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Physical Review A

Effect of atom pairs on the vacuum trapping state in micromasers: A Monte Carlo wave-function approach

Tarso B. Ledur Kist, Antonio Zelaquett Khoury, L. Davidovich

Published Sep 1, 1996• 9 citations
Publisher

Abstract

We calculate the lifetime of the vacuum trapping state in a micromaser, using both the Monte Carlo wave-function method and an analytic approximation, and show it to be a rapidly changing function of the average number of atoms in the cavity, when this number is much smaller than one. Our method leads to a realistic simulation of experiments, allowing for different field profiles, temperatures, and atomic velocity spreads. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2510

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We calculate the lifetime of the vacuum trapping state in a micromaser, using both the Monte Carlo wave-function method and an analytic approximation, and show it to be a rapidly changing function of the average number of atoms in the cavity, when this number is much smaller than one. Our method leads to a realistic simulation of experiments, allowing for different field profiles, temperatures, and atomic velocity spreads. \textcopyright{} 1996 The American Physical Society.
A scheme which stabilizes the trapping states in micromasers is proposed and studied. It uses an atomic beam composed of a mixture of two types of atoms. Numerical simulations based on the Monte Carlo wave-function method show that, despite collective events, it is possible to obtain a steady-state photon number distribution limited (``trapped'') to a certain domain of the photon number space. For the one-photon trapping condition this steady state approaches a Fock state in the limit of low cavity losses.
By applying a quantum-trajectory approach to a master equation for the cavity mode density operator, we investigate the dynamics and the trapping states of a micromaser or microlaser including the effects of cavity temperature, two-atom events, atomic velocity spread, and partial excitation of the atomic beam. In the description of two-atom collective effects we allow for the nonsimultaneous arrival of atoms in the cavity, generalizing to a mean number of atoms ${N}_{\mathrm{at}}\ensuremath{\approx}1,$ a recent treatment [M. I. Kolobov and F. Haake, Phys. Rev. A 55, 3033 (1997)]. We show that, in trapping regions, our treatment of two-atom events can give strikingly different effects with respect to the approximation of simultaneous arrival of atom pairs; e.g., detrapping instead of trapping, different times of approach to the steady state, and different photonstatistics. Also, we simulate micromaser dynamics with parameter values corresponding to the recent experimental observation of the trapping effect by Walther and collaborators [H. Weidinger et al., Technical Digest of the European Quantum Electronics Conference '98 (IEEE, Piscataway, NJ, 1998)].
We present the first quantum microscopic study of a micromaser with many atoms in the cavity. Excited atoms are injected in clusters with average number N‾\overline{N}N up to 100. The stationary state of radiation is evaluated by means of a novel Green-function Monte Carlo technique. For N‾<Nex\overline{N}<{N}_{\mathrm{ex}}N<Nex​ (Nex{N}_{\mathrm{ex}}Nex​ being the number of excited atoms entering the cavity in a photon lifetime) the system behaves similarly to the one-atom maser. At $\overline{N}\ensuremath{\simeq}{N}_{\mathrm{ex}}$ a transition occurs to a novel cluster behavior, where a fine structure of thresholds emerges.
We report a numerical simulation of the action of the one 85 Rb atom micromaser which shows that the micromaser field evolves towards a steady state equilibrium when the condition that Tp t int satisfies. In this steady state regime the cavity field reaches a steady state after a sufficient number of atoms have passed through the cavity. The cavity temperature T and the cavity quality factor Q can produce a quantitive change when one of them or the two are changed but they are not responsible for the qualitative changes in the micromaser field. Evidently the only responsible parameter for these qualitative changes is the repetition time T p namely if T p t int then the micromaser field evolution is towards a steady state equilibrium. In contrast when T p reduced to the order of t int then the micromaser field evolution is controlled by the trapping state dynamics – no steady state is apparent in this case. The first going-up trapping state at n=3 plays a significant role in the early dynamics of the micromaser field. Moreover the state of the field ultimately evolves towards a mixed state rather than a pure state.
We suggest an iterative, maximum-likelihood–based, method to reconstruct the photon number distribution of the steady-state cavity field of a micromaser starting from the statistics of the atoms leaving the cavity after the interaction. The scheme is based on measuring the atomic populations of probe atoms for different interaction times and works effectively using a small number of atoms and a limited sampling of the interaction times. The method has been tested by numerically simulated experiments showing that it may be reliably used in any micromaser regime, leading to high-fidelity reconstructions for single-peaked distributions as well as for double-peaked ones and for trapping states.
We investigate signals of trapping states in the micromaser system in terms of the average number ⟨n⟩⟨n⟩⟨n⟩ of cavity photons as well as a suitably defined correlation length of atoms leaving the cavity. In the description of collective two-atom effects we allow the mean number, ϵϵϵ, of pump atoms inside the cavity during the characteristic atomic cavity transit time to be as large as of order one. The master equation we consider, which describes the micromaser including collective two-atom effects, still exhibits trapping states for $ϵ\ensuremath{\ne}0$, even for a mean number of atoms inside the cavity close to one. We, however, argue more importantly that the trapping states are more pronounced in terms of the correlation length as compared to ⟨n⟩⟨n⟩⟨n⟩, i.e., we suggest that trapping states can be more clearly revealed experimentally in terms of the atom correlation length. For axion detection in the micromaser this observable may, therefore, be an essential ingredient.