Spin squeezing in a Bose-Einstein condensate on an atom chip

Spin squeezing in an ensemble of atoms can be used to improve the accuracy of frequency measurements in atomic clocks beyond the so called standard quantum limit. Recently a collaboration between the Atom chips group of Laboratoire Kastler Brossel and the Ludwig-Maximilians University in Munich allowed to implement an elegant method to generate spin squeezed states in a Bose-Einstein condensate of Rubidium atoms trapped on an atom chip.

Initially each atom is put in a superposition of two internal states 0 and 1. Due to interactions that create a nonlinearity for the atomic field, this factorized state evolves into a spin squeezed state. The nonlinearity is adjusted by controlling the overlap between the internal states wave functions. It is ``switched-on" for a well-chosen time to create the squeezing and it is "switched-off" afterwards. This squeezing scheme could be applied in chip based atomic clocks experiments such as the one going on in Syrte. Simultaneously, two other remarkable results in the field of spin squeezing on similar systems have been obtained in Heidelberg and in MIT.

(a) Using state-dependent microwave potentials, the wave functions of states 0 and 1 are separated spatially for a well-chosen time. This switches-on the atomic nonlinearity that generates the spin squeezing.

(b) Evolution of the system internal state represented as a collective spin S on the Bloch sphere. The length of the mean spin represents coherence between the states 0 and 1. The spin fluctuations in the orthogonal plane to the mean spin are isotropic for the initial state while they are reduced in the direction θ in the spin squeezed state.

(c) Reconstruction of the Wigner function of the spin squeezed state from experimental data. The black contour marks the points for which the Wigner function has decreased by 1/√e. The black circle is the same contour for the initial factorized state.

Publication

``Atom chip based generation of entanglement for quantum metrology", Max. F. Reidel, Pascal Böhi, Yun Li, T. W. Hänsch, A. Sinatra, P. Treutlein, Nature, 464, 1170 (2010). doi:10.1038/nature08988

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