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Physical Review A

Sub-Poissonian statistics in phase-sensitive linear light amplifiers and absorbers

M.‐A. Dupertuis, Stig Stenholm

Published Feb 1, 1988• 16 citations
Publisher

Abstract

We study the photon statistics at the output of phase-sensitive amplifiers and absorbers. It is argued that the photon statistics is independent of a detailed description of the rigged energy reservoir; therefore, we use a simple phenomenological model including only three parameters. The mean number of photons and the Mandel parameter Q at the output are studied as a function of the reservoir state and the input state. General conditions for sub-Poissonian output light are stated with use of three characteristic moments of the input state. We find an interesting intermediate regime where the device can have a sub-Poissonian output for a certain class of super-Poissonian input states.

DOI
10.1103/physreva.37.1226

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We study the photon statistics at the output of phase-sensitive amplifiers and absorbers. It is argued that the photon statistics is independent of a detailed description of the rigged energy reservoir; therefore, we use a simple phenomenological model including only three parameters. The mean number of photons and the Mandel parameter Q at the output are studied as a function of the reservoir state and the input state. General conditions for sub-Poissonian output light are stated with use of three characteristic moments of the input state. We find an interesting intermediate regime where the device can have a sub-Poissonian output for a certain class of super-Poissonian input states.
A parameteric study was performed of the sub-Poissonian photon statistics and higher-order squeezing characteristics of Bernouilli states undergoing a linear amplification process. The necessary and sufficient conditions on the amplifier gain under which the output light exhibits sub-Poissonian photon statistics or squeezing were compared with exact numerical results, and good agreement was obtained. On the other hand, it was shown that Bernouilli states exhibit higher-order squeezing for some parameter ranges. The degree of higher-order squeezing decreases, and its duration becomes shorter, as the phase of the Bernouilli state increases.
We make a comparison between the necessary and sufficient conditions on the gain of the linear amplifier under which the light output exhibits sub-Poissonian photon statistics or squeezing and exact numerical results, obtained by solving the master equation by means of matrix procedures, and find good agreement. We find numerically that higher-order squeezing persists in a region in which sub-Poissonian statistics and second-order squeezing have already disappeared, for certain parameter ranges of input binomial states.
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 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.
The necessary and sufficient conditions on the gain of the linear amplifier are determined under which the light output exhibits sub-Poissonian photon statistics or squeezing. It is found that for these effects the intensity gain must not exceed 2 under any circumstances. It is also shown that there exists a weaker sufficiency condition on the gain above which all nonclassical features of the field disappear. This suggests the possibility that other quantum effects may persist in the intermediate, still unexplored, domain of operation of the amplifier.
It has long been known that amplification will degrade an optical signal and will rapidly destroy any intrinsically quantum features that may have been associated with the input. However, devices that exhibit squeezed fluctuations in the gain or loss medium can reduce the detrimental effects of the inevitable amplifier noise. This makes it possible to retain nonclassical features (in particular squeezing) at higher levels of gain than is possible in conventional devices. In this paper we study the effect of these amplifiers on the photon-number fluctuations. We find that, for suitable inputs, phase-sensitive amplifiers can reduce the tendency for the photon-number distribution to spread and allow us to retain sub-Poissonian statistics at a higher level of gain than is possible in conventional devices.