This book discusses non-equilibrium quantum many-body dynamics, recently
explored in an analog quantum simulator of strongly correlated ultracold
atoms. The first part presents a field-theoretical analysis of the
experimental observability of the Higgs amplitude mode that emerges as a
relativistic collective excitation near a quantum phase transition of
superfluid Bose gases in an optical lattice potential. The author
presents the dynamical susceptibilities to external driving of the
microscopic parameters, taking into account a leading-order perturbative
correction from quantum and thermal fluctuations and shows clear
signatures of the Higgs mode in these observables. This is the first
result that strongly supports the stability of the Higgs mode in
three-dimensional optical lattices even in the presence of a spatially
inhomogeneous confinement potential and paves the way for desktop
observations of the Higgs mode.
In the second part, the author applies the semi-classical
truncated-Wigner approximation (TWA) to far-from-equilibrium quantum
dynamics. Specifically, he considers the recent experiments on
quantum-quench dynamics in a Bose-Hubbard quantum simulator. A direct
comparison shows remarkable agreement between the numerical results from
TWA and the experimental data. This result clearly indicates the
potential of such a semi-classical approach in reliably simulating
many-body systems using classical computers.
The book also includes several chapters providing comprehensive reviews
of the recent studies on cold-atomic quantum simulation and various
theoretical methods, including the Schwinger-boson approach in strongly
correlated systems and the phase-space semi-classical method for
far-from-equilibrium quantum dynamics. These chapters are highly
recommended to students and young researchers who are interested in
semi-classical approaches in non-equilibrium quantum dynamics.
