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Modern Physics Letters B

ATOM-OPTICAL BISTABILITY IN TRAPPED BOSE–EINSTEIN CONDENSATES

Zeng‐Bing Chen

Published Jan 10, 2000• 5 citations
Publisher

Abstract

The close similarities between nonlinear optics and nonlinear atom optics motivate us to demonstrate the possibility of atom-optical bistability for a trapped Bose–Einstein condensate. Driven by an intense, coherent input matter wave, the trapped Bose–Einstein condensate might display the bistability when the Born–Markov master equation for the condensate mode is used. The atom-optical bistability provides a way to control atom lasers with atom lasers.

DOI
10.1142/s0217984900000069

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The close similarities between nonlinear optics and nonlinear atom optics motivate us to demonstrate the possibility of atom-optical bistability for a trapped Bose–Einstein condensate. Driven by an intense, coherent input matter wave, the trapped Bose–Einstein condensate might display the bistability when the Born–Markov master equation for the condensate mode is used. The atom-optical bistability provides a way to control atom lasers with atom lasers.
Abstract By pumping energy into a trapped Bose-Einstein condensate it is possible to generate nonlinear coherent modes representing non-ground-state condensates. A Bose-condensed system of trapped atoms with nonlinear coherent modes is analogous to a finite-level atom considered in optics which can be excited by applying external fields. The excitation of finite-level atoms produces a variety of optical phenomena. In the similar way, the generation of nonlinear coherent modes in a trapped condensate results in many phenomena studied in what is termed atom optics. For example, there occur such effects as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, and a dynamic transition between Rabi and Josephson regimes. The possibility of creating mesoscopic entangled states of trapped atoms and entanglement production by atomic states in optical lattices are studied.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.
We consider a two-component Bose–Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser also excites the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity–condensate system is developed under the discrete mode approximation (DMA), while matter–field coupling has been considered beyond the rotating wave approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter–field coupling strength.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schrodinger equation (also called the Gross-Pitaevskii equation), to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.