| Quantum mechanics has derived many related fields, such as quantum biology, quantum metrology, quantum information and quantum computation, since it was found at the beginning of the last century. Moreover, the quantum information has been used in the practical application to secure communication, and it has much more superiority rather than the classical communication. For the quantum computation, its potential computing power couldn’t match by the classical computation. Nowadays, there are many complex problems which can’t be solved by classical computations in quantum many-body physics. So the quantum computer with powerful computing capacity at-tracts plenty of attention, and a lot of scientists are on the way to this goal. It is a so hard task and will take us a very long time. Though the quantum computer still seems far away, we can realize quantum simulation which was proposed by Feyman in1981, i.e., using a controllable quantum system to simulate another physical system which we want to solve, then we can get the knowledge of the target system’s feature through the quantum system. Quantum simulation is much easier to realize, and people have find some platforms, such as optical lattices, micro-cavity, ion traps, superconductive circuits, cold atoms and so on. By adjusting the external lasers, electrical fields or mag-netic fields, people have successfully simulated many physical models which can’t be solved with the classical computers, e.g., the ground state’s and dynamical features of quantum many body, high dimensional quantum frustrated magnetism, relativity effect, high temperature superconductivity and so on.In quantum many-body physics, nonlinear takes an important role, and it can be applied to quantum entanglement and quantum metrology. In this thesis, we have sim-ulated a kind of nontrival nonlinear coupling in the cavity-polariton system, and studied the nonliear terms’effect on the quantum phase transition and its application in quantum metrology. We’ve found stable3D soliton in the double component BEC with attractive interaction and spin-orbit coupling by numerical simulation. There are four main parts as follows:1. We put the cold atom ensembles in an optical microcavity, and there is a kind of quasiparticle called polariton in the strong coupling regime. Benefit from the high level of polariton’s controllability, we have realized a nonlinear coupling between two com-ponents which doesn’t exist in other systems, e.g. optical lattices. Furthermore, we find that the nonlinear terms can dramatically change the system’s dynamical characteristic and ground state’s feature.2. By extending the single cavity system to an array of cavities, we get an ex- tended two component Bose-Hubbard model. We find that the nonlinear terms can give rich phase diagram. It can change not only the degeneracy of the ground state in Mott regime but also the order of the phase transition from Mott state to superfluid state. Additionally, it can induce the abnormal "even-odd effect" in the Mott regions.3. The nonlinear terms are actually two axis twisting(TAT) Hamiltonian in spin squeezing if we map the two component Bose system into a spin system. Though there are already some theory schemes to realize TAT spin squeezing state, it has not been achieved experimentally due to these methods’complexity. Based on the idea which realizes the nonliear coupling in single cavity, we propose a cavity assisted TAT scheme which is easy to implement.4. As we know, there is no stable soliton in3D attractive Boson system without external potential fields. Extraordinarily, we find that the stable3D soliton can exist in free space if spin-orbit coupling is turned on. In addition, we’ve also studied the mobility and collision of the3D solitons. |
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