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arXiv:1303.0299 · Europhysics Letters (EPL)

Limit of spin squeezing in trapped Bose-Einstein condensates

Alice Sinatra, Yvan Castin, Emilia Witkowska

Published May 1, 2013• 8 citations
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Abstract

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.

DOI
10.1209/0295-5075/102/40001

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Etats comprimés de Spin dans un condensat de Bose-Einstein

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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.
Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
Squeezed states, special kinds of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors, they allow us to overcome the ‘classical’ projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as well as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum-enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial, we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose–Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
We consider a collection of atoms prepared in a Bose-Einstein condensate which interact via two-body elastic collisions. A resonant driving field couples two internal states which together constitute an effective spin 1/2 system for each atom, and from which a total spin for the gas can be defined. It is shown that in the limit of strong driving, the system dynamics reduces to a mechanism for spin squeezing similar to that of a recent proposal for undriven condensates. However, we find that the conditions for spatial stability in our driven system are complementary to those of the undriven system. Reasons for this difference, associated with the physics of dressed atom collisions, are discussed along with conditions for preparing and observing the spin squeezed state.
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.