We investigate entanglement dynamics for a nanomechanical resonator coupled to
an optical cavity field
through the analysis of the associated entanglement entropies.
The effects of time variation of several parameters,
such as
the optical frequency and the coupling strength, on the evolution of
entanglement entropies are analyzed.
We consider three
kinds
of entanglement entropies as the measures of the entanglement of
subsystems,
which are the linear entropy, the von Neumann entropy, and the Rényi entropy.
The analytic formulae of these entropies are derived in a rigorous way using
wave functions of the system.
In particular, we focus on
time behaviors of entanglement entropies
in the case where the optical frequency is modulated by a small oscillating factor.
We show that the entanglement entropies
emerge and increase as the coupling strength grows from zero.
The entanglement entropies fluctuate depending on the adiabatic variation of the
parameters and such fluctuations are significant especially in the strong coupling regime.
Our research
may deepen the
understanding of
the optomechanical entanglement,
which is crucial in
realizing hybrid quantum-information protocols in quantum computation,
quantum networks, and other domains in quantum science.
Entropic analysis of optomechanical entanglement for a nanomechanical resonator coupled to an optical cavity field
