Quadrature squeezing of the system consisting of nitrogen-vacancy centers in diamond coupled to cavity field and mechanical resonator

With the great improvement of nanotechnology, it is now possible to fabricate mechanical resonator with dimension on a micro and even nanometer scale. Because of its high vibration frequency, quality factor, very small mass, and low intrinsic dissipation, nanomechanical resonator has important applications in the field of high-precision displacement detection, force detection, mass measurement, and accurate quantum computation. Mechanical resonator is also a promising candidate for observing quantum effects in macroscopic objects. By coupling nanomechanical resonator to other solid-state system such as optical cavity, microwave cavity, nitrogen-vacancy center (NV center) and superconducting qubits, researchers have successfully cooled the mechanical resonator to its quantum ground state, which paves the way for observing nonclassical states in resonator such as superposition state and Fock state. On the other hand, the nitrogen-vacancy center in diamond has attracted more and more attention because of its advantages of long coherence time at room temperature, the ability to implement initialization and readout, and microwave control. Moreover, these NV centers can be used to detect weak magnetic field and electric field at room temperature. By using both laser field and microwave field, one can implement the manipulation, storage, and readout of the quantum information. In addition, because NV centers couple to both optical field and microwave field, they can also be used as a quantum interface between optical system and solid-state system. This provides a promising platform to study novel quantum phenomena based on NV centers separated by long distances. The nitrogen-vacancy center in diamond coupled to nanomechanical resonator can be used in precision measurement and quantum information processing, which has become a hot research topic. In this paper, we study the dynamics of quadrature squeezing of the phonon field in the system consisting of nitrogen-vacancy centers in diamond coupled to both cavity field and mechanical resonator. The effects of initial state of nitrogen-vacancy center and the coupling strength between nitrogen-vacancy center and mechanical resonator on the quadrature squeezing of the phonon field are analyzed. It is shown that the phonon field squeezed state with longtime and high-degree can be generated. The physical reason is that the mechanical resonator has the largest coherence. Moreover, the non-classical property of quadrature squeezing of mechanical resonator can be achieved by manipulating the initial state of nitrogen-vacancy center and magnetic field gradient. The proposal may provide a theoretical way to control and manipulate the quadrature squeezing of the phonon field. The results obtained here may have great significance and applications in the field of quantum information processing and precision measurement.