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arXiv:0904.2121

Rapid phase-diffusion between atomic and molecular Bose-Einstein condensates

Igor Tikhonenkov, Amichay Vardi

Published Apr 14, 2009• 0 citations
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Abstract

We study the collisional loss of atom-molecule coherence after coherently dissociating a small fraction of a molecular Bose-Einstein condensate into atoms. The obtained $n$-atoms states are two-atom (SU(1,1)) coherent states with number variance $Δn\propto n$ compared to $Δn\propto \sqrt{n}$ for the spin (SU(2)) coherent states formed by coherent splitting of an atomic condensate. Consequently, the Lorentzian atom-molecule phase-diffusion is faster than the Gaussian phase-diffusion between separated atomic condensates, by a $\sqrt{n}$ factor.

DOI
10.48550/arxiv.0904.2121

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We investigate phase diffusion of a two-component Bose-Einstein condensates prepared initially in arbitrary coherent spin state ∣θ0,ϕ0⟩|θ_0,ϕ_0\rangle∣θ0​,ϕ0​⟩. Analytical expression of the phase-diffusion time is presented for θ0≠π/2θ_0\neqπ/2θ0​=π/2 case. In comparison with the symmetrical case (i.e., θ0=π/2θ_0=π/2θ0​=π/2), we find that the diffusion process becomes slowly due to the reduced atom number variance.
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We investigate the creation of a relative phase between two Bose-Einstein condensates, initially in number states, by detection of atoms and show how the system approaches a coherent state. Two very distinct time scales are found: one for the creation of the interference is of the order of the detection time for a few single atoms and another, for the preparation of coherent states, of the order of the detection time for a significant fraction of the total number of atoms. Approximate analytic solutions are derived and compared with exact numerical results.