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Quantum Electronics and Laser Science Conference

Linewidth and photon statistics of a single atom laser

Perry R. Rice, B. D. Jones, Shohini Ghose

Published Jun 7, 1996• 0 citations
OpenAlex

Abstract

Summary form only given. The basic model considered in this paper is a single atom inside an optical cavity. We consider both three- and four-level atomic systems and use incoherent pumping for both. We present numerical results of the laser linewidth and the second-order intensity correlation function. These results are obtained with use of the quantum trajectory method, using the formalism of Carmichael.

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Summary form only given. The basic model considered in this paper is a single atom inside an optical cavity. We consider both three- and four-level atomic systems and use incoherent pumping for both. We present numerical results of the laser linewidth and the second-order intensity correlation function. These results are obtained with use of the quantum trajectory method, using the formalism of Carmichael.
We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.
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.
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 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.
We consider three- and four-level atomic lasers that are either incoherently (unidirectionally) or coherently (bidirectionally) pumped, the single-mode cavity being resonant with the laser transition. The intracavity Fano factor and the photocurrent spectral density are evaluated on the basis of rate equations. According to that approach, fluctuations are caused by jumps in active and detecting atoms. The algebra is simple. Whenever a comparison is made, the expressions obtained coincide with the previous results. The conditions under which the output light exhibits sub-Poissonian statistics are considered in detail. Analytical results, based on linearization, are verified by comparison with Monte Carlo simulations. An essentially exhaustive investigation of sub-Poissonian light generation by three- and four-level lasers has been performed. Only special forms were reported earlier.