Quantum chaos of the two-level atom

Graham, R.; Höhnerbach, M.

doi:10.1016/0375-9601(84)90094-x

Cited by 85 publications

(44 citation statements)

References 5 publications

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“…The Dicke model [1] has been known for a long time for its quantum phase transition (to a superradiant phase as the coupling exceeds a critical value) [2,3] and classical as well as quantum chaos [4][5][6][7][8][9]. Interest in the model has recently been renewed by an experimental realization (employing a double Bose-Einstein condensate coupled to an electromagnetic mode of a surrounding cavity) where the zero-temperature phase transition was observed [10].…”

Section: Introductionmentioning

confidence: 99%

Equilibration and macroscopic quantum fluctuations in the Dicke model

Altland

Haake

2012

New J. Phys.

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We discuss the unitary quantum dynamics of the Dicke model (spin and oscillator coupled). A suitable quasi-probability representing the quantum state turns out to obey a Fokker-Planck equation, with drift terms representing the underlying classical Hamiltonian flow and diffusion terms describing quantum fluctuations. We show (by projecting the dynamics onto a co-moving Poincaré section) how the interplay of deterministic drift and quantum diffusion generates equilibration to the microcanonical density, under conditions of global classical chaos. The pertinent photon statistics reveals macroscopic quantum fluctuations.

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Section: Introductionmentioning

confidence: 99%

Equilibration and macroscopic quantum fluctuations in the Dicke model

Altland

Haake

2012

New J. Phys.

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“…In the present case the regularity is rather striking (see Figs. [3][4][5]. Even for the large values of a> 0 and X (Fig.…”

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confidence: 97%

“…3,4 It is then very likely that the fully quantized version of the model can be considered as a simple example of a "quantumchaotic" system. 5 The Hamiltonian of the model reads …”

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confidence: 99%

Statistical Properties of the Spectrum of the Two-Level System

Kuş

1985

Phys. Rev. Lett.

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Several statistical properties of the energy levels of a two-level atom interacting with one mode of quantized electromagnetic field are investigated in connection with possible "quantum-chaotic" behavior of the system. PACS numbers: 03.65.Ge, 32.90. + aThe basic quantum-optical model of a two-level atom interacting with a single mode of a quantized electromagnetic field 1,2 has attracted renewed interest, since it has been shown that its semiclassical counterpart exhibits chaotic motion. 3,4 It is then very likely that the fully quantized version of the model can be considered as a simple example of a "quantumchaotic" system. 5 The Hamiltonian of the model reads

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“…Once in possession of a reliable numerical method, one can investigate several questions related to the model at hand, like for example the question of properly defining quantum chaos. Work on this point was done [32] shortly after the semiclassical case was studied by Milonni et al [31], leaving however several open questions. As a further example of investigations resting on numerical evaluations we can mention the work of Lo et al [47], who tested a conjecture raised by Bishop et al [46].…”

Section: Introductionmentioning

confidence: 98%

Micromaser Dynamics Beyond the Rotating-Wave Approximation

Zela

2001

Modern Challenges in Quantum Optics

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Abstract.We discuss the validity of the rotating-wave approximation (RWA) focussing in particular on the micromaser dynamics. We consider the full Hamiltonian -given by H = ω0σz + ωa-for the description of the atom-field interaction. We arrive at the conclusion that the so called counter-rotating terms, (aσ − and a + σ + ) -which are neglected within the RWA -could give rise to physically observable effects for a parameter range not too far from current experiments. Early studies assumed that effects not described within the RWA could be experimentally observed by going from the optical to the microwave domain. In principle, the micromaser could be used for that purpose. We focus on atomic correlations, as the atoms exiting the micromaser cavity constitute the only physical entity that can be subjected to measurements. Within the RWA the only allowed transitions are the so-called energy-conserving transitions. We consider additional transitions which, despite being small, could give rise to measurable effects that we have investigated in the present work.

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Quantum chaos of the two-level atom

Cited by 85 publications

References 5 publications

Equilibration and macroscopic quantum fluctuations in the Dicke model

Equilibration and macroscopic quantum fluctuations in the Dicke model

Statistical Properties of the Spectrum of the Two-Level System

Micromaser Dynamics Beyond the Rotating-Wave Approximation

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