Investigations Of Many-body Phenomena In Coupled Matter-light Systems

In the past decades, the fields of quantum optics and atomic physics have undergone a chain of rapid developments. The increasing level of experimental control over atomic and optical systems presents a new arena in which to explore strong interaction and con-densation phenomena, originally encountered only in condensed-matter physics. In this thesis, we address the many-body phenomena in two kinds of coupled matter-light sys-tem. The one is the celebrated Dicke model which is a basic model in quantum optics and laser physics. As composite Hamiltonian with not only fermionic but also photonic constituents, the Dicke model is an useful tool for exploring both cavity quantum electro-dynamics and many-body physics. The other is the quantum Fermi gas coupled with an optical cavity.In the beginning, we provide an introduction for the related experimental and theoret-ical backgrounds, as well as a brief outline of some fundamental conceptions. In chapter two, we generalize the Dicke model by including the Kerr-type nonlinear term and the counter-rotating interaction. The quantum phase transition of light can be investigated in such a model, since an additional nonlinearity is included. We solve the model in a straightforward numerical mean. It is shown that, in the ground state, the intracavity photons exhibit a third order quantum phase transition. When the atom-field coupling and the nonlinear coefficient are varied, the quantum state of photons evolves from the bunching to the antibunching. This phase transition originates from the competition between the atom-induced coupling and the effective photon-photon interaction (Kerr nonlinearity). We also demonstrate that the general properties of the phase transition do not qualitatively alter by the size of atomic ensemble and by the detuning between atoms and light.For the methodological purpose, we briefly introduce the notion and the formalism of many-body path integral in chapter three. Such a description provides a vehicle to system-atically identify, isolate, and develop a low-energy theory of collective mode. Moreover, the path integral is the main theoretical tool for the following two chapters. In chapter four, we turn to the discussion of quasiparticle condensation in our generalized Dicke model. By constructing the partition function as a path integral, the thermodynamical properties of the model are presented. On the mean-field level, it is shown that the polari-ton (i.e., coupled mode of atomic excitations with photons) condensation can occur and the Kerr nonlinearity affects the character of the polariton condensate. As the nonlinear coefficient increases, the condensate evolves from more photon-like to more exciton-like. Although the photon nonlinearity gives rise to a chemical potential greater than the pho-ton energy, the quasiparticle excitation spectrum is still fully gapped. For the condensate collective excitations, the nonlinearity destroys the Goldstone modes and mixes the phase modes with the amplitude modes, resulting four non-zero frequency collective modes. To close the chapter, the influence of the photon-exciton (the atomic excitations) detuning on the polariton condensate is also discussed.In chapter five, the system of ultracold Fermi gas coupled to a single mode cavity is investigated. We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) can be realized. By the func-tional integral formulism, in certain parameter regime we obtain an effective atom-only action which mimics the Fermi gas with tunable two-body interaction. First, we address the origin and features of the cavity-mediated interaction between fermions. We find that the matter-light coupling creates an effective s-wave scattering whose sign and ampli-tude are controlled by the parameters of cavity. Second, we discuss superfTuid properties on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, and momentum distribution. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and the external pumping field on the superfluidity are also studied.The last chapter presents a summary of this dissertation, and gives some outlook for the future investigations.