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arXiv:1511.03146 · Physical Review A

Parametric-squeezing amplification of Bose-Einstein condensates

Georg Jäger, Tarik Berrada, Jörg Schmiedmayer, Thorsten Schumm, Ulrich Hohenester

Published Nov 30, 2015• 11 citations
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Abstract

We theoretically investigate the creation of squeezed states of a Bose-Einstein condensate (BEC) trapped in a magnetic double-well potential. The number or phase squeezed states are created by modulating the tunnel coupling between the two wells periodically with twice the Josephson frequency, i.e., through parametric amplification. Simulations are performed with the multiconfigurational time-dependent Hartree method for bosons. We employ optimal control theory to bring the condensate to a complete halt at a final time, thus creating a highly squeezed state (squeezing factor of 0.12, ${\ensuremath{\xi}}_{S}^{2}=\ensuremath{-}18$ dB) suitable for atom interferometry.

DOI
10.1103/physreva.92.053632

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We theoretically investigate the creation of squeezed states of a Bose-Einstein condensate (BEC) trapped in a magnetic double-well potential. The number or phase squeezed states are created by modulating the tunnel coupling between the two wells periodically with twice the Josephson frequency, i.e., through parametric amplification. Simulations are performed with the multiconfigurational time-dependent Hartree method for bosons. We employ optimal control theory to bring the condensate to a complete halt at a final time, thus creating a highly squeezed state (squeezing factor of 0.12, \ensuremathξS2=\ensuremath−18{\ensuremath{\xi}}_{S}^{2}=\ensuremath{-}18\ensuremathξS2​=\ensuremath−18 dB) suitable for atom interferometry.
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 us 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 multiconfigurational 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 provide a scheme for the generation of controlled entangled number states of Bose-Einstein condensates in multiple wells, and also provide a novel method for the creation of squeezed states without severe adiabatic constraints on barrier heights. The condensate in a multiple well trap can be evolved, starting with a specific initial phase difference between the neighboring wells, to a tunable entangled state or a squeezed state. We propose a general formula for the initial phase difference between the neighboring wells that is valid for any number of wells, even and odd.
The spin-squeezing dynamics of a quasi-one-dimensional dipolar Bose gas trapped in a double-well potential is studied by employing the method of the multiconfigurational time-dependent Hartree for bosons. We find that optimal squeezing generated by the dipolar interaction can be improved over the one-axis twisting limit, and this squeezing is much stronger than that obtained by the contact interaction. Moreover, natural orbital-related squeezing can be controlled by the direction of the dipole moment, which provides control for storing the optimal spin squeezing. The origin of the squeezing as well as the relationship between spin squeezing and the two-order correlation function are also discussed.
In this paper, tunnelling dynamics of squeezed Bose–Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.
Squeezing via the interaction between the cavity light field and the Bose–Einstein Condensate (BEC) in a double-well potential is considered within the context of the two-mode approximation. For the cavity light field initially in a coherent state, it is shown that by choosing appropriate parameters, quadrature squeezing of the cavity light field can be achieved and it exhibits periodic oscillation. We also study the case in which BEC is tuned to resonance by periodically modulating the trapping potential, and the quadrature squeezing of the cavity field exhibits periodic collapse and revival effect. Both analytic and numerical calculations are performed, and they are found to be in good agreement with each other. The result shows that the quantum statistical properties of the cavity light field can be manipulated by its coupling with the condensates in the double-well potential. On the other hand, dynamical properties of the condensates in the double-well potential will be reflected by the quadrature squeezing of the light field.