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Register a new userSpin squeezing and EPR entanglement of two bimodal condensates in state-dependent potentials
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Krzysztof Pawlowski Mr
Publication date
2013
fields
Physics
and research's language is
English
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We propose and analyze a scheme to entangle the collective spin states of two spatially separated bimodal Bose-Einstein condensates. Using a four-mode approximation for the atomic field, we show that elastic collisions in a state-dependent potential simultaneously create spin-squeezing in each condensate and entangle the collective spins of the two condensates. We investigate mostly analytically the non-local quantum correlations that arise in this system at short times and show that Einstein-Podolsky-Rosen (EPR) entanglement is generated between the condensates. At long times we point out macroscopic entangled states and explain their structure. The scheme can be implemented with condensates in state-dependent microwave potentials on an atom chip.
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Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law ($1/r^{alpha}$) interactions in $D$ dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small $alpha$ the scaling of squeezing with system size is identical to the infinite-range ($alpha=0$) case. This indifference to the interaction range persists up to a critical value $alpha=2D/3$, above which squeezing degrades continuously. Boundary-induced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.
We study spin-1/2 fermions in spin dependent potentials under the emph{spin model approximation}, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin model approximation maps the interacting fermion problem to an ensemble of lattice spin models in energy space, where spin-spin interactions are long-ranged and spin-anisotropic. We show that the spin model approximation is accurate for weak interactions compared to the harmonic oscillator frequency, and captures the collective spin dynamics to timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections when realistic anharmonic potential corrections are taken into account. Additionally, we present numerical techniques that are useful for analysis of spin models on an energy lattice, including enacting a change of single-particle basis on a many-body state as an effective time evolution, and fitting of spatially inhomogeneous long-range interactions with exponentials. This latter technique is useful for constructing matrix product operators for use in DMRG analyses, and may have broader applicability within the tensor network community.
We study generation of non-local correlations by atomic interactions in a pair of bi-modal Bose-Einstein Condensates in state-dependent potentials including spatial dynamics. The wave-functions of the four components are described by combining a Fock state expansion with a time-dependent Hartree-Fock Ansatz, so that both the spatial dynamics and the local and non-local quantum correlations are accounted for. We find that despite the spatial dynamics, our protocole generates enough non-local entanglement to perform an EPR steering experiment with two spatially separated con-densates of a few thousands of atoms.
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We study entanglement and squeezing of two uncoupled impurities immersed in a Bose-Einstein condensate. We treat them as two quantum Brownian particles interacting with a bath composed of the Bogoliubov modes of the condensate. The Langevin-like quantum stochastic equations derived exhibit memory effects. We study two scenarios: (i) In the absence of an external potential, we observe sudden death of entanglement; (ii) In the presence of an external harmonic potential, entanglement survives even at the asymptotic time limit. Our study considers experimentally tunable parameters.
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