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Journal of Experimental and Theoretical Physics

Absorption-induced optical bistability and dissipative solitons in a BEC interferometer

Nikolay N. Rosanov, В. А. Смирнов, Sergey V. Fedorov

Published May 1, 2006• 6 citations
Publisher

Abstract

A model of the absorption-induced nonlinear response of an atomic Bose-Einstein condensate driven by a weak resonant laser beam is presented. The model takes into account the slow BEC decay due to spontaneous emission and magnetic-trap loss by binary collisions, as well as compensation of the decay by injection of ground-state atoms into the trap. It is shown that the nonlinear response is much stronger than in other nonlinear optical media. For a BEC interferometer driven by a monochromatic beam, the threshold intensity for hysteretic switching is found, and dissipative spatial solitons are demonstrated.

DOI
10.1134/s1063776106050013

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A model of the absorption-induced nonlinear response of an atomic Bose-Einstein condensate driven by a weak resonant laser beam is presented. The model takes into account the slow BEC decay due to spontaneous emission and magnetic-trap loss by binary collisions, as well as compensation of the decay by injection of ground-state atoms into the trap. It is shown that the nonlinear response is much stronger than in other nonlinear optical media. For a BEC interferometer driven by a monochromatic beam, the threshold intensity for hysteretic switching is found, and dissipative spatial solitons are demonstrated.
The polarization of an atomic Bose-Einstein condensate weakly excited by laser radiation at a nearly resonance frequency is determined. The coefficient of nonlinearity (cubic in field) in the refractive index of the condensate is calculated for the slow decay mode due to the spontaneous emission of excited atoms, as well as for the stationary mode, when the loss of atoms is compensated by the injection of atoms into the trap. In both cases, the cubic nonlinearity coefficients of the condensate are several orders of magnitude larger than the corresponding values for known nonlinear media. The conditions for observing hysteresis in an interferometer containing the condensate in the stationary state in the presence of an incident laser beam are specified.
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.
We present a theoretical analysis of a Bose-Einstein condensate (BEC) enclosed in an optical cavity driven by a modulated external laser beam where the cavity field variable is adiabatically eliminated. The modulation of the amplitude of the pump laser induces nonlinear resonances and the widespread presence of chaotic oscillations even when repulsive atom-atom interactions are negligible. Close to resonance, varying the modulation amplitude by just a few percent causes abrupt and erratic changes to the output laser intensity with peak power increasing by almost an order of magnitude. We also use a simplified model of the BEC-cavity system that considers only a small number of spatial modes of the BEC to show that, despite the disruptive presence of a modulation in the pump beam, the system can still be considered to be low-dimensional.
We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N = N(min), necessary for the existence of solitons. The VA predicts N(min) very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N = N(min) are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A, the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.