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Strongly correlated ultracold bosons in an optical lattice
In this thesis, we have investigated strongly correlated bosonic gases in an optical lattice, mostly based on a bosonic version of dynamical mean field theory and its real-space extension. Emphasis is put on possible novel quantum phenomena of these many-body systems and their corresponding underlying physics, including quantum magnetism, pair-superfluidity, thermodynamics, many-body cooling, new quantum phases in the presence of long-range interactions, and excitational properties. Our motivation is to simulate manybody phenomena relevant to strongly correlated materials with ultracold lattice gases, which provide an excellent playground for investigating quantum systems with an unprecedented level of precision and controllability. Due to their high controllability, ultracold gases can be regarded as a quantum simulator of many-body systems in solid-state physics, high energy astrophysics, and quantum optics. In this thesis, specifically, we have explored possible novel quantum phases, thermodynamic properties, many-body cooling schemes, and the spectroscopy of strongly correlated many-body quantum systems. The results presented in this thesis provide theoretical benchmarks for exploring quantum magnetism in upcoming experiments, and an important step towards studying quantum phenomena of ultracold gases in the presence of long-range interactions
Lattice supersolid phase of strongly correlated bosons in an optical cavity
We numerically simulate strongly correlated ultracold bosons coupled to a
high-finesse cavity field, pumped by a laser beam in the transverse direction.
Assuming a weak classical optical lattice added in the cavity direction, we
model this system by a generalized Bose-Hubbard model, which is solved by means
of bosonic dynamical mean-field theory. The complete phase diagram is
established, which contains two novel self-organized quantum phases, lattice
supersolid and checkerboard solid, in addition to conventional phases such as
superfluid and Mott insulator. At finite but low temperature, thermal
fluctuations are found to enhance the buildup of the self-organized phases. We
demonstrate that cavity-mediated long-range interactions can give rise to
stable lattice supersolid and checkerboard solid phases even in the regime of
strong s-wave scattering. In the presence of a harmonic trap, we discuss
coexistence of these self-organized phases, as relevant to experiments.Comment: 4 pages, 3 figure
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