Research Of The Nonclassical Property In A System Coupled To The Nanomechanical Resonator

At present, research on preparation and manipulation of quantum entanglement states and applications in quantum information processing is booming. The quest to demonstrate behavior described by quantum mechanics in the mechanical properties of nanoscale and larger struc-tures is of fundamental significance for understanding how the macroscopic classical world emerges by approximation from the quantum world, as well as for advancing the state of the art in ultra-sensitive measurement technology. Mechanical resonator has high Q factor, high vibration frequency, small size and other excellent characteristics. Due to these advantages, mechanical system has aroused wide concern in the physical, electron, engineering, biology, chemistry, medicine and other fields of science and technology. And mechanical system is ide-al candidate for studying quantum behavior of macroscopic objects. After cooling to near the ground state of the mechanical resonator, the electromechanical or optomechanical system in which the mechanical resonator couples to some small quantum systems such as quantum dots, cavity, atoms, single electron transistors can be used to study some fundamental quantum prin-ciples and novel quantum effects at the macroscale, e.g., preparing mechanical squeezed states, creating entanglement between the mechanical resonator and cavity fields, and so on. It paves the way towards the use of quantum communication and information transfer.In this thesis, we mainly study how to prepare and steer the nonclassical states of the mechanical resonator and study the photon blocking effect via quantum control of the system using the mechanical resonator.Firstly, in the strong Coulomb-blocked regime, we discuss how to squeeze the phonon mode of the mechanical resonator through the electromechanical coupling with the coupled quantum dots. We can trace over the operators of reservoirs and obtain the master equation for density matrix of the system (the mechanical resonator and the quantum dots) within the Born-Markov approximation. The electron injected from source electrode can be trapped in a quantum pure dressed state. Due to the combined interactions of the QDs with the two weak driving fields and the MR, the discrepancies between the transition frequency and that of the two weak driving fields are compensated by the phonons induced by the coupling of the MR and QDs, which enables some dissipative processes to occur resonantly. The phonons created and (or) annihilated in these processes are correlated thus leading to the quadrature squeezing of the MR. By tuning the gate voltage to control the energy structure of the QDs, the present squeezing scheme has strong resistance against the dephasing processes of the QDs in low temperature limit. The role of the temperature of the phonon reservoir is to damage squeezing of the MR. However, the quadrature squeezing of the MR still can be obtained for a comparatively higher temperature in our scheme.Then, we have studied the steady entanglement between the phonon mode of the mechan-ical resonator and the cavity mode. The cavity and the mechanical resonator are entangled by interacting with double two-level quantum dots driven by a strong laser field. We can trace over the quantum dots variables and obtain the dynamics of the cavity mode and the phonon mode of the mechanical resonator mode. By tuning the frequency of the strong laser field, the steady dressed-state population difference between the two quantum dots can be approximately obtained to unity, which is helpful in generation of the entanglement between the phonon mode of the mechanical resonator and the cavity mode.We can obtain the optimum entanglement between the phonon mode of the mechanical resonator and the cavity mode when the matching condition that the frequency of the phonon mode of the mechanical resonator mode is resonant with the dressed quantum dots is satisfied. Furthermore, when the mean number of the phonon mode and the cavity mode is different, the quantum vacuum fluctuation, which is brought in by the measurement of one of the two mode, gives rise to one-way EPR steering. In addition, through analyzing the purity, we find the conditions of the existence for the different types of EPR steering.We have proposed a scheme to entangle the mechanical modes of two movable mirrors in dissipative optmechanical system. Via feeding broadband two-mode squeezed light accompany-ing a coherent driving laser field into the cavity, the master equation for the cavity-mechanical resonator system is derived by following the general reservoir theory. In the weak coupling regime, in which the mechanical resonators are weakly coupled to the cavity modes, the com-plete destructive interference results in the EPR entanglement of the two-mode squeezed light perfectly transfer to the motion of the movable mirrors, generating stationary entanglement between the mechanical modes of the movable mirrors. We have also shown that in the moder-ate coupling regime, photonic excitation can preclude the complete destructive interference of quantum noise, leading to the entanglement between the two mirrors decreasing. However, en-tanglement transfer from the two-mode squeezed light to the movable mirrors is still achievable in this dissipative optomechanics.In the optomechanical system, the photon may impact the mechanical resonator through the effects of radiation pressure and the mechanical resonator in turn affects the photon. This will cause much influence, such as parametric amplifier, amplitude and phase modulation, and so on. Finally, we discuss the photonic crystal micro-optomechanical system. A two-level atom which is driven by a strong laser located inside a microscopic cavity engineered in a photonic band-gap material. Based on the polaron transformation, the rotating wave and secular approximation, we obtain the master equation of the system. We enter the effective truncation of the infinite ladder of dressed states for the atom-microcavity subsystem to a finite manifold due to the nonlinearity of the generalized Jaynes-Cumnings levels. Thus, there is a two-photon blockade. When the atom-microcavity is in the ground state, the mechanical oscillator can evolve into the dark state. So we can obtain the nonlinear coherent states of the phonon.