A theory of the quantum-beat laser is developed using a general Fokker-Planck approach. An explicit expression for the diffusion coefficient for the relative phase angle of the two modes is derived. It is shown that the diffusion coefficient can vanish under certain conditions.
We present a comprehensive quantum theory of correlated-emission lasers (CEL's) in a combination-mode approach, which is valid for both the quantum-beat laser and the CEL with injected atomic coherence. We first show that, under certain conditions, the linear master equation of the CEL's breaks down into two uncoupled equations in the combination modes, which are linear combinations of two CEL modes. One combination mode that is above threshold represents the average phase and the average amplitude of two CEL modes (called the sum mode), whereas the other that is below threshold represents the relative phase and the relative amplitude of the two CEL modes (called the relative mode). When the relative mode is in its vacuum state, the normally ordered variances of two Hermitian operators corresponding, respectively, to the relative phase and the relative amplitude vanish. Through deriving a nonlinear master equation for the CEL with injected atomic coherence in the combination modes, we show how a set of proper initial atomic conditions can keep the relative mode in its vacuum state. We obtain the Glauber P functions, the mean photon numbers, and the photon-number variances in both the combination modes and the CEL modes, and find the mode pullings of the CEL's and the natural linewidth of the sum mode. We also show a correspondence between the vacuum state of the relative mode and the vanishing of the relative-phase diffusion coefficient.
We present the nonlinear theory for lasing without population inversion in the degenerate \ensuremath{\Lambda}-type quantum-beam laser by using the density-operator method. The master equation for the degenerate quantum-beat laser is derived, from which the equation of motion for the mean photon number is obtained. The conditions for lasing without population inversion are discussed, which are the same for linear and nonlinear theories. The corresponding Fokker-Planck equation is obtained, and the possibility of diffusion coefficient reduction is discussed.
We calculate the phase-difference and phase-sum fluctuations of the quantum-beat laser, using the nonlinear model of Bergou et al. [Phys. Rev. A 38, 754 (1988)], and also making use of the phase operators defined by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)]. We found a vanishing phase-difference diffusion constant, in agreement with Bergou et al. However, the present formalism is more general, and includes shot noise as well as saturation effects for the relative and sum phase fluctuations.
A quantum theory of a \ensuremath{\Lambda}-type three-level single-mode quantum-beat laser with injected atomic coherences and with an external microwave field, which coherently drives the lower two nearly degenerate levels, is studied. A master equation for the field-density operator and the photon statistics is derived. The laser operation is analyzed in terms of the coefficients of the Fokker-Planck equation of the laser field. Noninversion lasing is found in both cases: without and with injected atomic coherences. At the same time, in the latter case large quantum-noise reduction is found, and for particular initial parameter choices the laser field is very near to a coherent state with exactly Poissonian photon-number distribution and near-Poissonian phase distribution.