Cavity Optomechanics And Spin Squeezing Based On Cavity Quantum Electrodynamics

Information science is a study about the motion laws and applications of infor-mation. In recent 30 years, the quantum information science, as a cross-field of in-formation science and quantum mechanics, has received widespread attention. Due to some novel properties of quantum information science, such as quantum state for-bidden cloning, linear superposition and quantum entanglement, it shows a very broad application prospect in quantum computing, quantum information and quantum metrol-ogy. Quantum computers with the ability of parallel computing can greatly improve the computing rate over classical computers, which has many potential applications in password cracking and quantum searching. By using the properties of quantum state forbidden cloning and quantum entanglement, quantum information has made a signifi-cant progress in the realization of quantum cryptography and quantum communication. Quantum metrology is also well promoted for the demand of measuring high precision quantity, and it has become a hot topic in quantum clocks, gravitational wave detection and so on, which has exceeded the classical limit, even approaching the Heisenberg limit in some areas.These anvantages of quantum information science attract people to seek all kinds of information carriers for realization of the quantum computer. There are various fac-tors to be considered on the physical implementation, and great progress has been made in the systems of iron trap, superconducting electronic circuit, cavity quantum elec-trodynamics device and molecular nuclear magnetic resonance. However, the actual physical systems have to face all sorts of decoherence, and more quantum qubits mean more serious decoherence. Fortunately many systems have distinct advantage in some aspects, so the hybrid system is also of great concern. Cavity optomechanical system shows future applications in quantum information storage, quantum chaos, wavelength conversion, especially the hybrid system with optomechanical system coupled to the atom or quantum dots, which is a very hot research recently. Cavity quantum electro-dynamics (C-QED) is an important field in studying the interaction between atoms and optical modes. In the optical cavity with a high quality factor, the photons interact with atoms many times, so the strong coupling between atoms and light field can be realized, which can be used to generate the spin squeezed state (SSS) for quantum metrology.In this thesis, we first introduce some basic knowledge of quantum information science in brief, and discuss the cavity optomechanical system and cavity quantum electrodynamics devices. For the cavity optomechanical system, we study some ba-sic properties and applications of this system, and analyze the hybrid system with op-tomechanical system coupled to the quantum dot, the input-output of single-photon and two-photon and phonon laser. For cavity quantum electrodynamics devices, we dis-cuss the preparation of spin squeezed states in detail, which mainly includes the study of detuning-enhanced cavity spin squeezing, phonon induced spin squeezing based on geometric phase and inducing spin squeezed nitrogen-vacancy (NV) centers via contin-uous driving in a steady state. The details are the following four aspects:1. The study of the cavity optomechanical system.Cavity optomechanical system is a very important system for the realization of quantum communication and quantum computation with rich physical phenomena and many potential applications. We make a simple discussion about the optomechanically induced transparency, Brillouin-scattering-induced transparency, non-reciprocal light storage and so on. In the hybrid system with optomechanical system coupled to the quantum dot, we find the phenomenon of vacuum cavity induced transparency, which is analyzed detailly in the weak and strong coupling. Besides, we compare vacuum cavity induced transparency to the transparency in the classical control light. Finally, for better unstanding the induced transparency phenomenon, we study the incoherent control of electromagnetically induced transparency (EIT) and Aulter-Townes splitting (ATS) in the unified framework of three-level system, and distinguish these similar phe-nomena. For the input-output of cavity optomechanical system, we obtain the single-photon emission and scattering via quadratic optomechanical coupling, which reveals that the even number of phonon is inspired. On the basis, we further study the two-photon input-output system in the real space. For the phonon laser, we propose several possible implementation schemes.2. Detuing-enhanced cavity spin squeezing.We theoretically discuss the effect of various parameters on cavity spin squeez-ing for the experimental scheme, and comparing with the near resonance case, it is surprising to find that the scaling of cavity squeezing on total atomic spin S can be sig-nificantly improved from S-2/5 to S-2/3 for large detuning. In addition, we find that the spin squeezing will be enhanced if the atoms are weakly coupled to the cavity or the laser detuning is very large. From our numerical solutions and analytical analysis, the large detuning is very important as the squeezing originates from the laser induced spin state dependent geometry phase. For the actual physical system, some noise is in-evitable. We study the influence of imperfect Raman scattering, and demonstrate that the optimal spin squeezing can be obtained with appropriate detuning. Since large de-tuning means less effective light field into the optical cavity, it takes longer time to achieve the optimal spin squeezing. The single spin dephasing has to be considered, which can be suppressed by the larger input power. The large detuning also means that other cavity modes may be activated, and our analysis shows that the effective coupling between the spin and the other cavity modes is very small, and the bad effect can be ignored. Finally, we take the parameters of experimental realization into the scheme, which shows that the improvement of spin squeezing by detuning is very feasible for experiments. As a supplement of spin squeezing, we also make some discussions about preparing the non-classical states by measurement based on this scheme.3. Phonon induced spin squeezing based on geometric phase in the system of nitrogen-vacancy (NV) centers.We propose a new approach for the realization of spin squeezing by an ensemble of NV centers coupled to a mechanical resonator. We discuss the spin squeezing with dif-ferent thermal excitation and quality factor of the mechanical mode, which shows that the ultimate degree of spin squeezing fully depends on the ratio between the thermal excitation and the quality factor Q:The geometric phase is insensitive to the phonon initial state because of its property, which is a very important advantage on experiment. In the realistic situations, the environmental thermal bathes are independently coupled to the every spin, which alsways leads to decoherence. We can suppress the noise by dynamical decoupling, and the ultimate limit of the ideal one-axis twisting spin squeez-ing can be obtained with enough high quality factor Q of the mechanical mode. Finally, we discuss the experimental schemes and parameters, and it concludes that the scheme is feasible with realistic experimental parameters.4. Inducing spin squeezed nitrogen-vacancy (NV) centers via continuous driving in a steady state.We present a new approach for the generation of nitrogen-vacancy (NV) spin squeezed steady state by continuously driving NV spins, which relies on the collective coupling of NV centers to a optical decay mode. Under the certain frequency matching, the ef-fective Hamiltonian can be obtained by rotating-wave approximation. The effective Hamiltonian demonstrates the existence of a collective NV spin dark-state, which can be deterministically prepared via dissipative means. The dark-state is the spin squeez-ing steady state, thus turning dissipation into a resource for entanglement. By exploring the dynamics of spin squeezing with various driving amplitudes and frequencies, we find that the higher frequency means less fluctuation and better squeezing, which is due to better meeting the rotating-wave approximation, however, the degree of the spin squeezing steady state fully depends on the driving amplitudes. Besides, we analyze the influence of photon noise on spin squeezing. Finally, we have a try on studying the phase transitions of spin squeezing under the frequency mismatching.