In this paper, we have introduced a physical scheme that allows
one to generate and control the nonclassical properties of
motional nonlinear coherent states and their superpositions
for an undamped vibrating micromechanical membrane inside
an optical cavity. We have shown that if the cavity field
is initially prepared in a Fock state, the motional state of
the membrane may evolve to a family of nonlinear coherent
states. We have been interested in analysing the nonclassical
properties of the generated state of the membrane, including
the quadrature squeezing and the sub-Poissonian statistics. In
particular, we have found that the Lamb–Dicke parameter and
the membrane’s reflectivity lead to an enhancement of the
nonclassical properties. As we have seen, with increasing
the Lamb–Dicke parameter and the membrane’s reflectivity,
the sub-Poissonian behaviour and quadrature squeezing of the
motional state of the membrane are considerably strengthened.
In addition, the scheme offers the possibility of generating
various types of the so-called nonlinear multicomponent
Schr¨odinger cat states of the membrane. We have shown
that the separation between nonlinear coherent components is
increased by increasing the parameters η and rc.
We have also extended our treatment to a more realistic situation in
which the photon leakage from the cavity as a relevant source
of decoherence is included and examined its influence on the
nonclassical characteristics of the generated motional states of
the membrane. We have shown that it is possible to control the
effect of the cavity field damping on the nonclassical behaviour
of the motional state of the membrane via the Lambe–Dicke
parameter and the membrane’s reflectivity. In particular,
we have found that the generated motional NLSCSs of the
membrane can be more robust against decoherence than the
usual Schr¨odinger cat states.
Gathered by: Sh.Barzanjeh(shabirbarzanjeh@gmail.com)
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