Quantum Dynamics of Correlated Fermions In- and Out-of-Equilibrium

This dissertation attempts to explore some interesting quantum dynamics of strongly correlated fermionic systems from a theorist's perspective, with whether and how it can be accessed experimentally in mind. Two correlated fermionic systems are studied: superconductors under the mean-field approximation (both in- and out-of-equilibrium), and a Sachdev-Ye-Kitaev-boson (SYK-boson) model (quench dynamics). Two experimental probes are considered when studying superconductors: time- and angle-resolved photoemission spectroscopy (tr-ARPES), and nonlinear optics, while the SYK-boson model may be simulated in the state-of-art cavity quantum electrodynamics (cavity-QED) experiments with cold atomic gases./nIn our studies of non-equilibrium superconductors, we look into how tr-ARPES reveals the dynamics of BCS-type, s-wave superconducting systems with time-varying order parameters. Approximate methods are discussed, based on previous approaches to either optical conductivity or quantum dot transport, to enable computationally efficient prediction of photoemission spectra. One use of such predictions is to enable extraction of the underlying order parameter dynamics from experimental data, which is topical given the rapidly growing use of tr-ARPES in studying unconventional superconductivity. The methods considered model the two-time lesser Green functions with an approximated lesser self-energy that describes relaxation by coupling of the system to two types of baths. The approach primarily used here also takes into consideration the relaxation of the excited states into equilibrium by explicitly including the level-broadening of the retarded and advanced Green functions. We present equilibrium and non-equilibrium calculations of tr-ARPES spectra from our model and discuss the signatures of different types of superconducting dynamics. We then use this theory to study the validity of the quasi-static theory that are widely used to understand superconducting gap dynamics from tr-ARPES spectra, and found that the quasi-static method cannot predict superconducting gap dynamics accurately when the gap changes too fast. Lastly, we try to find the possible signature of a time-reversal breaking superconductor in a tr-ARPES experiment by studying the gap dynamics of such systems. In this study, we found a possible Higgs oscillation./nIn our study of nonlinear optical responses of an inversion-breaking superconductor, we found that, even for a superconducting system that has a inversion-symmetric electronic degree of freedom, the system can still have an optical response when superconducting pairing breaks the inversion symmetry. We first show that any superconducting system with inversion ($\I$) and time-reversal ($\TR$) symmetries requires an $\I$-breaking order parameter to support optical transitions between particle-hole pair bands. We then use a 1D toy model of an $\I$-breaking superconductor to numerically calculate linear and nonlinear optical conductivities, including shift current and second harmonic generations (SHG) responses. We find that the magnitude of the signal is significantly larger in shift current/SHG responses than in the linear response due to the matrix element effect. We also present various scaling behaviors of the SHG signal, which may be relevant to the recent experimental observation of SHG in Cuprates. Finally, we confirm the generality of our observations regarding nonlinear responses of $\I$-breaking superconductors, by analyzing other models including a 1D three-band model and 2D square lattice model./nLast but not least, in our study of the quench dynamics of the SYK-boson model in large$-N$ limit, we study how various quench scenarios manifest themselves in the dynamics of both the fermions and bosons, and we also study how different boson frequency distributions affect the fermion dynamics. We found that one boson can drive a quantum Zeno effect of the fermions, while for many-boson cases, the fermion dynamics is complicated. Depending on the specific quench scenarios, the bosons can either drive an instability in the fermions, or induce a Zeno-like effect at longer times that could either be a slowly-decaying transient, or some perpetual motions.

Advisor: Moore, Joel E. JEM