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Journal of Physics Conference Series

Glauber-Sudarshan P function for a single-emitter laser

A.V. Vikentyev, V. Yu. Goryainov, Ларионов Николай Владимирович

Published Aug 1, 2016• 0 citations
Publisher

Abstract

We consider the model of a single-emitter laser: an incoherently pumped single two-level system interacting with a single cavity mode of finite finesse. In the stationary regime using normally-ordered diagonal representation of the density matrix over the coherent states we derive equation for the phase-averaged Glauber-Sudarshan P function. In the strong-coupling regime between atom and cavity mode the asymptotic solution of this equation is obtained. This solution is a linear combination of two basis solutions. We analyze one of them which was ignored in previous work without any discussions.

DOI
10.1088/1742-6596/735/1/012048

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We consider the model of a single-emitter laser: an incoherently pumped single two-level system interacting with a single cavity mode of finite finesse. In the stationary regime using normally-ordered diagonal representation of the density matrix over the coherent states we derive equation for the phase-averaged Glauber-Sudarshan P function. In the strong-coupling regime between atom and cavity mode the asymptotic solution of this equation is obtained. This solution is a linear combination of two basis solutions. We analyze one of them which was ignored in previous work without any discussions.
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.
Using two equivalent methods, the Heisenberg-Langevin and the master equation, we investigate the properties of a single-emitter nanolaser: an incoherently pumped single two-level system interacting with a single cavity mode of finite finesse. We are interested in a stationary generation regime when the mean number of photons inside the laser cavity is much larger than unity. In this case we linearize the Heisenberg-Langevin equations around the stationary classical solution and obtain analytical results for the linewidth, the quadrature fluctuation spectra, and the intracavity Mandel QQQ parameter. As the second method we use the master equation for the density operator of the laser field. Using the coherent-state representation of the density matrix we obtain the stationary solution for the Glauber PPP function of the laser mode and investigate the quantum statistics of the laser field and its threshold behavior. We compare the results of both methods with numerical simulations and find very good agreement. In the end we use our theoretical results for analyzing experiment with single-ion nanolasers.
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).
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.
We provide analytical results obtained in the framework of the quantum theory for a single-emitter nanolaser: an incoherently pumped single two-level system interacting with a single-cavity mode of finite finesse. In the good-cavity limit we analytically calculate the linewidth of such a laser, its amplitude fluctuation spectrum, and the intracavity Mandel QQQ parameter. Our analytical results are in very good agreement with numerical simulations of the master equation.
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.