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arXiv:physics/0412181

Multiple Thresholds and Many-Atom Dynamics in the Cavity QED Microlaser

Christopher M. Fang-Yen

Published Dec 31, 2004• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.physics/0412181

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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 report the observation of multiple laser thresholds in the many-atom cavity QED microlaser. Traveling-wave coupling and a supersonic atom beam are used to create a well-defined atom-cavity interaction. Multiple thresholds are observed as jumps in photon number due to oscillatory gain. Although the number of intracavity atoms is large, up to $N\ensuremath{\sim}{10}^{3}$, the dynamics of the microlaser agree with a single-atom theory. This agreement is supported by quantum trajectory simulations of a many-atom microlaser and a semiclassical microlaser theory. We discuss the relation of the microlaser with the micromaser and conventional lasers.
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.
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.
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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.