Nonclassical Properties Study Based On Superconducting Circuit System And BEC

Quantum information science, which applies the basic principles and theories of quantum mechanics to information science, was born in1980s. It mainly con-tains quantum computation, quantum communication, quantum metrology and so on. Due to the unique properties of quantum mechanics which are different from classical mechanics, such as linear superposition and interference of quantum states, quantum information shows many phenomena that are different from classical world, such as nonlocality and quantum entanglement. Also, quantum information owns many advan-tages over classical information due to these unique properties, such as the ability in the storage, computing and communication for large amounts of information; quantum parallelism resulting from the linear superposition of quantum states can greatly im-prove the speed of quantum computing; the existence of quantum no-cloning theorem and quantum entanglement guarantees the absolute security and the ability for long distance transmission of quantum information; quantum metrology makes the mea-surement accuracy exceeding the limit that the classical physics can achieve-standard quantum limit and approaching the quantum mechanics limit-Heisenberg limit.In this thesis, we introduce some basic theories of quantum information and sever-al research fields including quantum computing, quantum communication and quantum metrology in chapter1. We emphasize on spin squeezing which plays an important role in improving the measurement accuracy, and two-axis spin squeezing state is more pop-ular on account of its approaching to Heisenberg limit. Superconducting circuit system acting as one of the most promising physical schemes to realize quantum computing in future is often used to study some nonclassical phenomena in quantum information such as two-photon laser. In chapter2, we introduce some fundamental theories of superconducting circuit system, including the Josephson effect, superconducting qubit, superconducting transmission line resonator, and the interaction among them. Center-ing on these systems and nonclassical properties, we carry out our study as following:1、We theoretically study the system of a superconducting transmission line res-onator coupled to two interacting superconducting flux qubits, and propose a scheme to realize two-photon laser. When we neglect the incoherent process including the dis-sipation and pumping, it is shown that under certain conditions, the resonator mode can be tuned to two-photon resonance between the ground state and the highest excited state while the middle excited states are far-off resonance. Next, we consider the dissi-pation and the incoherent pumping, study the steady-state properties of the system such as the photon statistics, the spectrum and squeezing of the resonator. By analyzing the numerical results, we find that the population can be realized due to the competition between coherent coupling, incoherent pumping, and dissipation. Besides, it shows that the two-photon process between the highest excited state and the ground state is dominant, and at the parameters which can be achieved in experiment, the Fano factor is larger than one (F>1), which is expected in two-photon laser. All that demonstrate that such system may be appropriate for two-photon laser.2、We propose a scheme to transform the OAT into the effective TAT spin squeez-ing in BEC by continuous coherent driving. By carefully choosing and tuning the amplitude and frequency of the driving field, pure effective TAT Hamiltonian can be realized and a Heisenberg limited noise reduction oc∝N-1is obtained, where N is the number of atoms. Compared with the scheme proposed by Y. C. Liu et al[Phys. Rev. Lett.107,013601(2001)], our proposal uses a continuous field instead of pulse se-quences, which is more friendly for experiments and is promising in future. What’s more, compared with the scheme proposed by L. M. Duan et al[Phys. Rev. A87,051801(2013)], our scheme is spin number independent and needs a shorter evolution time.