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arXiv:quant-ph/9811086 · Optics Letters

Effect of dissipative forces on the theory of a single-atom microlaser

N. Nayak

Published Jan 1, 1999• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/ol.24.000013

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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.
We consider a single-atom laser (microlaser) operating on three-level atoms interacting with a two-mode cavity. The quantum statistical properties of the cavity field at steady state are investigated by the quantum trajectory method which is a Monte Carlo simulation applied to open quantum systems. It is found that a steady-state solution exists even when the detailed balance condition may not be guaranteed. The differences between a single-mode microlaser and a two-mode microlaser are highlighted. The second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ of a single mode is studied and special attention is paid to the one-photon trapping state, for which a simple formula is derived for its correlation function. We show the effects of the velocity spread of the atoms used to pump the microlaser cavity on the second-order correlation function, trapping states, and phase transitions of the cavity field.
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.
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.
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.
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.