Squeezing generation and revivals in a cavityion system

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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
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A ion inside a Paul trap in a cavity
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is being shined by two laser fields
The lasers and the cavity mode are quasi resonant
to a electronic transition of the ion.
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Level scheme
atomic transition frequency
cavity frequency
vibration frequency
laser frequencies
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A effective Hamiltonian

RWA adiabatic elimination of the upper state
( Lamb-Dicke parameter )
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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
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The system reaches the steady state
A product of the vacuum of the cavity field and
an ideal squeezed state of the motion of the ion

Very large squeezing
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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

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Periodically, the state of motion returns to
the same ideal squeezed state
The cavity field also returns periodically to the
initial vacuum state
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The solution for the reduced density operators at
any time are squeezed thermal states
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Behaviour of n with time
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Squeezing
revivals
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Remarks and conclusions
, the two subsystems

• For

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
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References

• 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).