Squeezing generation, revivals and entanglement in a cavity-ion system in contact with a thermal reservoir

We consider a system consisting of a single two-level ion in a harmonic trap, which is localized inside an optical cavity in contact with a thermal bath and subjected to the action of two external lasers. We are able to obtain an analytical solution for the total density operator of the system and show that squeezing in the motion of the ion and in the cavity field is generated. We also show that complete revivals of the states of the motion of the ion and of the cavity field occur periodically when the temperature is zero. The correlations and entanglement between the motion and the cavity field are studied. We found that for T not equal 0 entanglement may either disappear completely for finite times or disappear and appear during finite intervals.