Dynamical Response of a Bose-Einstein Condensate to a Discontinuous Change in Internal State

Abstract

A two-photon transition is used to convert an arbitrary fraction of the 87 Rb atoms in a |F = 1, m f = −1 condensate to the |F = 2, m f = 1 state. Transferring the entire population imposes a discontinuous change on the condensate's mean-field repulsion, which leaves a residual ringing in the condensate width. A calculation based on Gross-Pitaevskii theory agrees well with the observed behavior, and from the comparison we obtain the ratio of the intraspecies scattering lengths for the two states, a |1,−1 /a |2,1 =1.062(12). [5], and limited condensate number [6]. There has been excellent quantitative agreement between these experiments and theory, made possible by both experimental advances and the fact that the interactions can be modeled relatively simply. Despite complicated interatomic potentials, the mean-field interaction in condensates is well-characterized by a single parameter, the s-wave scattering length a. Previous quantitative experiments on interactions have all been done using singlecomponent condensates with a constant value of a, but several authors have proposed using external optical or magnetic fields to shift the mean-field interaction by perturbing the interatomic potential [7][8][9].We present a method for the creation of condensate mixtures using radiofrequency (rf) and microwave fields. We are able to transfer abruptly a trapped condensate of one hyperfine state into a coherent superposition of two trapped hyperfine states, and then watch the subsequent dynamical behavior. This approach makes possible a variety of two-species BEC studies. In this paper, we examine quantitatively one special case, in which all condensate atoms are converted from one state to another. Since these two states have slightly different values of a, the sudden change in self-interaction gives rise to oscillatory spatial behavior of the condensate wave function [10]. The scattering length ratio can be extracted from a model using analytical equations of motion for the condensate widths [10-12] based on Gross-Pitaevskii theory.The first demonstration of a binary mixture of condensates by Myatt et al.[13] produced overlapping condensates of the 5S 1/2 |F = 1, m f = −1 and |F = 2, m f = 2 states of 87 Rb. The ratio of the magnetic moments of these states is 1:2, so the condensates experience different potentials in a magnetic trap and are displaced unequally from the trap center by gravity. Due to an accidental coincidence between the singlet and triplet scattering lengths of 87 Rb, collisional loss is reduced and any mixture of spin states will be relatively long-lived [13][14][15]. Here, we use mixtures of |1, −1 and |2, 1 states, which possess several advantages. First, these two states have essentially identical magnetic moments, and hence feel identical confining potentials. Second, one can conveniently and quickly change atoms from the |1, −1 state to the |2, 1 state by a two-photon transition (microwave plus rf). Finally, we can selectively image the different components using appropriately tuned lasers.The ...

Spin current generation and relaxation in a quenched spin-orbit-coupled Bose-Einstein condensate

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