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Fortschritte der Physik

Entangled Atoms in Micromaser Physics

Berthold‐Georg Englert, Berthold‐Georg Englert, M. Löffler, Markus Löffler, Oliver J. Benson, Oliver J. Benson, Benjamin T. H. Varcoe, M. Weidinger, HERBERT WALTHER, HERBERT WALTHER

Published Nov 1, 1998• 72 citations

Abstract

A micromaser in standard operation produces entangled two-level atoms. This entanglement can be investigated in the correlations of atoms leaving the micromaser cavity in the upper and lower maser levels. The correlations contribute to the stabilization of the photon number in the cavity and are thus vital for the generation of sub-Poissonian statistics in the maser field. We review how various statistical signatures for this entanglement are calculated in micromaser theory, and report recent measurements that demonstrate the case. Ways are described leading to an optimal entanglement for the atoms in the micromaser.

DOI: 10.1002/(sici)1521-3978(199811)46:6/8<897::aid-prop897>3.0.co;2-2

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A micromaser in standard operation produces entangled two-level atoms. This entanglement can be investigated in the correlations of atoms leaving the micromaser cavity in the upper and lower maser levels. The correlations contribute to the stabilization of the photon number in the cavity and are thus vital for the generation of sub-Poissonian statistics in the maser field. We review how various statistical signatures for this entanglement are calculated in micromaser theory, and report recent measurements that demonstrate the case. Ways are described leading to an optimal entanglement for the atoms in the micromaser.

We describe the first investigation of the nonclassical radiation field of a micromaser. The maser cavity is cooled to 0.5 K to exclude thermal photons and has a quality factor 3\ifmmode\times\else\texttimes\fi{}

{10}^{10}

. Velocity-selected Rydberg atoms pump the maser. The photon statistics in the cavity are measured via the statistics of the atoms leaving the cavity in the lower maser level. Taking into account a detection efficiency of 10%, their fluctuations are reduced up to 40% below the Poisson level. This corresponds to photon-number fluctuations in the cavity of up to 70% below the vacuum-state limit.

The lifetimes of Rydberg atoms have been considered in micromaser theory. The difference from the usual micromaser theory [P. Filipowicz, J. Javanainen, and P. Meystre, Phys. Rev. A 34, 3077 (1986)] without level decay rates is discussed. It is shown that when the atom-field interaction time is large, the quantum collapse and revival are significantly different from the prediction of the usual micromaser theory. The relation between the photon fluctuation and the fluctuation of the population of the lower level after interacting with a maser field is also discussed. We found that the consistency of the sub-Poisson statistics of the lower-level population and photon number is violated.

Correlation measurements on the states of two-level atoms having passed through a micromaser at different times can be used to infer properties of the quantum state of the radiation field in the cavity. Long(short) correlation length in time is to some extent associated with super(sub)-Poissonian photon statistics. The correlation length is also an indicator of a phase structure much richer than what is revealed by the usual single-time observables, like the atomic inversion or the Mandel quality factor. In realistic experimental situations the correlations may extend over many times the decay time of the cavity. Our assertions are verified by comparing theoretical calculations with a high-precision Monte-Carlo simulation of the micromaser system.

We present the quantum theory of the two-mode micromaser operating on \ensuremath{\Lambda}-type three-level atoms. The explicit expression of the detailed-balance steady-state photon distribution is derived. The photon statistics and the correlation between the modes are studied. It is shown that due to the strong anticorrelation between the modes the fluctuations in the total number of photons may be sub-Poissonian even when the fluctuations in the number of photons in each mode are super-Poissonian.

We present the quantum theory of a microscopic maser operating on a degenerate two-photon transition between levels of the same parity. We derive both a master equation and a Fokker-Planck equation for this system, and show that quantum effects may have a substantial influence on the behavior of the maser. They modify the oscillation threshold and make external triggering of this maser unnecessary, whereas, according to semiclassical theory, such a triggering is required to start up the maser oscillation. We derive the phase-diffusion properties of the field and show that the diffusion coefficient is complex in this case, its imaginary part being associated with a frequency shift of the field inside the cavity. We show that, in steady state, the photon-number statistics is sub-Poissonian for a wide range of pumping rates.