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arXiv:cond-mat/0106611 · Laser Physics

Symmetries and Decoherence of Two-Component Confined Atomic Clouds: Study of the Atomic Echo in the two-component Bose-Einstein Condensate

Anatoly B. Kuklov, N. Chensincki, Joseph L. Birman

Published Jun 28, 2001• 2 citations
arXivHTMLPDF

Abstract

Implications of the internal symmetries on the dynamics of the trapped two-component atomic vapors are discussed. In the cases of $^{87}$Rb (bosons) as well as of $^{40}$K (fermions) trapped in the two hyperfine states, the intrinsic $su(2)$ symmetry can be realized with a very good precision. Such a symmetry protects the global operators, which are the generators of the symmetry, from any decoherence. The case of boson-fermion mixture is discussed as well. The role of external factors, breaking the symmetry, in inducing the decoherence of the global operators is considered. It is shown that, the loss of the correlations is not faster than the rates of the induced heating or losses, provided the noise is characterized by short correlation length. The case of the extrinsic long-ranged fluctuations is also considered. Intrinsic mechanisms of decoherence of the correlators of the condensate operators of the two-component condensate are analyzed. The atomic echo is discussed as a test for the reversibility of the phase diffusion effect. The intensity and the profile of the multiple echo are calculated numerically as well as analytically.

DOI
10.48550/arxiv.cond-mat/0106611

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Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
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A binary mixture of interacting Bose-Einstein condensates (BEC) in the presence of fragmentation-driving external lattice potentials forms two interdependent mean-field lattices made of each component. These effective mean-field lattices, like ordinary optical lattices, can induce additional fragmentation and phase coherence loss of BECs between lattice sites. In this study, we consider the nonequilibrium dynamics of two hyperfine states of one-dimensional Bose-Einstein condensates, subjected to state-dependent optical lattices. Our numerical calculations using the truncated Wigner approximation (TWA) show that phase coherence in a mixture of two-component BECs can be lost not just by optical lattices, but by mean-field lattices gradually formed by other components, and we reveal that such an effect of internal mean-field lattices, however, is limited, contrary to external optical lattices, in regard to phase decoherence.