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Register a new userLong Phase Coherence Time and Number Squeezing of two Bose-Einstein Condensates on an Atom Chip
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We measured the relative phase of two Bose-Einstein condensates confined in an radio frequency induced double well potential on an atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after splitting, a factor of 10 beyond the phase diffusion limit expected for a coherent state in our experimental conditions (20 ms). The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrated a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.
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The recombination of two split Bose-Einstein condensates on an atom chip is shown to result in heating which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms between 10 and 40% and provides a robust way to read out the phase of an atom interferometer without the need for ballistic expansion. The heating may be caused by the dissipation of dark solitons created during the merging of the condensates.
We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.
We present a permanent magnetic film atom chip based on perpendicularly magnetized TbGdFeCo films. This chip routinely produces a Bose-Einstein condensate (BEC) of 10^5 87Rb atoms using the magnetic film potential. Fragmentation observed near the film surface provides unique opportunities to study BEC in a disordered potential. We show this potential can be used to simultaneously produce multiple spatially separated condensates. We exploit part of this potential to realize a time-dependent double well system for splitting a condensate.
We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.
We investigate spin squeezing of a two-mode boson system with a Josephson coupling. An exact relation between the squeezing and the single-particle coherence at the maximal-squeezing time is discovered, which provides a more direct way to measure the squeezing by readout the coherence in atomic interference experiments. We prove explicitly that the strongest squeezing is along the $J_z$ axis, indicating the appearance of atom number-squeezed state. Power laws of the strongest squeezing and the optimal coupling with particle number $N$ are obtained based upon a wide range of numerical simulations.
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