Dynamics and nonclassical properties of an opto-mechanical system prepared in four-headed cat state and number state

• New non-classical states could be generated in an opto-mechanical system composed of four-headed cat state (4HCS) and number state.
• The nonclassicality of photonic/mechanical mode is the strongest when initial photonic mode is 4HCS, comparing to the ESCS and coherent state.
• The larger initial value of photonic(or mechanical) mode will improve the nonclassicality of the photonic (or mechanical) mode.
• The Wigner functions of multicomponet time-dependent displaced number states are appeared in the phase space of mechanical mode.
• Our results have potential application on manipulation and preparation of nonclassical state of opto-mechanical system.

The nonlinear interaction between an optical field and a mechanical resonator of an opto-mechanical system plays an important role in quantum optics and quantum information. This work applies the nonlinearity of opto-mechanical system to generate a nonclassical state for an initial state composed of four-headed cat state of photonic mode and number state of mechanical mode. It is interesting to find that the Wigner function of a mechanical mode is composed of finite Wigner functions of time-dependent displaced number states, which is very useful in quantum information process. Furthermore, nonclassical properties of the photonic and mechanical modes are investigated by using Wigner function. An interesting result is that the negative volume of Wigner function for the photonic (or mechanical) mode increases with parameter α (or k), which means that the larger initial value of photonic (or mechanical) mode will improve the nonclassicality of the photonic (or mechanical) mode. We also investigate the influence of different initial photonic states on the nonclassicality of mechanical and photonic modes.