  We propose a scheme to realize optical nonreciprocal response and conversion
in a Tavis-Cummings coupling optomechanical system, where a single cavity mode
interacts with the vibrational mode of a flexible membrane with an embedded
ensemble of two-level quantum emitters. Due to the introduction of the
Tavis-Cummings interaction, we find that the phases between the mechanical mode
and the optical mode, as well as between the mechanical mode and the dopant
mode, are correlated with each other, and further give the analytical
relationship between them. By optimizing the system parameters, especially the
relative phase between two paths, the optimal nonreciprocal response can be
achieved. Under the frequency domain, we derive the transmission matrix of the
system analytically based on the input-output relation and study the influence
of the system parameters on the nonreciprocal response of the quantum input
signal. Moreover, compared with the conventional optomechanical systems, the
Tavis-Cummings coupling optomechanical system exhibits richer nonreciprocal
conversion phenomena among the optical mode, mechanical mode, and dopant mode,
which provide a new applicable way of achieving the phonon-photon transducer
and the optomechanical circulator in future practice.
