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Journal of Experimental and Theoretical Physics Letters

Giant optical nonlinearity of an atomic Bose-Einstein condensate and low-threshold bistability

N. N. Rosanov, В. А. Смирнов

Published Jul 1, 2005• 1 citation
Publisher

Abstract

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.

DOI
10.1134/1.2045333

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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.
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.
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Nonlinear coherent modes are the collective states of trapped Bose atoms, corresponding to different energy levels. These modes can be created starting from the ground-state condensate that can be excited by means of a resonant alternating field. A thorough theory for the resonant excitation of the coherent modes is presented. The necessary and sufficient conditions for the feasibility of this process are found. Temporal behavior of fractional populations and of relative phases exhibits dynamic critical phenomena on a critical line of the parametric manifold. The origin of these critical phenomena is elucidated by analyzing the structure of the phase space. An atomic cloud, containing the coherent modes, possesses several interesting features, such as interference patterns, interference current, spin squeezing, and massive entanglement. The developed theory suggests a generalization of resonant effects in optics to nonlinear systems of Bose-condensed atoms.
Systems with atomic coherence can have interesting optical properties, such as non-absorbing resonances or an index of refraction at a frequency of vanishing absorption many orders of magnitude larger than is otherwise possible. This chapter shows that phaseonium can display a large nonlinear Kerr-effect near the atomic resonance while retaining complete transparency. Near resonance nonlinearities are usually accompanied by a large absorption of the medium. A three-level atom is initially prepared in a coherent superposition of the two lower levels. This can be achieved for example by a coherent pulse excitation. The Kerr-coefficient is defined as the coefficient of the first nonlinear correction to the index of refraction.