Laser experiments with single atoms as a test of basic physics

Diedrich, F.; Krause, Joachim; Rempe, Gerhard; Scully, Marlan O.; Walther, H.

doi:10.1109/3.968

Cited by 79 publications

(16 citation statements)

References 27 publications

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“…Predictions from this model have been verified by experiment [3,4]. Many predictions have also been made concerning systems containing a Kerr medium that has an effective Hamiltonian of an anharmonic oscillator [5].…”

Section: Introductionmentioning

confidence: 76%

Quasiprobability distributions for the cavity-damped Jaynes-Cummings model with an additional Kerr medium

Werner

Risken

1991

Phys. Rev. A

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A cavity-damped Jaynes-Cummings model with a Kerr-like medium filling the cavity is investigated in the rotating-wave approximation.We introduce six operators with respect to the light field whose equations of motion are transformed to six coupled partial diR'erential equations using the s-parametrized quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882Rev. 177, (1969]. Equations of motion for expansion coefficients of the distribution functions are solved by a Runge-Kutta procedure for vector tridiagonal relations. Starting with an initial coherent state for the cavity field and the atom in its upper state, we find that revivals of the atomic inversion are more pronounced for a given damping constant compared. to the case of no Kerr medium. Also, quadrature squeezing is less affected by weak cavity damping and thermal noise compared to the standard haynes-Cummings model. The effect of damping on interesting non-Gaussian structures is also discussed.

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Section: Introductionmentioning

confidence: 76%

Quasiprobability distributions for the cavity-damped Jaynes-Cummings model with an additional Kerr medium

Werner

Risken

1991

Phys. Rev. A

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“…8,23 Also, the Rydberg atom can be excited by a two-photon transition. 24 We shall consider here an atom undergoing transitions between two levels (excited and ground levels) through a (k − 1) nonresonant intermediate levels.…”

Section: The Hamiltonian Model and Its Solutionmentioning

confidence: 99%

Intensity Dependent Coupling Hamiltonian via Multi-Photon Interaction in a Kerr Medium

Zait

2003

Int. J. Mod. Phys. B

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We study the dynamics and quantum characteristics of a single two-level atom interacting with a single mode cavity field undergoing a multi-photon processes in the presence of a nonlinear Kerr-like medium. The wavefunctions of the multi-photon system are obtained when the atom starts in the excited and in the ground state. The atomic inversion, the squeezing of the radiation field and the quasiprobability distribution Q-function of the field are discussed. Numerical results for these characteristics are presented when the atom starts in the excited state and the field mode in a coherent state. The influence of the presence and absence of the number operator and the Kerr medium for the oneand two-photon processes on the evolution of these characteristics are analyzed.

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“…The origin of chaos is the nonlinear resistance of the quantum particle against localization inside the box which apart from the term q depends on the Bloch variables according to the last term in (9). It is instructive to isolate the effect of this term.…”

mentioning

confidence: 99%

“…We mention the case of a two-level system interacting with the electromagnetic field of a laser cavity [4,5], the micromaser [6], nuclear collective motion [7], and the exciton transfer in a nonlinear molecular dimer perturbed by an intermolecular vibration [8]. It was demonstrated recently [9] that the number of photons in the electromagnetic maser field can be changed essentially in units of 1 from one photon (quantum limit) to a large number of photons (classical limit). Thus, the importance of quantum corrections in the "classical" subsystem (the cavity field) can be controlled to an astonishing degree.…”

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confidence: 99%

Quantum chaos in the Born-Oppenheimer approximation

Blümel

Esser

1994

Phys. Rev. Lett.

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We show that exponential instabilities and quantum chaos occur in a system with a mixed classical-quantum description. This type of chaos is of general importance and may occur in any quantum system which divides in a natural way into a fast (quantum) and a slow (classical) subsystem.PACS numbers: 05.45.+b Current research in quantum chaos is mainly focused on the classical-quantum correspondence in the semiclassical regime of classically chaotic dynamical systems [1 -3]. But yet another main avenue of quantum chaos research may derive from the observation that for some quantum systems of theoretical and practical importance the system divides in a natural way into two interacting subsystems, one of which is treated quantum mechanically, whereas the other is treated in the classical approximation.The mixed quantum-classical description of a dynamical system is justified whenever the quantum effects of one subsystem are negligible compared to the other or when the quantization of the whole system poses a severe challenge and the classical treatment of one part has to serve as a necessary guide in the further investigation. In fact, there are many examples in the physics literature where such a mixed description was already successfully applied. We mention the case of a two-level system interacting with the electromagnetic field of a laser cavity [4,5], the micromaser [6], nuclear collective motion [7], and the exciton transfer in a nonlinear molecular dimer perturbed by an intermolecular vibration [8]. It was demonstrated recently [9] that the number of photons in the electromagnetic maser field can be changed essentially in units of 1 from one photon (quantum limit) to a large number of photons (classical limit). Thus, the importance of quantum corrections in the "classical" subsystem (the cavity field) can be controlled to an astonishing degree. The molecular physics example of the nonlinear dimers is instructive because it provides an example for the justification of the division into a quantum and a classical subsystem. Describing the strong intramolecular interactions in the molecules constituting the dimer in the framework of the nonlinear discrete self-trapping equation (see, e.g. , [10,11]) one can use the weakness of the intermolecular forces between the molecules (and correspondingly small frequencies) to use a classical approximation for the intermolecular vibrations perturbing the transfer dynamics. In this case the density matrix dynamics for the exciton transfer of the quantum subsystem is characterized by a homoclinic structure on the Bloch sphere from which by perturbation with the classical oscillator a stochastic layer and chaos develops [8]. A further example is provided by a quantum system with a classical boundary moving in an anharmonic potential [12]. All the models discussed above are characterized by a mixed quantum-classical description. One of the main purposes of this Letter is to show that such systems can display quantum chaos and arise quite naturally within the framework of the Born...

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Laser experiments with single atoms as a test of basic physics

Cited by 79 publications

References 27 publications

Quasiprobability distributions for the cavity-damped Jaynes-Cummings model with an additional Kerr medium

Quasiprobability distributions for the cavity-damped Jaynes-Cummings model with an additional Kerr medium

Intensity Dependent Coupling Hamiltonian via Multi-Photon Interaction in a Kerr Medium

Quantum chaos in the Born-Oppenheimer approximation

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