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arXiv:1109.2401 · Frontiers of Physics

Spin squeezing in Bose—Einstein condensates: Limits imposed by decoherence and non-zero temperature

Alice Sinatra, Jean-Christophe Dornstetter, Yvan Castin

Published Dec 12, 2011• 42 citations
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Abstract

We consider dynamically generated spin squeezing in interacting bimodal condensates. We show that particle losses and non-zero temperature effects in a multimode theory completely change the scaling of the best squeezing for large atom numbers. We present the new scalings and we give approximate analytical expressions for the squeezing in the thermodynamic limit. Besides reviewing our recent theoretical results, we give here a simple physical picture of how decoherence acts to limit the squeezing. We show in particular that under certain conditions the decoherence due to losses and non-zero temperature acts as a simple dephasing.

DOI
10.1007/s11467-011-0219-7

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We consider dynamically generated spin squeezing in interacting bimodal condensates. We show that particle losses and non-zero temperature effects in a multimode theory completely change the scaling of the best squeezing for large atom numbers. We present the new scalings and we give approximate analytical expressions for the squeezing in the thermodynamic limit. Besides reviewing our recent theoretical results, we give here a simple physical picture of how decoherence acts to limit the squeezing. We show in particular that under certain conditions the decoherence due to losses and non-zero temperature acts as a simple dephasing.
Spin squeezed states are multi-particle entangled states that have practical interest in quantum metrology and atomic interferometer. In this thesis, we study theoretically realistic schemes for the production of spin squeezed states using the coherent interactions between cold atoms in a bimodal Bose-Einstein condensate. In particular, we include decoherence process such as particle losses, as well as spatial dynamics which limit the maximum squeezing reachable in a real experiment. We find that the effect of losses cannot be neglected as soon as the lost fraction of particles is of the order of the squeezing parameter. The analytical solution that we find, using Monte-Carlo wave functions approach, allows us to perform an optimization for the spin squeezing with respect to the experiment parameters. The method that we develop to study the entangled spatial and spin dynamics of interacting bimodal BEC allows a full analytical treatment for spin squeezing in some cases and can be used in the general case without the need of heavy numerics. We apply our theoretical studies to an experiment for spin squeezing recently realized successfully on an atom chip. Finally, we study the spin squeezing in a related but different system of a BEC with two external modes coherently coupled by the tunnel effect. We study this problem with a dynamical two-mode model for T << Tc and within a multimode approach in thermal equilibrium for T ~ Tc.
The evolution of an interacting two-component Bose-Einstein condensate from an initial phase state leads to a spin squeezed state that may be used in atomic clocks to increase the signal-to-noise ratio, opening the way to quantum metrology. The efficiency of spin squeezing is limited by the finite temperature of the gas, as was shown theoretically in a spatially homogeneous system. Here we determine the limit of spin squeezing in the realistic trapped case, with classical field simulations, and with a completely analytical treatment that includes the quantum case.
We study the limitations for entanglement due to collisional decoherence in a Bose-Einstein condensate. Specifically we consider relative number squeezing between photons and atoms coupled out from a homogeneous condensate. We study the decay of excited quasiparticle modes due to collisions in condensates of atoms with one or two internal degrees of freedom. The time evolution of these modes is determined in the linear response approximation to the deviation from equilibrium. We use Heisenberg-Langevin equations to derive equations of motion for the densities and higher correlation functions which determine the squeezing. In this way we can show that decoherence due to quasiparticle interactions imposes an important limit on the degree of number squeezing which may be achieved. Our results are also relevant for the determination of decoherence times in other experiments based on entanglement, e.g. the slowing and stopping of light in condensed atomic gases using dark states.