1. Squeezing generation and revivals in a cavity-ion system Nicim Zagury Instituto de Física, Universidade Federal Rio de Janeiro, Brazil colaboradores: R. Rangel. L. Carvalho

2. A ion inside a Paul trap in a cavity

3. …is being shined by two laser fields The lasers and the cavity mode are quasi resonant to a electronic transition of the ion.

4. Level scheme atomic transition frequency cavity frequency vibration frequency laser frequencies

5. A effective Hamiltonian = RWA + adiabatic elimination of the upper state: ( Lamb-Dicke parameter )

6. Master Equation Even though we have considered a bad cavity, we were able to obtain an analytical solution for the total density operator of the system

7. A product of the vacuum of the cavity field and an ideal squeezed state of the motion of the ion The system reaches the steady state: Very large squeezing:

8. For finite times the two subsystems are, in general, entangled, but periodically at times and they disentangle. Remarkably, even though there is dissipation there is a complete “revival” of the state of the motion at t = and of the state of the field at t=

9. The cavity field also returns periodically to the initial vacuum state Periodically, the state of motion returns to the same ideal squeezed state

10. The solution for the reduced density operators at any time are “squeezed thermal states”:

11. Behaviour of n with time

12. Squeezing revivals

14. Remarks and conclusions 1.For, the two subsystems disentangle periodically at given times  n and  n ´ 2. Although there is dissipation the the state of motion and the cavity field and ¨revive¨ completely at  n and  n ´ Respectively 3. At any time the reduced density matrices correspond to squeezed thermal states 4. These results can be easily generalized for a initial coherent state

15. [1] H. Zeng and F. Lin, Phys. Rev. A 50, R3589 (1994). [2] E. Massoni, M. Orszag, Opt. Comm. 190, 239 (2001) [3] R. Rangel, E. Massoni, and N. Zagury, Phys. Rev. A 69, 023805 (2004). References