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arXiv:quant-ph/0106005 · Physical Review A

Limitations of entanglement between photons and atoms coupled out from a Bose-Einstein condensate

Thomas Gasenzer, David C K Roberts, Keith R. Burnett

Published Jan 10, 2002• 34 citations
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Abstract

We study the limitations on the relative number squeezing between photons and atoms coupled out from a homogeneous Bose-Einstein condensate. We consider the coupling between the translational atomic states by two photon Bragg processes, with one of the photon modes involved in the Bragg process in a coherent state and the other initially unpopulated. We start with an interacting Bose condensate at zero temperature and compute the time evolution for the system. We study the squeezing, i.e., the variance of the occupation number difference between the second photon and the atomic center-of-mass mode. We discuss how collisions between the atoms and photon rescattering affect the degree of squeezing which may be reached in such experiments.

DOI
10.1103/physreva.65.021605

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We study the limitations on the relative number squeezing between photons and atoms coupled out from a homogeneous Bose-Einstein condensate. We consider the coupling between the translational atomic states by two photon Bragg processes, with one of the photon modes involved in the Bragg process in a coherent state and the other initially unpopulated. We start with an interacting Bose condensate at zero temperature and compute the time evolution for the system. We study the squeezing, i.e., the variance of the occupation number difference between the second photon and the atomic center-of-mass mode. We discuss how collisions between the atoms and photon rescattering affect the degree of squeezing which may be reached in such experiments.
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.
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The entanglement in the system which consists of two-mode squeezed vacuum state and Bose- Einstein condensate in two-photon process is investigated.The entanglement of field-atom and the entangle- ment between the two-mode field are investigated using the quantum reduced entropy and quantum relative entropy,respectively.The influences of the initial squeezed parameter of field and the interaction between atoms on the evolution of the entanglement of field-atom and one of two modes of field are discussed.
We consider a Bose-Einstein condensate that is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled state called a spin-squeezed state. This evolution is analyzed in detail by developing a Bogoliubov theory that describes the entanglement of the atoms. Our calculation is a consistent expansion in 1/N,1/\sqrt{N},1/N​, where N is the number of particles in the condensate, and our theory predicts that it is possible to produce spin-squeezing by at least a factor of 1/N.1/\sqrt{N}.1/N​. Within the Bogoliubov approximation this result is independent of temperature.
We investigate the system of Bose-Einstein condensates interacting with SU(1, 1) coherent state in two-photon transition process, the entanglement of atom-field and the entanglement between the two-mode light field using the quantum reduced entropy and quantum relative entropy are studied, respectively . The influences of the coherent parameter of light field, two-mode photon number difference and interaction between atoms on the evolution of the entanglement of atom-field and the entanglement between the two-mode light field have been discussed.
We discuss how the nature of the relative phase between two entangled condensates differs depending on whether the entanglement is established by measurements or by coupling. In the former case, the limit of the resulting phase resolution scales inversely with the square root of the number of atoms. This limit can be surpassed, however, when the condensates are entangled by coupling and can reach the fundamental Heisenberg limit where the phase resolution scales inversely with the number of atoms involved.