Revivals made simple: Poisson summation formula as a key to the revivals in the Jaynes-Cummings model

Fleischhauer, Michael; Schleich, W. P.

doi:10.1103/physreva.47.4258

Cited by 102 publications

(80 citation statements)

References 42 publications

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“…Identifying (ρ(τ ) − |φ (A) φ (A) |)/τ with dρ/dt, we recover the master equation (41). The Monte-Carlo approach has many advantages.…”

Section: Monte Carlo Trajectoriesmentioning

confidence: 99%

“…This revival is directly linked to the quantization of the Rabi oscillation spectrum and, hence, to the field energy quantization itself. This explains the theoretical interest devoted to this phenomenon [39,40,41,42]. We give below an enlightening interpretation of the collapse and revival in terms of complementarity.…”

Section: Quantum Rabi Oscillations In a Mesoscopic Fieldmentioning

confidence: 99%

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Monitoring the Decoherence of Mesoscopic Quantum Superpositions in a Cavity

Raimond

Haroche

2006

Quantum Decoherence

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Abstract. Decoherence is an extremely fast and efficient environment-induced process transforming macroscopic quantum superpositions into statistical mixtures. It is an essential step in quantum measurement and a formidable obstacle for a practical use of quantum superpositions (quantum computing for instance). For large objects, decoherence is so fast that its dynamics is unobservable. Mesoscopic fields stored in a high-quality superconducting millimeter-wave cavity, a modern equivalent to Einstein's 'photon box', are ideal tools to reveal the dynamics of the decoherence process. Their interaction with a single circular Rydberg atom prepares them in a quantum superposition of fields, containing a few photons, with different classical phases. The evolution of this 'Schrödinger cat' state can be later probed with a 'quantum mouse', another atom, assessing its coherence. We describe here the experiments performed along these lines at ENS, and stress the deep links between decoherence and complementarity.

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“…Identifying (ρ(τ ) − |φ (A) φ (A) |)/τ with dρ/dt, we recover the master equation (41). The Monte-Carlo approach has many advantages.…”

Section: Monte Carlo Trajectoriesmentioning

confidence: 99%

Section: Quantum Rabi Oscillations In a Mesoscopic Fieldmentioning

confidence: 99%

Monitoring the Decoherence of Mesoscopic Quantum Superpositions in a Cavity

Raimond

Haroche

2006

Quantum Decoherence

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“…The quantity Tr[ ρ 2 A (t) ] can now be re-written in a form where quantum revivals become explicitly by making use of a Poisson summation technique [14]. As above, we consider a probability distribution p n is peaked around n =n with σ n /n ≪ 1.…”

Section: Eq (18)mentioning

confidence: 99%

“…If p(n) varies slowly as compared to the variation of S ν (n) one can evaluate f ν (t) for ν = 0 by a stationary phase approximation [14]. For a Gaussian distribution with meann and…”

Section: Eq (18)mentioning

confidence: 99%

On the preparation of pure states in resonant microcavities

Rekdal

Skagerstam

Knight

2004

Journal of Modern Optics

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We consider the time evolution of the radiation field (R) and a two-level atom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with an initial general pure quantum state for the radiation field. It is then shown, using the Cauchy-Schwarz inequality and also a Poisson resummation technique, that perfect coherence of the atom can in general never be achieved. The atom and the radiation field are, however, to a good approximation in a pure state |ψ A⊗R = |ψ A ⊗ |ψ R in the middle of what has been traditionally called the "collapse region", independent of the initial state of the atoms, provided that the initial pure state of the radiation field has a photon number probability distribution which is sufficiently peaked and phase differences that do not vary significantly around this peak. An approximative analytic expression for the quantity Tr[ ρ 2 A (t) ], where ρ A (t) is the reduced density matrix for the atom, is derived. We also show that under quite general circumstances an initial entangled pure state will be disentangled to the pure state |ψ A⊗R .1

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“…[9,12] it is shown that the equilibrium distribution Eq. (2) can be re-written in a form which is rapidly convergent in the large N limit by making use of a Poisson summation technique [13]. In terms of the scaled photon number variable x = n/N the stationary probability distribution can be written in the from…”

Section: The Dynamical Systemmentioning

confidence: 99%

Noise and order in cavity quantum electrodynamics

Rekdal¹,

Skagerstam²

2002

Physica A: Statistical Mechanics and its Applications

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In this paper we investigate the various aspects of noise and order in the micromaser system. In particular, we study the effect of adding fluctuations to the atom cavity transit time or to the atom-photon frequency detuning. By including such noise-producing mechanisms we study the probability and the joint probability for excited atoms to leave the cavity. The influence of such fluctuations on the phase structure of the micromaser as well as on the longtime atom correlation length is also discussed. We also derive the asymptotic form of micromaser observables.

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Revivals made simple: Poisson summation formula as a key to the revivals in the Jaynes-Cummings model

Cited by 102 publications

References 42 publications

Monitoring the Decoherence of Mesoscopic Quantum Superpositions in a Cavity

Monitoring the Decoherence of Mesoscopic Quantum Superpositions in a Cavity

On the preparation of pure states in resonant microcavities

Noise and order in cavity quantum electrodynamics

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