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arXiv:1811.04672 · Laser Physics Letters

Effect of saturated absorption on sub-Poissonian lasing

Yu. M. Golubev, T. Yu. Golubeva, E. A. Vashukevich, Sergey V. Fedorov, Nikolay N. Rosanov

Published Dec 21, 2018• 3 citations
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Abstract

Abstract This paper discusses the effect of saturated absorption on the quantum features of a sub-Poissonian laser. It is shown that when both media (laser and absorbing) are saturated, the appearance of an additional element in the cavity does not lead to the demolition of the quantum properties (regular statistics of photons and quadrature squeezing) of laser radiation.

DOI
10.1088/1612-202x/aaf69e

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Abstract This paper discusses the effect of saturated absorption on the quantum features of a sub-Poissonian laser. It is shown that when both media (laser and absorbing) are saturated, the appearance of an additional element in the cavity does not lead to the demolition of the quantum properties (regular statistics of photons and quadrature squeezing) of laser radiation.
It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.
A recent analysis of the influence of the pump statistics on the laser output fluctuations is applied to the experimentally feasible case of a laser being pumped by light coming from a separate pump field cavity that is driven by a broad-band squeezed vacuum plus a coherent driving field. In contrast to the 'squeezed-reservoir laser', where a reservoir of squeezed modes coming from all directions coupled to the dipole moment of the lasing transition and leads to atomic phase decay inhibition and phase locking of the laser field, here the squeezed light merely pumps the gain atoms, that is gives rise to inversion of the laser transition. In analogy to photodetection theory the photon statistics of the laser output is calculated as a function of the photon statistics of the absorbed squeezed pump light. For the case of a squeezed pump field chosen to display sub-Poissonian statistics, it is demonstrated that the Mandel Q-parameter of the laser cavity output can theoretically reach the optimum value of Q=- 1 / 2 , similar to the case of a deterministic pumping mechanism.
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.
Using an extension of the Scully—Lamb laser theory we show that by insertion of nonlinear elements in the cavity, laser light with nonclassical sub—Poissonian photon statistics can be generated. For an N—photon absorber in the limit of small saturation the variance of the photon number distribution can be reduced by a factor of (+1/N) compared to Poissonian limit of the usual laser. When we generalize the type of such nonlinear elements to the case of a nonlinear feedback or Raman type nonlinear transition, the noise in the laser intensity can be reduced even further and approach the ideal limit, characterized by a Mandel Q parameter of Q = —1. Furthermore we show how this noise reduction via nonlinearities can be combined with a regular pump mechanism, which recently has been sugessted as a way to generate sub—Poissonian light. It turns out that in certain configurations the effect of both methods can be combined. Finally we show how this nonclassical behaviour is also reflected in a reduction of the output intensity power spectra below the shot noise level.
According to the exact solution of a two-level atomic system interacting with a single-mode field in a cavity and including a pumping mechanism, sub-Poissonian photon statistics can be generated either by regular pumping or by resonance absorption of the lower level. When the atomic lifetime is much smaller than the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\gg}1), which corresponds to a usual laser system, the sub-Poissonian photon distribution can be obtained only by regular pumping. On the other hand, if the atomic lifetime is comparable with the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\le}1), the sub-Poissonian photon distribution can be generated by both mechanisms.