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A tunable multiple windows optomechanically induced transparency (OMIT) with a squeezed field is investigated in a system consisting of an optomechanical cavity coupled to a charged nanomechanical resonator (NAMR) via Coulomb interaction. Such a multiple OMIT can be achieved by adjusting the frequency of the charged NAMR and can be observed even with a single-photon squeezed field. In addition, this multiple OMIT for the quantized fields can be robust against cavity decay and environmental temperature. Specifically, the model under our consideration might be applied to precision measurement the frequency difference of two NAMRs within the reach of current techniques.

We study the tunable optomechanically induced absorption (OMIA) with the quantized field in the system, which consists of a driven cavity and a mechanical resonator with a super-conducting charge qubit via Jaynes-Cummings interaction. Such a OMIA can be achieved by controlling the strength of the Jaynes-Cummings interaction. Moreover, our work shows this OMIA for the quantized fields can be robust against cavity decay in somehow. With the combination of optomechanically induced transparency (OMIT), our proposal may have paved a new avenue towards quantum photon router.

The parity symmetry and parity breaking in the super-Ohmic spin-boson model (SBM) is studied by using the coherent-state approach. We show that the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias, and then it can be restored by involving an additional spin into the SBM to couple with the original spin by an Ising interaction. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom.