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Laser Physics Letters

Quantum theory of laser soliton

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

Published Nov 26, 2019• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ab5645

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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.
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.
Abstract The Heisenberg–Langevin equation for a spatial laser soliton is constructed within consistent quantum electrodynamics. Canonical variables for the generation field and for a two-level material medium consisting of a medium that generates a laser and a medium that realizes saturable absorption are discussed in detail. It is assumed that the laser generation evolves in time much more slowly than the atomic medium. This makes it possible to apply the adiabatic approximation and construct a closed equation for the amplitude of the laser field. The equation has been derived paying special attention to the definition of Langevin sources, which play a decisive role in the formation of quantum statistical features of solitons. To ensure the observation procedure of the quantum squeezing of a soliton, the laser generation has been synchronized by applying an external weak electromagnetic field.
In the framework of consistent quantum electrodynamics, derived is the Heisenberg-Langevin equation for spatial laser soliton. Discussed are in detail the canonical variables for the generation field and for a material two-level medium consisting of a medium that forms laser generation and saturated absorption medium. It is assumed that laser generation evolves in time much slower than the atomic medium. This makes it possible to apply adiabatic approximation and construct a closed equation for the amplitude of the laser field. When deriving the equation special attention is paid to the definition of Langevin sources that play a decisive role in the formation of quantum statistical features of solitons. In order to provide a procedure of observation of soliton quantum squeezing, synchronization of laser generation by an external weak electromagnetic beam is introduced.
Abstract An analysis of weak quantum fluctuations of a spatial soliton in a laser with fast saturable absorption in the possible presence of weak holding radiation is carried out. In the c-number representation with adiabatic elimination of atomic variables, the master Heisenberg–Langevin equation is linearized in the vicinity of a stable classical (in the absence of fluctuations) laser soliton. The linearized equation’s solution is constructed on the basis of the spectral expansion in eigenfunctions of the evolution operator unperturbed by fluctuations. The discrete spectrum of this operator is found and used to determine the mean values of the squared fluctuations of the coordinates of the soliton center and its momentum. A comparison is made with similar fluctuations in driven interferometers with Kerr non-linearity of the medium.
We investigate the quantum squeezing of slow-light solitons generated in a $\mathrm{\ensuremath{\Lambda}}$-shaped three-level atomic system working under condition of electromagnetically induced transparency (EIT). Starting from the Heisenberg-Langevin and Maxwell equations governing the quantum dynamics of atoms and probe laser field, we derive a quantum nonlinear Schr\"odinger equation controlling the evolution of the probe-field envelope. By using a direct perturbation approach to diagonalize the effective Hamiltonian (where the atomic variables have been eliminated), we carry out a detailed calculation on the quantum fluctuations of a slow-light soliton, expanded as a superposition of the complete and orthonormalized set of eigenfunctions obtained by solving the Bogoliubov-de Gennes (BdG) equations describing the quantum fluctuations. We show that due to the giant Kerr nonlinearity contributed from the EIT effect, significant quantum squeezing of the slow-light soliton can be realized within a short propagation distance. The results reported here are helpful for understanding the quantum property of slow-light solitons and for realizing light squeezing via EIT in cold atomic gases experimentally.