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Physical Review A

Collective effects in the microlaser

Mikhail I. Kolobov, Fritz Haake

Published Apr 1, 1997• 19 citations
Publisher

Abstract

In a microlaser experiment performed by An et al. with collaborators [Phys. Rev. Lett. 73, 3375 (1994)] an atomic beam interacts with a microcavity field under such conditions that the average number of atoms in the cavity is less than unity. However, due to the random statistics of atoms in the beam, the probability of two atoms being in the cavity simultaneously in time is not negligible. This must lead to collective two-atom effects that are not included in the standard microlaser model. We have developed a theory that incorporates such collective effects. This theory allows a better understanding of the observed experimental results and predicts some different features of the microlaser.

DOI
10.1103/physreva.55.3033

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Physical Review A•Jun 1, 1997•14 citations
In a microlaser experiment performed by An et al. with collaborators [Phys. Rev. Lett. 73, 3375 (1994)] an atomic beam interacts with a microcavity field under such conditions that the average number of atoms in the cavity is less than unity. However, due to the random statistics of atoms in the beam, the probability of two atoms being in the cavity simultaneously in time is not negligible. This must lead to collective two-atom effects that are not included in the standard microlaser model. We have developed a theory that incorporates such collective effects. This theory allows a better understanding of the observed experimental results and predicts some different features of the microlaser.
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 have achieved the first realization of a single atom microlaser, a laser oscillator with only one atom in an optical resonator. In the experiment a beam of two-level barium atoms traverses an ultrahigh Q single-mode cavity. The atoms are inverted by a (pi) -pulse field before they enter the cavity. Laser oscillation ((lambda) equals 791 nm) has been observed, with the mean number of atoms inside the mode <N> as small as 0.1, resulting in the mean number of photons in the mode <N> or 0.14. To understand the results quantitatively we used a fully-quantized one-atom microlaser theory adapted from its counterpart micromaser theory. The present theory was found to be in good agreement with the data for small <N> and <n>. Discrepancy between experiment and theory was observed for <n> very much greater than 1 and <N> approximately equal to 1. This discrepancy may be explained by the standing-wave nature of the cavity mode, in combination with the saturation effect occurring at large cavity photon number, as well as by the breakdown of single-atom interaction assumption in the theory for <N> greater than or equal to 1.
This thesis describes a study of a cavity QED microlaser in which many atoms are present simultaneously and atom-cavity interaction is well-defined. The microlaser is found to display multiple thresholds analogous to first-order phase transitions of the cavity field. Hysteresis is observed as a function of atom-cavity detuning and number of atoms. Data is compared with a rate equation model and fully quantized treatment based on micromaser theory. Good agreement between theory and experiment is found when the cavity is resonant with atoms of the most probable velocity, but long lifetimes of metastable states preclude the observation of true steady-state transition points. For nonzero atom-cavity detuning the microlaser displays broadenings and shifts which are not yet well-understood. Quantum trajectory simulations are performed to investigate many-atom and finite transit time effects in the microlaser. We show that over a wide range of parameters the many-atom microlaser scales with the single-atom theory, with a perturbation in the photon statistics due to cavity decay during the atom transit time.
A single-atom microlaser involving Poissonian input of atoms with a fixed flight time through an optical resonator is described. The influence of the cavity reservoir during the interactions of successive individual atoms with the cavity field is included in the analysis. Atomic decay is also considered, as it is nonnegligible in the optical regime. During the random intervals of absence of any atom in the cavity, the field evolves under its own dynamics. The steady-state characteristics of the cavity field are discussed. Away from laser threshold, the field can be nonclassical in nature.
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.