By J. M. Ziman

This can be a textbook of complicated quantum thought for graduate scholars and learn staff which provides a hooked up mathematical derivation of the real effects, targeting the valuable rules with out burdening the exposition with tricky aspect or pointless rigour, and explains, within the easiest attainable phrases, the symbols and ideas which regularly confront the lively learn employee in good country, nuclear and high-energy physics, and in theoretical chemistry. Professor Ziman brings to his job the sympathetic suggestions of a lecturer who has no longer forgotten the problems that he himself needed to surmount in studying his topic.

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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).

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