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arXiv:2009.04563 · International Conference on Electrical Engineering and Photonics (EExPolytech)

Behavior of a Single-Atom Laser in the Sub-Poissonian Regime

Ларионов Николай Владимирович

Published Oct 15, 2020• 2 citations
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Abstract

In the present work the model of a single-atom laser generating in the regime when incoherent pumping rate coincides with the cavity decay rate is theoretically investigated. Using the stationary equation for phase averaged Glauber P function the analytical expressions for mean number of photons and its dispersion are obtained. In the limiting case of the strong-coupling regime the exact expression for the photon number distribution function is derived. Obtained results describe the sub-Poissonian photon statistics and show an increase in mean number of photons to non-zero value when the pumping tends to zero.

DOI
10.1109/eexpolytech50912.2020.9243955

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In the present work the model of a single-atom laser generating in the regime when incoherent pumping rate coincides with the cavity decay rate is theoretically investigated. Using the stationary equation for phase averaged Glauber P function the analytical expressions for mean number of photons and its dispersion are obtained. In the limiting case of the strong-coupling regime the exact expression for the photon number distribution function is derived. Obtained results describe the sub-Poissonian photon statistics and show an increase in mean number of photons to non-zero value when the pumping tends to zero.
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).
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.
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.
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.
The effect of the pump-noise on the statistical properties of the output photon-number is discussed. The master equation for the radiation field valid for any pump fluctuation with steady atomic injection is presented. Far above threshold, the characteristic function for the photon-number distribution is derived without truncating the master equation, the mean value and fluctuation of the output photon-number are also calculated. Thereby the condition of generating sub-Poissonian light is derived and the effect of the pump-noise on the higher-order moment of the output photon-number distribution is analyzed.
Using the master equation approach, we investigate the stationary regime of a single-emitter laser: an incoherently pumped single two-level system interacting with a single cavity mode of finite finesse. We analyze the closed equation for the phase-averaged Glauber-Sudarshan P function and obtain its approximate solution. This solution has some advantages over the previous results. In particular, it describes conversion from the classical-like probability distribution to the oscillating quasi-probability when transition from weak- to strong-coupling regime takes place.