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arXiv:0809.5161 · Journal of Physics B Atomic Molecular and Optical Physics

A perturbative approach to inelastic collisions in a Bose–Einstein condensate

Robert B. Mann, Matthew B. Young, Ivette Fuentes

Published Apr 11, 2011• 1 citation
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Abstract

It has recently been discovered that for certain rates of mode-exchange collisions analytic solutions can be found for a Hamiltonian describing the two-mode Bose-Einstein condensate. We proceed to study the behavior of the system using perturbation theory if the coupling constants only approximately match these parameter constraints. We find that the model is robust to such perturbations. We study the effects of degeneracy on the perturbations and find that the induced changes differ greatly from the non-degenerate case. We also model inelastic collisions that result in particle loss or condensate decay as external perturbations and use this formalism to examine the effects of three-body recombination and background collisions.

DOI
10.1088/0953-4075/44/8/085301

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It has recently been discovered that for certain rates of mode-exchange collisions analytic solutions can be found for a Hamiltonian describing the two-mode Bose-Einstein condensate. We proceed to study the behavior of the system using perturbation theory if the coupling constants only approximately match these parameter constraints. We find that the model is robust to such perturbations. We study the effects of degeneracy on the perturbations and find that the induced changes differ greatly from the non-degenerate case. We also model inelastic collisions that result in particle loss or condensate decay as external perturbations and use this formalism to examine the effects of three-body recombination and background collisions.
Mode-exchange collisions occur in multimode Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, little is known about mode-exchange collisions in the case when particles do not escape the trap. We show that these processes are relevant in quantum properties of the system such as the evolution of the relative population, the self-trapping effect, and the probability distribution of particles. Surprisingly, including mode-exchange terms in the model of the two-mode condensate allows for an exact analytical solution. Using this solution, we show that collisions favor the generation of entanglement between the modes of the condensate.
We study the effects of three-body collisions in the physical properties of a two-mode Bose-Einstein condensate. The model introduced here includes two-body and three-body elastic and mode-exchange collisions and can be solved analytically. We will use this fact to show that three-body interactions can produce drastic changes in the probability distribution of the ground state and the dynamics of the relative population. In particular, we find that three-body interactions under certain circumstances may inhibit the collapse of the relative population.
In this paper, we study the stability of three-dimensional Bose-Einstein condensates of finite temperatures at which both elastic and inelastic collisions are taken into account. The modeled governing Gross-Pitaevski equation reveals inclusion of both real and imaginary components in the nonlinear terms. We find the stability region for a wide range of two- and three-body interaction terms with the inclusion of both gain and loss effects by using the Jacobian matrix. We investigate the stability of the system for possible different state of those cases. The stability properties of three-dimensional condensates are strongly altered by tuning the gain rate of their elastic collisions. These strong losses impose severe limitations for using Feshbach resonances. We finally sustain our semi analytical findings with the results of inclusive numerical simulations.
Atomic Bose-Einstein condensates are singular forms of matter with the coherence between constituent atoms as a defining characteristic. Although this viewpoint is increasingly validated through experimental findings, the mechanisms behind the observed losses are still understood with classical recombinant collision arguments between particles within the condensate itself. By incorporating a general interparticle interaction into the Hamiltonian, a coherent decay rate can be obtained, thus providing a direct link between the observed losses and the microscopic two-body parameters. Appearing in the lifetime, the interaction strength, lambda, is expressed as lambda=8 pia/(1-delta), where the small parameter delta is obtained from a fit to experimental loss data. Most importantly, the lowest order rate exhibits a novel density dependence (rho{3/2}) that can be identified in low temperature tests.
Attractive Bose-Einstein condensates are investigated with numerical continuation methods capturing stationary solutions of the Gross-Pitaevskii equation. The branches of stable (elliptic) and unstable (hyperbolic) solutions are found to meet at a critical particle number through a generic Hamiltonian saddle node bifurcation. The condensate decay rates corresponding to macroscopic quantum tunneling, two and three body inelastic collisions, and thermally induced collapse are computed from the exact numerical solutions. These rates show experimentally significant differences with previously published rates. Universal scaling laws stemming from the bifurcation are derived.
We studied spin-dependent two-body inelastic collisions in F=2F=2F=2 87Rb^{87}\text{R}\text{b}87Rb Bose-Einstein condensates both experimentally and theoretically. The 87Rb^{87}\text{R}\text{b}87Rb condensates were confined in an optical trap and selectively prepared in various spin states in the F=2F=2F=2 manifold at a magnetic field of 3.0 G. The measured atom loss rates depend on the spin states of colliding atoms. We measured two fundamental loss coefficients for two-body inelastic collisions with total spins of 0 and 2. The loss coefficients determine the loss rates of all the spin pairs. The experimental results for mixtures of all spin combinations are in good agreement with numerical solutions of the Gross-Pitaevskii equations that include the effect of a magnetic field gradient.