We discuss the effect of spatial dynamics in two-component Bose-Einstein condensates on spin squeezing and transfer to squeezed light. We also present a general treatment of squeezing transfer from atomic spins to light fields.
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 develop a cumulant based formalism to deterministically calculate the lowest order quantum fluctuations of a two-component Bose-Einstein condensate. We use this to study spin squeezing induced by the atom-atom interaction nonlinearity. Our formalism naturally accounts for the multimode spatial description of the condensate, extending previous spin squeezing work which assumed a single spatial mode. We study spin squeezing in both the miscible and immiscible (phase separating) regimes for the scattering lengths. In the miscible regime, we find the squeezing parameter deviates very little from the single spatial mode approach, while in the phase separating regime, we find the squeezing is slightly reduced, though significant squeezing still occurs.
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.