3. Atomic spin squeezing and quantum state transfer in the continuous variable regime

We also study different schemes to reduce the quantum fluctuations of atomic variables. Since an ensemble of two-level atoms is formally equivalent to an ensemble of spins 1/2, the fact that the atomic spin components do not commute prevents from perfectly knowing the state of all the components. Consequently, there exists a standard quantum noise for the atoms [1]. It is this noise which presently limits the atomic clocks precision for instance [2]. As for the field the notions of coherent atomic state and squeezed atomic states can be defined.

We have shown that the atom/field interaction in cavity could allow for producing such squeezed atomic states. Two regimes have been studied:

- a non-linear regime in which the atoms interact with one or several fields, initially in coherent states. When the interaction is strong enough, quantum correlations are created between the atoms and it is possible to obtain a noise reduction for the spin components [3,4,5,6].

- a linear regime in which one of the incident field is a broadband squeezed vacuum. In certain configurations, we have shown that it is possible to transfer almost perfectly the field squeezing to the atomic spin [5,7], thus paving the way towards an atomic quantum memory.

We are currently trying to test and implement experimentally these theoretical predictions.

[1] M. Kitawaga, M. Ueda, Phys. Rev. A 47, 5138 (1993)

[2] D.J. Wineland, J.J. Bollinger, W.M. Itao, D.J. Heinzen, Phys. Rev. A 50, 67 (1994)

[3] L. Vernac, M. Pinard, E. Giacobino, Phys. Rev. A 60, 2346 (2000)

[4] L. Vernac, M. Pinard, V. Josse, E. Giacobino, Eur. Phys. J. D 18, 129 (2002)

[5] A. Dantan, M. Pinard, V. Josse, N. Nayak, P.R. Berman, Phys. Rev. A 67, 045801 (2003) [quant-ph/0209012]

[6] A. Dantan, M. Pinard, P.R. Berman, Eur. Phys. J. D (2003) [quant-ph/0302012]

[7] L. Vernac, M. Pinard, E. Giacobino, Eur. Phys. J. D 17,125 (2001)