Directional Quantum Amplification And Nonlinearity In Optomechanical Systems

Optomechanical system(OMS)is a system,which is to study the interaction between radiation pressure and mechanical vibration.Due to the excellent characteristics of miniaturization,easily integrated on-chip and free magnetic fields,OMS has been greatly used as a promising platform for developing various quantum devices.It has many interesting phenomena,such as optomechanically induced transparency(OMIT),optomechanically induced nonreciprocity,photon blockade and ground state cooling of mechanical oscillator.As is well known,when the OMS is used,its surrounding environment quantum noise will inevitably make its properties fragile.Therefore,we shall study the nonreciprocal photon transmission with quantum noise via cross-Kerr nonlinear,and photon blockade and nonlinearity amplification in a parity-time-symmetry(PT)system.(i)From the Maxwell equations of classical electromagnetic field,the Hamiltonian of free electromagnetic field is derived.And then we can obtain an effective Hamiltonian for the OMS that includes a nonlinear Kerr effect by using the Born-Oppenheimer approximation and unitary transformation.(ii)The nonreciprocal photon transmission between two optical modes which are nonlinearly coupled in a cross-Kerr type,is investigated by using a damped auxiliary optical mode as their common engineered reservoir.The optical nonreciprocity is created by using the quantum interference between the nonlinear coupling induced by the cross-Kerr nonlinearity and the dissipative coupling mediated by the adiabatic elimination of the auxiliary optical mode.The photon transmission probabilities in forward and backward directions for the relative phase? between the two couplings are symmetric about the resonance with the probabilities for the phase?-?,and are exchange symmetric with those in the case of the phase 2?-?.By tuning the dissipative coupling,in addition to the photon nonreciprocity being improved,the nonreciprocal photon amplification is produced.Meanwhile,it is found that not only can the cross-Kerr nonlinearity lead to a broadband optical nonreciprocity,but also it effectively produces the optical squeezing in the present scheme.The combination of the photon nonreciprocity with the optical squeezing will be useful in the realization of the quantum information processing with noise reduction.(iii)We study the photon blockade effects in a PT-symmetry system,which consists of a passive and an active nonlinear cavity via evanescent field coupling.We find the actually different photon blockade behaviors in PT-symmetry and PT-symmetry broken regimes,which is related to the PT phase transition.Furthermore,it is shown that the effects of supermode field localization in the PT-symmetry will dynamically enhanced the inner cavity nonlinearity,which leads to photon blockade.The results obtained may provide insight into the crossover between the photon blockade and PT-symmetric theory.