Mg. Benedict et A. Czirjak, Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms, PHYS REV A, 60(5), 1999, pp. 4034-4044
We consider a class of states in an ensemble of two-level atoms: a mesoscop
ic superposition of two distinct atomic coherent states, which can be regar
ded as atomic analogs of the states usually called Schrodinger-cat states i
n quantum optics. According to the relation of the constituents, we define
polar and nonpolar cat states. The properties of these are investigated by
the aid of the spherical Wigner function. We show that nonpolar cat states
generally exhibit squeezing, the measure of which depends on the separation
of the components of the cat, and also on the number of the constituent at
oms. By solving the master equation for the polar cat state embedded in an
external environment, we determine the characteristic times of decoherence
and dissipation, and also the characteristic time of a new; parameter, the
nonclassicality of the state. This latter one is introduced by the help of
the Wigner function, which is used also to visualize the process. The depen
dence of the characteristic times on the number of atoms of the cat and on
the temperature of the environment shows that the decoherence of polar cat
states is surprisingly slow. [S1050-2947(99)01611-X].