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**Sample text**

We show that the interaction with a single, non-resonant atom transforms a coherent state into a cat, whose decoherence is then theoretically analyzed. We explain how a probe atom, a ‘quantum mouse’ can be used to assess the decoherence of the cavity cat. Finally, Section 4 is devoted to the perspectives opened for these decoherence studies: creation of very large cats by resonant atom-ﬁeld interaction, direct measurement of the cat’s Wigner function, providing a detailed insight into the decoherence mechanisms and creation of non-local cat states, merging the EinsteinPodolsky-Rosen [9] non-locality and decoherence.

We conclude by giving an alternative expression of W ([18] and L. Davidovich, private communication). Using: |x − x x = e−i(x−x )p D(x + ip)| − 2 2 , (38) and x+ x x |= |D(−x − ip)ei(x+x )p , 2 2 (39) Monitoring Mesoscopic Decoherence in a Cavity 47 which follow directly from the deﬁnition of D(α) and replacing |x ± x /2 in Eq. (36) by the expressions given by Eqs. (38) and (39), noting ﬁnally that P|x /2 = | − x /2 [see Eq. (32)], we get: 2 T r[D(−α)ρD(α)P] . (40) π The Wigner distribution at α is the expectation value in the state translated by −α of the ﬁeld parity operator.

P. 425. Edited by W. H. Zurek. Redwood City: Addison-Wesley, 1990. [30] R. B. Griﬃths, Consistent Histories and the Interpretation of Quantum Mechanics, J. Stat. Phys. 36, 219 (1984). [31] F. Haake and D. F. Walls, In Quantum Optics IV. Edited by J. D. Harvey, and D. F. Walls. Berlin: Springer Verlag, 1986. [32] S. Habib, K. Shizume and W. H. Zurek, Decoherence, Chaos, and the Correspondence Principle, Phys. Rev. Lett. 80 (20), 4361 (1998). [33] S. Haroche, Entanglement, Mesoscopic Superpositions and Decoherence Studies with Atoms and Photons in a Cavity, Physica Scripta T76, 159 (1998).