Quantum theory of laser soliton

Abstract

The Heisenberg-Langevin equation for a spatial laser soliton in a wide-aperture laser with saturable absorption is constructed within the framework of consistent quantum electrodynamics. We discuss in detail the canonical variables for the generation field and the material two-level medium, consisting of centres providing amplification and absorption. It is assumed that laser generation evolves in time much more slowly than an atomic media. This assumption makes it possible to apply the adiabatic approximation and construct a closed equation for the amplitude of a laser field. Much attention is paid to the formulation of Langevin sources when deriving the equation since they play a decisive role in the formation of solitons' quantum statistical features. To provide an appropriate procedure for observing the quantum squeezing of a soliton, synchronization of laser generation by an external weak electromagnetic field is considered. Here we also present the results of the analysis of a classical laser soliton (neglecting the quantum fluctuations), which serves as the basis for further consideration of quantum effects.

Quantum field fluctuations in the vicinity of a classical laser soliton

“…We proceed from the equation for the amplitude of the electromagnetic field E in the c-number representation obtained in [17] and [18] for a wide-aperture laser with the adiabatic elimination of atomic variables. For a slab laser (transverse one-dimensional scheme) in dimensionless variables, it has the form…”

“…We will consider only stationary regimes corresponding to the mode-locking regime; the range of the scheme parameters in which this regime is stable is given in [17].…”

“…In a series of works [13][14][15] (see also [16]), a theory of such fluctuations is developed for spatial dissipative solitons in driven wide-aperture interferometers with Kerr non-linearity. Finally, the master Heisenberg-Langevin equation for solitons in lasers with saturable absorber was derived in [17] and [18]. In this paper, we consider weak quantum field fluctuations in the vicinity of a stable classical soliton (in the absence of noise) in a wide-aperture laser with fast saturable absorption, including the case of the presence or absence of weak holding radiation.…”

“…In this paper, we consider weak quantum field fluctuations in the vicinity of a stable classical soliton (in the absence of noise) in a wide-aperture laser with fast saturable absorption, including the case of the presence or absence of weak holding radiation. The starting point is the master Heisenberg-Langevin equation derived in [17] and [18]. It is challenging to solve this stochastic non-linear equation directly, so, for this purpose, we use the master equation, linearized on the basis of the spectral expansion in eigenfunctions of the evolution operator unperturbed by fluctuations, see [13][14][15].…”