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Chinese Physics Letters

Statistical Properties of Lasers with Sub-Poissonian Pump

Ming Yuan Yang, Cao Li, Wu Da-Jin, Zaiguang Li

Published Sep 1, 1998• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0256-307x/15/9/010

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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 photon-number distribution of lasers generated via pump-noise suppression is derived in the photon-number representation. The derivation shows that the negative probability emerging in the calculation of the photon-number distribution in the photon-number representation is not caused by the representation itself but by the truncation of the master equation. Here without truncating the master equation we derive the characteristic function and the distribution function of the photon-number distribution of the laser system with regular pump and with spontaneous atomic decays being eliminated. It is convenient to use the characteristic function to calculate any order of the moment of the photon-number distribution. Such a method can be used to some more general cases, in which the laser system has imperfectly regular pump and the spontaneous atomic decays are also considered.
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.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.
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.
Theoretical and experimental results of investigations into the quantum noise of multimode laser radiation are considered. The feasibility of generating light with a photon-number-squeezed (sub-Poissonian) photon distribution by a multimode laser with a homogeneously broadened line is analyzed. The conditions of noisy and noiseless (regular) pumping are considered. Photon-number fluctuations of the net laser radiation summed over all generated modes are calculated in the approximation of equidistant equal modes, as are photon-number fluctuations in an individual mode inside and outside the resonator. Output-radiation noise spectra and photon-number fluctuations are calculated for solid-state (neodymium glass, Nd:YAG) and semiconductor lasers. Theoretical results are compared with a number of experimental data obtained for semiconductor lasers in recent years.
We show that the injection of an external field in a laser helps to improve amplitude squeezing and sub-Poissonian light generation close to threshold, but spoils quantum noise reduction for very high pumping rates. A general nonlinear theory is developed for the resonant case (no detunings), without any assumption on the relative magnitudes of field and atomic decay constants, thus encompassing a large class of lasers. Several possible pumping schemes are accommodated, ranging from regular to Poissonian. We carry out a detailed stability analysis of the general equations of motion, relating it to the noise-reduction problem. Both the photon-number variance inside the cavity and the homodyne spectra of the output are discussed.