Coherent states, phase states, and condensed states

Igor Tikhonenkov, Amichay Vardi

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.

Brian P. Anderson

Xubing Tang, Fan Hong‐Yi

For studying the interference between two Bose–Einstein condensates we introduce the atomic coherent state (ACS) in the Schwinger bosonic realization along with the phase operator to directly calculate the interference pattern with steady relative phase cos ϕ. Eigenstates of the density operator of condensates are classified as ACS is also demonstrated. The entangled state representation is used in some calculations.

Monique Combescure, Didier Robert

Igor Tikhonenkov, Amichay Vardi

We propose to implement a sub-shot-noise matter-wave interferometer via the stimulated dissociation of a molecular Bose-Einstein condensate and study the collisional loss of atom-molecule coherence during its phase-acquisition time. The obtained $n$-atom states are two-atom [SU(1,1)] coherent states with number variance $\ensuremath{\Delta}n\ensuremath{\propto}n$ compared to $\ensuremath{\Delta}n\ensuremath{\propto}\sqrt{n}$ 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.