  We investigate the influence of vibrational phonon modes on the entanglement
through a quantum dot molecule under the bias voltage-driven field. The
molecular quantum dot system can be realized by coupled quantum dots in the
middle of the suspended carbon nanotube. This system would be described by the
Anderson-Holstein model and also can be analyzed by the polaron master equation
in Markovian regime. In the presence of electron-phonon interaction, we study
the entanglement as a function of bias voltage and temperature. Despite
entanglement degradation because of phonon decoherence, we employ an asymmetric
coupling protocol to preserve the entanglement in a significant level and also
we apply the easy tunable bias voltage driven to engineer its behavior. In
dynamics of entanglement, we demonstrate the phenomenon of thermal entanglement
degradation and rebirth through the increase of temperature. In this process,
thermal entanglement revival is intensively affected by the strength of phonon
decoherence. Such that, stronger revival is occurred for higher phonon coupling
amount. With an applied time-dependent bias voltage, the entanglement evolution
shows periodic revival by time and in response to bias voltage rising, it
illustrates decreasing and grows steadily to reach the flat form with
considerable magnitude.
