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Optics and Spectroscopy

Quantum statistical properties of one-atom lasers

T. B. Karlovich, S. Ya. Kilin

Published Sep 1, 2001• 26 citations
Publisher

Abstract

Properties of a laser formed by a high-Q cavity and a single incoherently excited atom are studied on the basis of analytical solutions obtained for the quasi-probability P -function. Expressions for the boundaries separating various operating regimes of a one-atom laser (below threshold, above threshold, and self-quenching) are found. It is shown that lasing without inversion and lasing with the decay rate of the excited state exceeding the pump intensity are possible in the system. The degree of coherence of laser radiation is studied.

DOI
10.1134/1.1405210

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Properties of a laser formed by a high-Q cavity and a single incoherently excited atom are studied on the basis of analytical solutions obtained for the quasi-probability P -function. Expressions for the boundaries separating various operating regimes of a one-atom laser (below threshold, above threshold, and self-quenching) are found. It is shown that lasing without inversion and lasing with the decay rate of the excited state exceeding the pump intensity are possible in the system. The degree of coherence of laser radiation is studied.
The quantum statistical properties of the radiation of a one-atom two-level laser with incoherent pumping are analyzed. Solution of the Liouville equation for the density operator in the basis of Fock states shows that stationary radiation from a single-mode laser with incoherent pumping can be in a squeezed (sub-Poissonian) stationary state if the rate of spontaneous decay is lower than the rate of cavity losses and the pump rate. Inside the cavity the Fano factor reaches F =0.85 (15% squeezing). Multiple squeezing ( F =0.19) is possible in the transient lasing regime. Significant squeezing obtains at the cavity output; the spectral Fano factor at zero frequency is 0.36 under optimal conditions.
Based on the approximation of strong correlations between an atom and an intracavity field, which implies the equal probabilities of finding the atom in the ground state and n photons in the field and of finding the atom in an excited state and n −1 photons in the field, it is shown that the conditional states of a field generated by a single-atom laser are described by the diagonal part of the generalized coherent Mittag-Leffler state. The quasi-distributions P and Q of the intracavity-field probability amplitude are found, and the boundedness of the Glauber function on a segment is shown. The possibility of inversionless lasing is demonstrated, and the absence of a lasing threshold is found for some region of parameters. The regimes of generation of the amplitude-squeezed states of the field are studied and the parameters of the system providing the maximum squeezing are determined. It is shown that the atom-field states are entangled at weak pump intensities.
We analyze a laser system consisting of N closed three-level atoms confined in a single-mode cavity and derive the conditions for the onset of lasing without inversion or with inversion. We calculate the steady-state gain and lasing in the system and show that far above the lasing threshold, depending on the pumping and decay rates, the inversionless laser may operate in three different regimes, where the intensity of the laser depends linearly on N, is proportional to \ensuremath{\surd}N , or independent of N.
Although conventional lasers operate with a large number of intracavity atoms, the lasing properties of a single atom in a resonant cavity have been theoretically investigated for more than a decade. Here we report the experimental realization of such a one-atom laser operated in a regime of strong coupling. Our experiment exploits recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. In this regime the observed characteristics of the atom-cavity system are qualitatively different from those of the familiar many atom case. Specifically, we present measurements of intracavity photon number versus pump intensity that exhibit "thresholdless" behavior, and infer that the output flux from the cavity mode exceeds that from atomic fluorescence by more than tenfold. Observations of the second-order intensity correlation function demonstrate that our one-atom laser generates manifestly nonclassical light that exhibits both photon antibunching and sub-Poissonian photon statistics.
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.
Abstract A model of single-atom laser with incoherent pumping is investigated theoretically. In the stationary case, a linear homogeneous differential equation for the phase-averaged Husimi Q function is derived from the equation for the density operator of the system. In the regime in which the coupling of the cavity mode with an atom is much stronger than the coupling of the mode with the reservoir ensuring its damping, the asymptotic solution is obtained to this equation. This solution makes it possible to describe some statistical features of the single-atom laser (in particular, the weak sub-Poissonian photon statistics).