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, Z2 symmetry breaking, PT symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.
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    Effective dynamics of a tracer particle in a dense homogeneous quantum gas
    Jeblick, M; Mitrouskas, D; Petrat, S; Pickl, P
    We investigate the mean field regime of the dynamics of a tracer particle in a homogenous quantum gas. For a bosonic gas, we show that this regime is constrained by the well known requirement of an appropriate mean field scaling of the interaction. For fermions, however, we find an important qualitative difference. Not only are fermions much more homogeneously distributed than bosons but also deviations from the mean are due only to fast degrees of freedom in the gas. This observation leads to an explanation of why a tracer particle behaves freely in the dense homogeneous fermion gas despite of a non-scaled interaction, i.e., despite of non-vanishing statistical fluctuations. Finally, we indicate how the gained insight can be rigorously justified.
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    Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas
    (Communications in Mathematical Physics, 2014-06) Deckert, DA; Fröhlich, J; Pickl, P; Pizzo, A
    We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density → ∞). Our estimates allow us to interchange the thermodynamic with the mean-field limit. © 2014 Springer-Verlag Berlin Heidelberg.
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    Free Time Evolution of a Tracer Particle Coupled to a Fermi Gas in the High-Density Limit
    (Communications in Mathematical Physics, 2017-11) Jeblick, M; Mitrouskas, D; Petrat, S; Pickl, P
    © 2017, Springer-Verlag GmbH Germany. The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g = 1 (i.e., not in the weak coupling regime), and prove closeness of the time evolution to an effective dynamics for large densities of the gas and for long time scales of the order of some power of the density. The effective dynamics is generated by the free Hamiltonian with a large but constant energy shift which is given at leading order by the spatially homogeneous mean field potential of the gas particles. Here, the mean field approximation turns out to be accurate although the fluctuations of the potential around its mean value can be arbitrarily large. Our result is in contrast to a dense bosonic gas in which the free motion of a tracer particle would be disturbed already on a very short time scale. The proof is based on the use of strong phase cancellations in the deviations of the microscopic dynamics from the mean field time evolution.
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    Interference of chiral Andreev edge states
    (Nature Physics, 2020-08-01) Zhao, Lingfei; Arnault, Ethan G; Bondarev, Alexey; Seredinski, Andrew; Larson, Trevyn; Draelos, Anne W; Li, Hengming; Watanabe, Kenji; Taniguchi, Takashi; Amet, François; Baranger, Harold U; Finkelstein, Gleb
    © 2020, The Author(s), under exclusive licence to Springer Nature Limited. The search for topological excitations such as Majorana fermions has spurred interest in the boundaries between distinct quantum states. Here, we explore an interface between two prototypical phases of electrons with conceptually different ground states: the integer quantum Hall insulator and the s-wave superconductor. We find clear signatures of hybridized electron and hole states similar to chiral Majorana fermions, which we refer to as chiral Andreev edge states (CAESs). These propagate along the interface in the direction determined by the magnetic field and their interference can turn an incoming electron into an outgoing electron or hole, depending on the phase accumulated by the CAESs along their path. Our results demonstrate that these excitations can propagate and interfere over a significant length, opening future possibilities for their coherent manipulation.
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    Lindblad equation and its semi-classical limit of the Anderson-Holstein model
    (2017-04-23) Cao, Y; Lu, J
    For multi-level open quantum system, the interaction between different levels could pose challenge to understand the quantum system both analytically and numerically. In this work, we study the approximation of the dynamics of the Anderson-Holstein model, as a model of multi-level open quantum system, by Redfield and Lindblad equations. Both equations have a desirable property that if the density operators for different levels is diagonal initially, they remain to be diagonal for any time. Thanks to this nice property, the semi-classical limit of both Redfield and Lindblad equations could be derived explicitly; the resulting classical master equations share similar structures of transport and hopping terms. The Redfield and Lindblad equations are also compared from the angle of time dependent perturbation theory.
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    One-dimensional waveguide coupled to multiple qubits: Photon-photon correlations
    (EPJ Quantum Technology, 2014-12-01) Fang, YLL; Zheng, H; Baranger, HU
    For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation L. We study the correlations by calculating the second-order correlation function g 2 (t) in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function g2(t) including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation L could be readily explored with our approach.
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    Random logic networks: From classical Boolean to quantum dynamics
    (Physical Review E) Kluge, Lucas; Socolar, Joshua ES; Schöll, Eckehard
    We investigate dynamical properties of a quantum generalization of classical reversible Boolean networks. The state of each node is encoded as a single qubit, and classical Boolean logic operations are supplemented by controlled bit-flip and Hadamard operations. We consider synchronous updating schemes in which each qubit is updated at each step based on stored values of the qubits from the previous step. We investigate the periodic or quasiperiodic behavior of quantum networks, and we analyze the propagation of single site perturbations through the quantum networks with input degree one. A non-classical mechanism for perturbation propagation leads to substantially different evolution of the Hamming distance between the original and perturbed states.
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    Spontaneous Pair Creation Revisited
    Pickl, P; Duerr, D
    Recently the so called Spontaneous Pair Creation of electron positron pairs in a strong external field has been rigorously established. We give here the heuristic core of the proof, since the results differ from those given in earlier works.
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    Unveiling environmental entanglement in strongly dissipative qubits
    (arXiv, 2013-01-30) Bera, Soumya; Florens, Serge; Baranger, Harold; Roch, Nicolas; Nazir, Ahsan; Chin, Alex
    The coupling of a qubit to a macroscopic reservoir plays a fundamental role in understanding the complex transition from the quantum to the classical world. Considering a harmonic environment, we use both intuitive arguments and numerical many-body quantum tomography to study the structure of the complete wavefunction arising in the strong-coupling regime, reached for intense qubit-environment interaction. The resulting strongly-correlated many-body ground state is built from quantum superpositions of adiabatic (polaron-like) and non-adiabatic (antipolaron-like) contributions from the bath of quantum oscillators. The emerging Schrödinger cat environmental wavefunctions can be described quantitatively via simple variational coherent states. In contrast to qubit-environment entanglement, we show that non-classicality and entanglement among the modes in the reservoir are crucial for the stabilization of qubit superpositions in regimes where standard theories predict an effectively classical spin.
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    Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature
    (2017-04-23) Watson, AB; Lu, J; Weinstein, MI
    We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two dimensionless parameters: (re-scaled) Planck's constant and the ratio of the lattice spacing to the scale of variation of the external potential. We consider the special case where both parameters are equal and denote this parameter $\epsilon$. In the limit $\epsilon \downarrow 0$, we prove the existence of solutions known as semiclassical wavepackets which are asymptotic up to `Ehrenfest time' $t \sim \ln 1/\epsilon$. To leading order, the center of mass and average quasi-momentum of these solutions evolve along trajectories generated by the classical Hamiltonian given by the sum of the Bloch band energy and the external potential. We then derive all corrections to the evolution of these observables proportional to $\epsilon$. The corrections depend on the gauge-invariant Berry curvature of the Bloch band, and a coupling to the evolution of the wave-packet envelope which satisfies Schr\"{o}dinger's equation with a time-dependent harmonic oscillator Hamiltonian. This infinite dimensional coupled `particle-field' system may be derived from an `extended' $\epsilon$-dependent Hamiltonian. It is known that such coupling of observables (discrete particle-like degrees of freedom) to the wave-envelope (continuum field-like degrees of freedom) can have a significant impact on the overall dynamics.