Quantum behavior of a dc SQUID phase qubit

Mitra, Kaushik; Strauch, Frederick W.; Lobb, C. J.; Anderson, J. R.; Wellstood, F. C.; Tiesinga, Eite

doi:10.1103/physrevb.77.214512

Cited by 22 publications

(42 citation statements)

References 23 publications

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“…[79,80]. In the context of many-body quantum systems, a LET is predicted to occur in systems as different as voltage-biased 2D gases, [81][82][83] noise-driven resistively shunted Josephson junctions, [84,85] and BECs of exciton polaritons. [86,87] This effect has a close analogy to the eigenstate thermalization hypothesis (ETH).…”

Section: Effective Low-frequency Temperaturementioning

confidence: 99%

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

et al. 2018

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The Dicke model describes the coupling between a quantized cavity field and a large ensemble of two‐level atoms. When the number of atoms tends to infinity, this model can undergo a transition to a superradiant phase, belonging to the mean‐field Ising universality class. The superradiant transition was first predicted for atoms in thermal equilibrium and was recently realized with a quantum simulator made of atoms in an optical cavity, subject to both dissipation and driving. This progress report offers an introduction to some theoretical concepts relevant to the Dicke model, reviewing the critical properties of the superradiant phase transition and the distinction between equilibrium and nonequilibrium conditions. In addition, it explains the fundamental difference between the superradiant phase transition and the more common lasing transition. This report mostly focuses on the steady states of atoms in single‐mode optical cavities, but it also mentions some aspects of real‐time dynamics, as well as other quantum simulators, including superconducting qubits, trapped ions, and using spin–orbit coupling for cold atoms. These realizations differ in regard to whether they describe equilibrium or nonequilibrium systems.

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Section: Effective Low-frequency Temperaturementioning

confidence: 99%

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

et al. 2018

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“…By adjusting the form of the spectral distribution, the properties of the bath can be adjusted to represent a variety of environments consisting of, for example, solid state materials, solvates, and protein molecules. This model has been used to solve various problems of practical interest, in particular to investigate tunneling processes, 2,3,10 chemical reaction, 11,12 non-adiabatic transition, 13,14 0021 quantum device systems, 15 ratchet rectification, 16,17 to evaluate the efficiency of SQUID rings 18,19 and to analyze the line shapes in laser spectra. 20,21 While the Brownian model itself is fairly simple, it is somewhat difficult to apply in the quantum mechanical case not only analytically but also numerically, due to the infinite number of bath degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

Tanimura

2015

The Journal of Chemical Physics

134

237

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We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first-and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and systembath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

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“…Quantum coherence and its destruction by coupling to a dissipative environment play an important role in the transport phenomena of a particle moving in a potential [1][2][3]. Well known examples include electron transfer in molecular and biological systems [4,5], many chemical reactions [6][7][8], SQUID rings [9,10], quantum ratchets [11,12], nonlinear optical processes [13][14][15][16][17] and tunneling processes in device systems [18,19]. Such systems are commonly modeled as one-dimensional or two-dimensional potential systems coupled to heat bath degrees of freedom, which drive the systems toward the thermal equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

Sakurai

Tanimura

2014

New J. Phys.

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The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of non-perturbative and non-Markovian treatment. We employ a Caldeira-Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study non-Markovian and nonperturbative thermal effects at finite temperature in a rigorous manner. We study current variation in time and the current-voltage (I -V ) relation of the resonant tunneling diode for several widths of the contact region, which consists of doped GaAs. Hysteresis and both single and double plateau-like behavior are observed in the negative differential resistance (NDR) region. While all of the current oscillations decay in time in the NDR region in the case of a strong system-bath coupling, there exist self-excited high-frequency current oscillations in some parts of the plateau in the NDR region in the case of weak coupling. We find that the effective potential in the oscillating case possesses a basin-like form on the emitter side (emitter basin) and that the current oscillation results from tunneling between the emitter basin and the quantum well in the barriers.

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Quantum behavior of a dc SQUID phase qubit

Cited by 22 publications

References 23 publications

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

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