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Journal of Modern Optics

Quantum control of Bose–Einstein condensates using Feshbach resonance

Seok Jin Choi, N. P. Bigelow

Published Feb 28, 2005• 5 citations
Publisher

Abstract

We present a method to execute quantum control in Bose–Einstein condensates via Feshbach resonance. By switching an initially positive scattering length to zero, it is possible to generate a breather mode that results from quantum interference. The density oscillation is accompanied by a periodic enhancement of the quantum mechanical squeezing in the amplitude quadrature.

DOI
10.1080/09500340512331323475

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We present a method to execute quantum control in Bose–Einstein condensates via Feshbach resonance. By switching an initially positive scattering length to zero, it is possible to generate a breather mode that results from quantum interference. The density oscillation is accompanied by a periodic enhancement of the quantum mechanical squeezing in the amplitude quadrature.
An experimentally realizable scheme of periodic sign-changing modulation of the scattering length is proposed for Bose-Einstein condensates similar to dispersion-management schemes in fiber optics. Because of controlling the scattering length via the Feshbach resonance, the scheme is named Feshbach-resonance management. The modulational-instability analysis of the quasiuniform condensate driven by this scheme leads to an analog of the Kronig-Penney model. The ensuing stable localized structures are found. These include breathers, which oscillate between the Thomas-Fermi and Gaussian configuration, or may be similar to the 2-soliton state of the nonlinear Schrödinger equation, and a nearly static state ("odd soliton") with a nested dark soliton. An overall phase diagram for breathers is constructed, and full stability of the odd solitons is numerically established.
We discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate induced by a sudden change in the scattering length from a large positive to a small negative value. We also consider the condensate dynamics that results from a single pulse in the magnetic field, due to which the scattering length is rapidly increased from zero to a large value and then after some time rapidly decreased again to its initial value. We focus primarily on the consequences of the quantum evaporation process on the dynamics of the Bose-Einstein condensate, but also discuss the effects of atom-molecule coherence.
We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.
We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially noninteracting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalism.