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Journal of the Physical Society of Japan

The “Actual” versus “Virtual” Experiments on Quantum Collapse and Revival

Young-Tak Chough

Published Feb 15, 1999• 5 citations
Publisher

Abstract

We modeled an atomic beam micromaser experiment [G. Rempe et al. : Phys. Rev. Lett. 58 (1987) 353] as well as a more recently reported cavity-QED experiment of a similar type [M. Brune et al. : Phys. Rev. Lett. 76 (1996) 1800] using the theory of quantum trajectories in order to see to what degree agreement between theory and experiment can be achieved. We compared our computations with the analysis based upon a “quantum theory of micromaser” [P. Filipowicz et al. : Phys. Rev. A 34 (1986) 3077] for the purpose of reliability check. We found rather nonnegligible differences between the results of theories and of experiments.

DOI
10.1143/jpsj.68.414

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We modeled an atomic beam micromaser experiment [G. Rempe et al. : Phys. Rev. Lett. 58 (1987) 353] as well as a more recently reported cavity-QED experiment of a similar type [M. Brune et al. : Phys. Rev. Lett. 76 (1996) 1800] using the theory of quantum trajectories in order to see to what degree agreement between theory and experiment can be achieved. We compared our computations with the analysis based upon a “quantum theory of micromaser” [P. Filipowicz et al. : Phys. Rev. A 34 (1986) 3077] for the purpose of reliability check. We found rather nonnegligible differences between the results of theories and of experiments.
In a recent microlaser experiment [K. An et al., Phys. Rev. Lett. 73, 3375 (1994)], a thresholdlike transition of intracavity mean photon number as a function of intracavity mean atom number has been observed. In this paper the behavior is explored with quantum trajectory simulations. It is shown that the transition is caused by enhanced atom-cavity Rabi interaction due to the increase of the intracavity photon number as the intracavity atom number is increased. The transition is further accentuated by the position-dependent variation of the coupling constant in the Fabry-P\'erot cavity. In addition, it is demonstrated that multiatom collective effects are negligible in the microlaser under consideration, in which atoms are injected into the cavity at random times and the product of the coupling constant and atom-cavity interaction time is much less than \ensuremath{\pi}. In this case the analytic theory of the one-atom micromaser [P. Filipowicz et al., Phys. Rev. A 34, 3077 (1986)] can be extrapolated into the multiatom region, assuming uniform atom-cavity coupling throughout the cavity and monovelocity atomic injection. Finally, simulations are performed which account for spatial variation of coupling constant, velocity distribution of injected atoms, and spontaneous atomic decay in the actual experiment. The results are in good agreement with experiment.
Ab initio quantum trajectory simulations of a cavity QED system comprising an atomic beam traversing a coherently driven standing-wave cavity are carried out. The intensity correlation function in transmission is computed and compared with the experimental measurements of Rempe et al. [Phys. Rev. Lett. 67, 1727 (1991)] and Foster et al. [Phys. Rev. A 61, 053821 (2000)]. It is shown that atomic beam density fluctuations induced by the motion of the atoms can account for the reported disagreement of the experimental results with theory (by an overall scale factor of 2 to 4). Moderate misalignments of the atomic beam produce large intracavity photon number fluctuations which significantly degrade the quantum correlations. One parameter fits to the experimental data are made in the weak-field limit with the adjustable parameter being the atomic beam tilt. Departures of the experimental conditions from the weak-field limit are discussed.
The paper continues the analysis of vacuum Rabi oscillations we started in part I [Phys. Rev. A 79, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic-oscillator Lie algebras. The zero-temperature master equation, derived in part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic fields by a gas of harmonic-oscillator wave packets. The representation is known to introduce automatic regularizations that in irreducible representations would have to be justified by ad hoc arguments. Predictions based on this representation are characterized in thermodynamic limit by a single parameter $\ensuremath{\varsigma}$, responsible for collapses and revivals of Rabi oscillations in exact vacuum. Collapses and revivals disappear in the limit $\ensuremath{\varsigma}\ensuremath{\rightarrow}\ensuremath{\infty}$. Observation of a finite $\ensuremath{\varsigma}$ would mean that cavity quantum fields are described by a non-Wightmanian theory, where vacuum states are zero-temperature Bose-Einstein condensates of a NNN-particle bosonic oscillator gas and, thus, are nonunique. The data collected in the experiment of Brune et al. [Phys. Rev. Lett. 76, 1800 (1996)] are consistent with any $\ensuremath{\varsigma}>400$.