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arXiv:1201.1688 · Physical Review A

Quantum theory of frequency pulling in the cavity-QED microlaser

Hyun-Gue Hong, Kyungwon An

Published Feb 24, 2012• 3 citations

Abstract

The spectrum of the cavity-QED microlaser or micromaser is expected to show distinctive features of the coherent light-matter interaction, which are obscured in the conventional Schawlow-Townes linewidth theory. However, the spectral studies have been limited to resonant atom-cavity interaction so far. Here we consider the dispersive interaction in the off-resonance case, from which we uncover a quantum frequency pulling effect in the microlaser or micromaser spectrum. We present a quantum theory of the spectrum which introduces the notion of a frequency-pulling distribution associated with the photon number. In contrast to the conventional laser, periodic variation of the mean frequency pulling is observed with increasing pump parameter and it is attributed to the strong atom-cavity coupling. The pulling distribution gives rise to a spectral broadening, which can be dominant over the nondispersive broadening addressed in the previous works. We also developed a corresponding semiclassical theory and discuss how the introduction of the frequency shift fits in with the extended quantum theory.

DOI: 10.1103/physreva.85.023836

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The spectrum of the cavity-QED microlaser or micromaser is expected to show distinctive features of the coherent light-matter interaction, which are obscured in the conventional Schawlow-Townes linewidth theory. However, the spectral studies have been limited to resonant atom-cavity interaction so far. Here we consider the dispersive interaction in the off-resonance case, from which we uncover a quantum frequency pulling effect in the microlaser or micromaser spectrum. We present a quantum theory of the spectrum which introduces the notion of a frequency-pulling distribution associated with the photon number. In contrast to the conventional laser, periodic variation of the mean frequency pulling is observed with increasing pump parameter and it is attributed to the strong atom-cavity coupling. The pulling distribution gives rise to a spectral broadening, which can be dominant over the nondispersive broadening addressed in the previous works. We also developed a corresponding semiclassical theory and discuss how the introduction of the frequency shift fits in with the extended quantum theory.

Summary form only given. We have investigated the wave properties manifested in the first-order coherence or the spectrum of the cavity-QED microlaser by using a high-sensitive photon-counting-based heterodyne spectroscopy. The emission spectrum exhibited a linewidth broadening due to the quantum frequency pulling effect, namely the frequency pulling dependent on the intracavity atom- and photon-number intrinsic distributions, in the presence of nonzero atom-cavity detuning. We also observed a large per-atom frequency pulling (2.1 kHz maximally), enhanced by the strong atom-cavity coupling. Moreover, a stepwise change in the frequency pulling, associated with the coherent Rabi oscillations, was observed with the increased pumping over multiple thresholds.

We report the first experimental observation of the cavity-QED microlaser spectrum, specifically the unconventional frequency pulling brought by a strong atom-cavity coupling at off resonance. The pulling is enhanced quadratically by the atom-cavity coupling to result in a sensitive response to the number of pumping atoms (2.1 kHz per atom maximally). Periodic variation of the pulling due to the coherent Rabi oscillation is also observed as the number of pumping atoms is increased across multiple thresholds.

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.

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 the observation of multiple thresholds in the cavity-quantum electrodynamics microlaser there was deviation from the result predicted by uniform atom-cavity coupling theory, notably a frequency-pushing behavior. We analyze in the semiclassical limit the tilted injection of atoms, originally used to achieve a spatially uniform atom-cavity coupling, and show that the deviation originates from the interference between the induced dipole moments associated with two traveling-wave components of a standing-wave cavity mode. The criteria for sufficiently reduced interference and thus uniform atom-cavity interactions are derived in analytic considerations and verified by numerical calculation. Our analysis is well supported by experimental data.