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arXiv:quant-ph/9907085

Output Spectrum of Single-Atom Lasers

James Clemens, Perry R. Rice, Leno M. Pedrotti

Published Jul 26, 1999• 0 citations
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Abstract

We consider a laser composed of a single atom in a microcavity, with a coherent or incoherent pump. We consider both three- and four-level gain schemes, and examine the output spectrum of such lasers. We find that the linewidth generally scales as the inverse of the photon number. For large atom-field coupling, a vacuum-Rabi doublet structure is obtained. In the three-level case, this vacuum-Rabi splitting is apparent only for small intracavity photon numbers, and vanishes for large pumps. In the four-level scheme, the vacuum-Rabi structure appears at a nonzero pump level, and is maintained for large pumps, even when the intracavity photon number is larger than unity. This behavior is explained utilizing the quantum trajectory approach.

DOI
10.48550/arxiv.quant-ph/9907085

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We consider a laser composed of a single atom in a microcavity, with a coherent or incoherent pump. We consider both three- and four-level gain schemes, and examine the output spectrum of such lasers. We find that the linewidth generally scales as the inverse of the photon number. For large atom-field coupling, a vacuum-Rabi doublet structure is obtained. In the three-level case, this vacuum-Rabi splitting is apparent only for small intracavity photon numbers, and vanishes for large pumps. In the four-level scheme, the vacuum-Rabi structure appears at a nonzero pump level, and is maintained for large pumps, even when the intracavity photon number is larger than unity. This behavior is explained utilizing the quantum trajectory approach.
We calculate the output spectrum of a single-atom laser in a microcavity across a wide range of operating conditions. We considered both three-level and four-level atomic level structures. We used a numerical routine to calculate spectra that is more efficient than others used previously. We found that the linewidth of a single-atom laser generally scales as the inverse of the photon number and that there is no pump value at which an abrupt change occurs that might locate a lasing threshold. For a three-level gain atom we found vacuum–Rabi splitting similar to that found by Loffler et al. [Phys. Rev. A 55, 3923 (1997)] and used quantum trajectory theory to obtain a new interpretation of the results. For a four-level gain atom the vacuum–Rabi structure can appear at a small nonzero pump level and is maintained for large pumps, even when the intracavity photon number is larger than unity and the laser is on. We use the quantum trajectory approach to explain these results.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.
Our recent paper reports the experimental realization of a one-atom laser in a regime of strong coupling [J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Nature (London) 425, 268 (2003)]. Here we provide the supporting theoretical analysis relevant to the operating regime of our experiment. By way of a simplified four-state model, we investigate the passage from the domain of conventional laser theory into the regime of strong coupling for a single intracavity atom pumped by coherent external fields. The four-state model is also employed to exhibit the vacuum-Rabi splitting and to calculate the optical spectrum. We next extend this model to incorporate the relevant Zeeman hyperfine states as well as a simple description of the pumping processes in the presence of polarization gradients and atomic motion. This extended model is employed to make quantitative comparisons with our earlier measurements for the intracavity photon number versus pump strength and for the photon statistics as expressed by the intensity correlation function ${g}^{(2)}(\ensuremath{\tau})$.
The emission spectrum of a single-emitter laser in a photonic crystal is presented. We consider a coherently pumped two-level emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal. We show that the cavity spectrum consists of both elastic and inelastic components, for which we derive analytical expressions. Our study reveals enhanced, spectrally narrower emission resulting from the radiation reservoir of the photonic crystal. The cavity field spectral characteristics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. At high pump intensities and for large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, the emitted intensity originating from the elastic spectral component increases with the intensity of the pump and the elastic component dominates the spectrum. In the case of a vanishing photon density of states in the spectral range surrounding the lower Mollow sideband and no dipolar dephasing, the cavity spectrum is elastic.
We propose a cavity quantum electrodynamic system consisting of a five-level atom coupled to a single mode of the cavity electromagnetic field. The study is focused on the regime of strong coupling between the cavity and atom. Pump laser fields and cavity fields connect the split energy levels of the atom. Instead of the well-known two-level Dicke model obtained by adiabatic elimination of the high-energy levels, we consider the pump lasers' detunings to the atomic transitions to be very small such that we can examine the influence of the higher-energy states. We have studied the effect of an external coherent drive and incoherent pumping on these higher-energy levels and observed the enhancement of intracavity photon numbers due to quantum coherence effects. The amplification of intracavity photons is achieved even without a population inversion. However, the effect of the coherent and incoherent drive is negligible for very large detunings when the higher-energy states are adiabatically eliminated. At zero and small detunings, the system reaches the steady state at an earlier instant of time for higher incoherent pumping. We find an almost agreeable steady-state behavior of the system's exact full quantum dynamics model and its semiclassical approximation. Our model tries to accurately simulate the open system by considering the cavity decay, spontaneous decay, and dephasing of the system.