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Physical Review A

Dynamic stability of dressed condensate mixtures

S. D. Jenkins, T. A. B. Kennedy

Published Nov 17, 2003• 44 citations
Publisher

Abstract

We analyze the dynamical stability of common spatial, or breathe-together, modes for a system of two trapped interacting Bose-Einstein condensates, when the condensates are resonantly coupled by a strong driving field. We show analytically that the dynamical stability is governed by a set of dressed atom collision parameters, and that the driving field typically destabilizes breathe-together modes which are stable in the absence of driving and vice versa. By means of numerical solutions we illustrate the consequences of this phenomenon for a number of interacting condensates consisting of pairs of ground hyperfine states of both sodium and rubidium.

DOI
10.1103/physreva.68.053607

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We analyze the dynamical stability of common spatial, or breathe-together, modes for a system of two trapped interacting Bose-Einstein condensates, when the condensates are resonantly coupled by a strong driving field. We show analytically that the dynamical stability is governed by a set of dressed atom collision parameters, and that the driving field typically destabilizes breathe-together modes which are stable in the absence of driving and vice versa. By means of numerical solutions we illustrate the consequences of this phenomenon for a number of interacting condensates consisting of pairs of ground hyperfine states of both sodium and rubidium.
We consider a collection of atoms prepared in a Bose-Einstein condensate which interact via two-body elastic collisions. A resonant driving field couples two internal states which together constitute an effective spin 1/2 system for each atom, and from which a total spin for the gas can be defined. It is shown that in the limit of strong driving, the system dynamics reduces to a mechanism for spin squeezing similar to that of a recent proposal for undriven condensates. However, we find that the conditions for spatial stability in our driven system are complementary to those of the undriven system. Reasons for this difference, associated with the physics of dressed atom collisions, are discussed along with conditions for preparing and observing the spin squeezed state.
Bose-Einstein condensates with attractive interatomic interactions undergo collective collapse beyond a critical number. We show theoretically that if the low-lying collective modes of the condensate are excited, the radial breathing mode further destabilizes the condensate. Remarkably, excitation of the quadrupolar surface mode causes the condensate to become more stable, imparting quasiangular momentum to it. A significantly larger number of atoms may then occupy the condensate. Efforts are under way for the experimental realization of these effects.
We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.
The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can transform two atoms into a molecule and vice versa. We find an interesting oscillation of the number of atoms and molecules for a BEC of fixed mass. This oscillation is a consequence of continuous transformation in the condensate of two atoms into a molecule and vice versa. For the study of collapse an absorptive contact interaction and an imaginary quartic three-body recombination term are included in the GP equation. It is possible to have a collapse of one or both components when one or more of the nonlinear terms in the GP equation are attractive in nature, respectively.
We study the dynamics of two Bose–Einstein condensates (BECs) tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.