arXiv:1011.3211 · Chinese Physics B

Phase diffusion of a two-component Bose–Einstein condensates: exact and short-time solutions for arbitrary coherent spin state

Jin Guang-Ri, Wang Bo-Bo, Lü Yan-Wu

Published Feb 1, 2010• 5 citations

Abstract

We investigate phase diffusion of a two-component Bose-Einstein condensates prepared initially in arbitrary coherent spin state $|θ_0,ϕ_0\rangle$. Analytical expression of the phase-diffusion time is presented for $θ_0\neqπ/2$ case. In comparison with the symmetrical case (i.e., $θ_0=π/2$), we find that the diffusion process becomes slowly due to the reduced atom number variance.

DOI: 10.1088/1674-1056/19/2/020502

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arXiv:1011.3211 · Chinese Physics B

Phase diffusion of a two-component Bose–Einstein condensates: exact and short-time solutions for arbitrary coherent spin state

Jin Guang-Ri, Wang Bo-Bo, Lü Yan-Wu

Published Feb 1, 2010• 5 citations

arXiv HTML PDF

Abstract

We investigate phase diffusion of a two-component Bose-Einstein condensates prepared initially in arbitrary coherent spin state

|θ_0,ϕ_0\rangle

. Analytical expression of the phase-diffusion time is presented for

θ_0\neqπ/2

case. In comparison with the symmetrical case (i.e.,

θ_0=π/2

), we find that the diffusion process becomes slowly due to the reduced atom number variance.

DOI: 10.1088/1674-1056/19/2/020502

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arXiv:cond-mat/0302464Physical Review AJul 30, 200318 citations

We investigate phase diffusion of a two-component Bose-Einstein condensates prepared initially in arbitrary coherent spin state

|θ_0,ϕ_0\rangle

. Analytical expression of the phase-diffusion time is presented for

θ_0\neqπ/2

case. In comparison with the symmetrical case (i.e.,

θ_0=π/2

), we find that the diffusion process becomes slowly due to the reduced atom number variance.

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.

(N),

the total magnetization

(\mathcal{M}),

and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recovering the two broken continuous symmetries [U(1) and SO(2)] when N and

\mathcal{M}

are conserved, as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with antiferromagnetic interactions.