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arXiv:1110.1956 · Progress in optical science and photonics

Temporal Quantum Fluctuations in the Fringe-Visibility of Atom Interferometers with Interacting Bose-Einstein Condensate

Doron Cohen, Amichay Vardi

Published Jan 1, 2012• 0 citations
arXivHTMLPDF
DOI
10.1007/10091_2012_2

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The role of source cloud spatial coherence in a Mach-Zehnder-type atom interferometer is experimentally investigated. The visibility and contrast of a Bose-Einstein condensate (BEC) and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100100%100 nearly independent of $\ensuremath{\pi}$ pulse efficiency, while thermal sources have fringe visibilities limited to the $\ensuremath{\pi}$ pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond the thermal source.
Using criteria based on superselection rules that apply to massive bosons but not to photons, we analyze the quantum correlations between the two condensate modes of a Bose-Einstein condensate interferometer [described in Egorov et al., Phys. Rev. A 84, 021605 (2011)]. We show that the observation of interference fringes can only be explained by Einstein-Podolsky-Rosen steering correlations between the two modes. Moreover, the size of the two-mode correlation linked to the fringe visibility will place a lower bound on the mean number of atoms of the (pure) two-mode steerable state. In order to determine the two-mode correlations, we develop a multimode theory describing the dynamics of the condensate atoms and the thermal fraction through the interferometer sequence, in agreement with the experimentally measured fringe visibility. We thus present experimental evidence for two-mode entangled states genuinely involving 40 000 87Rb^{87}\mathrm{Rb}87Rb atoms, and for two-way steerability between two groups of 20 000 indistinguishable atoms.
In our original paper (Altin et al 2011 New J. Phys. 13 065020), we presented the results from a Ramsey atom interferometer operating with an optically trapped sample of up to 10 6 Bose-condensed 87 Rb atoms in the m F = 0 clock states. We were unable to observe projection noise fluctuations on the interferometer output, which we attribute to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross–Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions accounts for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 × 10 4 atoms, we observe a coherence time of τ = 1.0 +0.5 −0.3 s.