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Brink, Alec Maassen van den; Zagoskin, A. M.

doi:10.1023/a:1019657303471

Cited by 4 publications

(9 citation statements)

References 33 publications

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“…At even larger effective temperatures all available transition frequencies are densely spaced close to the resonator frequency, see level diagram in Fig. 2 The resulting harmonic spectrum resembles that of two uncoupled linear oscillators, a situation where not the absolute energies but the energy differences of the system are degenerate [3,15]. In contrast to the regime of strong coherent driving, where nonclassicality can persist at large excitation numbers [16,17], the phase noise of the thermal field used in our experiments renders the two high-excitation dressed-state ladders indistinguishable.…”

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confidence: 97%

Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

et al. 2010

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The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation-or effective temperature-is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.

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confidence: 97%

Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

et al. 2010

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“…We thank the referees for their constructive comments and suggestions and for bringing Refs. [2,21,22] to our attention. We also thank Dr. S. Garmon for proofreading the manuscript.…”

Section: Acknowledgmentsmentioning

confidence: 93%

“…In contrast to the discussion in Ref. [2], in which the authors considered an exact symmetry S of the Liouville operator in the sense of [S, L] = 0, we consider a symmetry U of the collision operator K(b) up to a similarity transformation, K(b ′ ) = U K(b)U † , where b labels the different thermal states of the system. A natural setting for formulating our discussion is provided by the thermofield dynamics (TFD) formalism [13].…”

Section: Introductionmentioning

confidence: 99%

Thermal symmetry of the Markovian master equation

Tay

Petrosky

2007

Phys. Rev. A

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The quantum Markovian master equation of the reduced dynamics of a harmonic oscillator coupled to a thermal reservoir is shown to possess thermal symmetry. This symmetry is revealed by a Bogoliubov transformation that can be represented by a hyperbolic rotation acting on the Liouville space of the reduced dynamics. The Liouville space is obtained as an extension of the Hilbert space through the introduction of tilde variables used in the thermofield dynamics formalism. The angle of rotation depends on the temperature of the reservoir, as well as the value of Planck's constant. This symmetry relates the thermal states of the system at any two temperatures. This includes absolute zero, at which purely quantum effects are revealed. The Caldeira-Leggett equation and the classical Fokker-Planck equation also possess thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov transformation in related fields and discuss the effects of the symmetry on the shape of a Gaussian wave packet.

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“…At high temperatures the frequencies of different allowed transitions are densely packed near the oscillator's frequency. This situation is called Liouvillian degeneracy as, formally, different modes of the Liouville evolution operator are almost degenerate [9]. We show that the secular approximation, widely used within the Bloch-Redfield formalism, fails due to the Liouvillian degeneracy.…”

Section: Introductionmentioning

confidence: 90%

Cavity quantum electrodynamics in superconducting circuits: Susceptibility at elevated temperatures

2004

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We study the properties of superconducting electrical circuits, realizing cavity QED. In particular we explore the limit of strong coupling, low dissipation, and elevated temperatures relevant for current and future experiments. We concentrate on the cavity susceptibility as it can be directly experimentally addressed, i.e., as the impedance or the reflection coefficient of the cavity. To this end we investigate the dissipative Jaynes-Cummings model in the strong coupling regime at high temperatures. The dynamics is investigated within the Bloch-Redfield formalism. At low temperatures, when only the few lowest levels are occupied the susceptibility can be presented as a sum of contributions from independent level-to-level transitions. This corresponds to the secular (random phase) approximation in the Bloch-Redfield formalism. At temperatures comparable to and higher than the oscillator frequency, many transitions become important and a multiple-peak structure appears. We show that in this regime the secular approximation breaks down, as soon as the peaks start to overlap. In other words, the susceptibility is no longer a sum of contributions from independent transitions. We treat the dynamics of the system numerically by exact diagonalization of the Hamiltonian of the qubit plus up to 200 states of the oscillator. We compare the results obtained with and without the secular approximation and find a qualitative discrepancy already at moderate temperatures.

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Untitled

Cited by 4 publications

References 33 publications

Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

Thermal symmetry of the Markovian master equation

Cavity quantum electrodynamics in superconducting circuits: Susceptibility at elevated temperatures

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