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Physical Review A

Sub-Poissonian atomic statistics in a micromaser

Gerhard Rempe, HERBERT WALTHER

Published Aug 1, 1990• 134 citations
Publisher

Abstract

It is shown analytically that under certain experimental conditions the steady-state photon statistics of a micromaser field are directly connected to the fluctuation in number of the atoms in transition from the upper to the lower maser level under the influence of the maser field. The analytical results are compared to the results of a computer simulation of the maser process.

DOI
10.1103/physreva.42.1650

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It is shown analytically that under certain experimental conditions the steady-state photon statistics of a micromaser field are directly connected to the fluctuation in number of the atoms in transition from the upper to the lower maser level under the influence of the maser field. The analytical results are compared to the results of a computer simulation of the maser process.
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{}1010{10}^{10}1010. 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.
We present a theory of the micromaser including the effect of the arrival-time statistics of the active atoms in the theoretical treatments. Our starting point is an approach that explicitly incorporates the effect of pump statistics into the dynamical description of lasers and masers. We show that the application of standard laser theory to the micromaser is tantamount to the tacit assumption of Poissonian arrival-time statistics. Hence standard laser theory and the theory of the micromaser are, in general, not equivalent, but the latter contains the former, as a limiting case, for completely random arrival times. We show, as an application, that the steady-state value of the average photon number (first moment) is essentially unaffected by the pump statistics since it depends only on the flux of active atoms (average number of atoms entering the cavity per unit time) provided the flux is constant. The intensity fluctuations (second moment), however, exhibit a stronger dependence on the pump statistics. In particular, for sub-Poissonian pump statistics the sub-Poissonian character of the field is enhanced.
The author presents a tutorial review of the quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interaction with the individual reservoirs, i.e. the interactions are uncorrelated. In their approach, which is based on discrete mapping rather than a maser equation, corrections to reservoir theory arise due to correlations between these interactions. The magnitude of these terms is characterized by the quantity p/N ex . Here p, the parameter describing pump beam fluctuations, is the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p<0 to super-Poissonian pump beam fluctuations. N ex is the number of atoms passing through the cavity during the lifetime of the intercavity field. The conventional reservoir limit (standard laser theory) is recovered if p=0 and/or N ex is large. In all other cases the interactions with the gain and loss reservoirs are correlated. The author presents analytical results to demonstrate the effect of pump regularity on steady-state problems (photon statistics, mean number of photons and photon number variance) as well as on transient phenomena (correlation function and spectrum). In particular, it is shown that the approach to equilibrium can have non-Markovian character.
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 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 a theory which can explain the micromaser as well as its optical counterpart, the microlaser, for appropriate values of dissipative parameters. We show that, in both the the cases, the cavity radiation fields can have sub-Poissonian photon statistics. We further analyse if it is possible to attain a Fock state of the radiation field. The microlaser is precluded for such analysics due to the damping of its lasing levels making transitions at optical frequencies. Hence, we focus our attention on the micromaser and our exact simulation of the dynamics shows that it is not possible to generate a Fock state of the cavity radiation field.