The Jaynes-Cummings model thermal revivals

Arroyo-Correa, Gabriel; Sanchez-Mondragon, J. J.

doi:10.1088/0954-8998/2/6/001

Cited by 16 publications

(4 citation statements)

References 12 publications

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“…[12,13]). The JC model predicts non-classical phenomena, such as revivals of the initial excited state of the atom [15]- [20], experimental signs of which have been reported [21].…”

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confidence: 90%

Dynamics, correlations, and phases of the micromaser

1996

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The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time of flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time of flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times of flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them.

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“…[12,13]). The JC model predicts non-classical phenomena, such as revivals of the initial excited state of the atom [15]- [20], experimental signs of which have been reported [21].…”

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confidence: 90%

Dynamics, correlations, and phases of the micromaser

1996

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“…In this case conventional forms of lightmatter interaction Hamiltonian yield the so-called quantum Rabi model (QRM), which consists of a linear interaction between the radiation mode and the qubit. Performing the rotating-wave approximation (RWA) then yields the celebrated Jaynes-Cummings model (JCM), which owing to its simple exact solution, has provided deep physical understanding in a wide range of contexts [15][16][17][18]. In the ultrastrong-coupling regime 0.1 < g/ω < 1 the RWA is no longer valid [3,5,11] and it is therefore widely believed that the Jaynes-Cummings model breaks down.…”

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confidence: 99%

Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED

2019

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Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this JCM provides more accurate predictions than the QRM for the ground state, and often for the first excited state as well. Thus, Jaynes-Cummings physics is not restricted to light-matter coupling below the ultrastrong limit. Among the many implications is that the system’s ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling.

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“…Because the infinite series is a superposition of the trigonometric function of √ nt for n = 0, 1, 2, ... and it cannot be a Fourier series, the value of the sum of the series varies in an unpredictable manner as the time t progresses. Arroyo-Correa and Sanchez-Mondragon try to discuss the thermal JCM and evaluate the atomic population inversion, which is described by this intractable infinite series, using a technique of the complex analysis [14]. Chumakov et al examine a new analytical approach to obtain an approximate sum of this series, which is reliable for a small initial mean photon number [15].…”

Section: Introductionmentioning

confidence: 99%

Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes–Cummings model

Azuma¹,

Ban²

2014

Physica D: Nonlinear Phenomena

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We study a quasiperiodic structure in the time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, motion of the Bloch vector seems to be in disorder. Because of the thermal photon distribution, both a norm and a direction of the Bloch vector change hard at random. In this paper, taking a different viewpoint compared with ones that we have been used to, we investigate quasiperiodicity of the Bloch vector's trajectories. Introducing the concept of the quasiperiodic motion, we can explain the confused behaviour of the system as an intermediate state between periodic and chaotic motions. More specifically, we discuss the following two facts: (1) If we adjust the time interval ∆t properly, figures consisting of plotted dots at the constant time interval acquire scale invariance under replacement of ∆t by s∆t, where s(> 1) is an arbitrary real but not transcendental number. (2) We can compute values of the time variable t, which let |S z (t)| (the absolute value of the z-component of the Bloch vector) be very small, with the Diophantine approximation (a rational approximation of an irrational number).

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The Jaynes-Cummings model thermal revivals

Cited by 16 publications

References 12 publications

Dynamics, correlations, and phases of the micromaser

Dynamics, correlations, and phases of the micromaser

Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED

Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes–Cummings model

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