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Physical Review Letters

Observation of quantum collapse and revival in a one-atom maser

Gerhard Rempe, HERBERT WALTHER, N. Klein

Published Jan 26, 1987• 1,427 citations
Publisher

Abstract

The dynamics of the interaction of a single Rydberg atom with a single mode of an electromagnetic field in a superconducting cavity was investigated. Velocity-selected atoms were used and the evolution of the atomic inversion as atom and field exchange energy was observed. The quantum collapse and revival predicted by the Jaynes-Cummings model were demonstrated experimentally for the first time. The evaluation of the dynamic behavior of the atoms allows us to determine the statistics of the few photons in the cavity.

DOI
10.1103/physrevlett.58.353

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Two experiments with single atoms are reviewed. In the first experiment, the interaction of a single Rydberg atom with a single mode of an electromagnetic field was investigated. The quantum collapse and revivals of the atomic inversion predicted by the Jaynes-Cummings model were demonstrated for the first time. In the second experiment, a single atomic ion stored in a radio-frequency trap was probed by resonance fluorescence. In the fluorescent light, antibunching and sub-Poissonian photon statistics were detected. Furthermore, 'crystallization' and 'evaporation' of few ions in a trap were observed as the stored ions were cooled by the laser light and heated by the radio-frequency field of the trap.>

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The dynamics of the interaction of a single Rydberg atom with a single mode of an electromagnetic field in a superconducting cavity was investigated. Velocity-selected atoms were used and the evolution of the atomic inversion as atom and field exchange energy was observed. The quantum collapse and revival predicted by the Jaynes-Cummings model were demonstrated experimentally for the first time. The evaluation of the dynamic behavior of the atoms allows us to determine the statistics of the few photons in the cavity.
Experiments on the interaction of a single atom with a single mode of a resonant electromagnetic field in a cavity are reviewed. The atoms used in these experiments were Rydberg atoms with a very large principal quantum number. Another important ingredient is a superconductivity cavity, the quality factor of which is high enough for a periodic energy exchange between atom and cavity field to be observed. The dynamics of the atom-field interaction predicted by theory was measured. Some of the features are explicitly a consequence of the quantum nature of the electromagnetic field: The statistical and discrete nature of the photon field leads to new dynamic characteristics such as collapse and revivals in the Rabi nutation.
Recent experiments with the one-atom maser /1/ have demonstrated that it is possible to study the interaction of single Rydberg atoms with a single quantized mode /2/ of a resonant electromagnetic field in a superconducting cavity. The quality factor is high enough to observe the periodic energy exchange between the atom and the field. The statistical and discrete nature of the photon field leads to new dynamic characteristics such as collapse and revial in the Rabi nutation /3/. Most of the observed effects are purely quantum features /4/.
Recent experiments with the one-atom maser1 have demonstrated that it is possible to study the interaction of single Rydberg atoms with a single quantized mode2 of a resonant electromagnetic field in a super conducting cavity. The quality factor is high enough to observe the periodic energy exchange between the atom and field. The statistical and discrete nature of the photon field leads to new dynamic characteristics such as collapse and revival in the Rabi nu tation.3 Most of the observed effects are purely quantum features.4
A distinctive signature of the granulated nature of the electromagnetic field is the revivals known to occur in the dynamics of a two-level atom interacting with a single-field mode (Jaynes-Cummings model). The development of high-Q single-mode cavities combined with progress in Rydberg atom spectroscopy has led to a possibility of verifying these predictions. Revival experiments using micromasers have been performed by Walther et al. Here the cavity mode is first allowed to reach a steady state, and then probe atoms are injected into the resonator. By measuring their state as they exit the cavity, one can infer the state of the field. We show that the micromaser experiences Jaynes-Cummingslike revivals when the pump parameter θ is varied. However, in contrast to the conventional Jaynes-Cummings situation, which considers initially coherent fields, the micromaser photon statistics are usually not Poissonian and depend sensitively on θ. The micromaser revivals cannot be explained by a semiclassical theory or linearized quantum fluctuations about the semiclassical solution. Rather, an exact quantum treatment, considering fully the granularity of the cavity mode, is required.
A single atom coupled to a quantized mode of an electromagnetic cavity, driven by an external coherent field, is described by the Hamiltonian H djc = ig(a†σ− − aσ+) + iε(a† − a), where (a†, a) and (σ+, σ) are the raising and lowering operators for the cavity mode and atom, respectively. This is the single atom version of the Hamiltonian used in the study of optical bistability. It describes the evolution of the atom-cavity system on time scales much smaller than the inverse spontaneous emission and cavity decay rates. For 2ε/g < 1, HDJC possesses a discrete set of interaction eigenstates1 with eigenvalues E n ± = ± g n [ 1 − ( 2 ε / g ) 2 ] 3 / 4 . These form a renormalized version of the usual Jaynes-Cummings eigenstates2, which correctly take into account the effect of the driving field to all orders of magnitude. We investigate the collapse and revival nature of the dynamical evolution of the single atom in a cavity, with and without dissipation and above and below the threshold 2ε/g = 1 of the driven Jaynes-Cummings Hamiltonian.
Two experiments with single atoms are reviewed. In the first experiment, the interaction of a single Rydberg atom with a single mode of an electromagnetic field was investigated. The quantum collapse and revivals of the atomic inversion predicted by the Jaynes-Cummings model were demonstrated for the first time. In the second experiment, a single atomic ion stored in a radio-frequency trap was probed by resonance fluorescence. In the fluorescent light, antibunching and sub-Poissonian photon statistics were detected. Furthermore, 'crystallization' and 'evaporation' of few ions in a trap were observed as the stored ions were cooled by the laser light and heated by the radio-frequency field of the trap.>