Nonequilibrium Properties of Strongly Correlated One-dimensional Quantum Gases

Abstract

Okinawa Institute of Science and Technology Graduate UniversityDoctor of PhilosophyUnderstanding and controlling nonequilibrium quantum systems offers promising routes to applications unattainable in equilibrium systems. While equilibrium physics benefits from well-established approaches, such as minimizing free energy and obtaining various thermodynamic quantities, nonequilibrium systems possess less general guiding principles and approaches. Furthermore, strong correlations plays a crucial role in various quantum phenomena, such as high-temperature superconductors or superfluid helium, yet analyzing strongly correlated quantum systems remains exceedingly challenging. This is because these systems often require rigorous analysis beyond the standard perturbation theory, leading to the necessity of dealing with the large Hilbert space dimensions, which makes theoretical analysis difficult. However, in the case of a one-dimensional strongly interacting Bose gas called Tonks–Girardeau (TG) gas, an exact mapping to a noninteracting fermions is possible, providing a unique platform to study a strongly correlated many-body systems. This thesis aims to advance the theoretical understanding of nonequilibrium strongly correlated quantum systems from two distinct perspectives: integrability and Floquet physics. First, I investigate the nonequilibrium dynamics of strongly correlated TG bosons immersed in a weakly correlated Bose–Einstein condensate. I show that the TG bosons form an integrable soliton-train supported by the condensate. Moreover, since a gas of the noninteracting fermions follows the same governing equations, the quantum statistical nature of the soliton-train can be addressed, leading to the notion of a quantum soliton-trains. Next, I study the TG gas under a strong external time-periodic drive. By computing the nonequilibrium Green’s function exactly, I reveal the excitation spectrum of this Floquet-engineered material. Employing Floquet spectral function theory and the Bose–Fermi mapping theorem, I uncover the existence of nonequilibrium Lieb excitations when the underlying mapped fermions form a Floquet–Fermi sea.doctoral thesi