Spin-squeezed atomic crystal

We propose a method to obtain a regular arrangement of two-level atoms in a three-dimensional optical lattice with unit filling, where all the atoms share internal state coherence and metrologically useful quantum correlations. Such a spin-squeezed atomic crystal is obtained by adiabatically raising an optical lattice in an interacting two-component Bose-Einstein condensate. The scheme could be directly implemented on a microwave transition with state-of-the art techniques and used in optical-lattice atomic clocks with bosonic atoms to strongly suppress the collisional shift and benefit from the spins quantum correlations at the same time

Spin Squeezing in Finite Temperature Bose-Einstein Condensates : Scaling with the system size

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction $/N$ in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.Comment: 31 pages 8 figures, follow up of Sinatra et al PRL (2011), final version; Casagrand

Metrologically useful states of spin-1 Bose condensates with macroscopic magnetization

We study theoretically the usefulness of spin-1 Bose condensates with macroscopic magnetization in a homogeneous magnetic field for quantum metrology. We demonstrate Heisenberg scaling of the quantum Fisher information for states in thermal equilibrium. The scaling applies to both antiferromagnetic and ferromagnetic interactions. The effect preserves as long as fluctuations of magnetization are sufficiently small. Scaling of the quantum Fisher information with the total particle number is derived within the mean-field approach in the zero temperature limit and exactly in the high magnetic field limit for any temperature. The precision gain is intuitively explained owing to subtle features of the quasi-distribution function in phase space.Comment: 9 pages, 5 figure