The coherence and tunability of Feshbach-resonant gasses enable the experimental studies of highly nonequiblirum quantum many-body states, with a particular focus on the dynamics following a quantum Hamiltonian quench Hi to Hf. These have raised numerous fundamental questions on thermalization under unitary time evolution of a closed quantum system. In my dissertation, I studied the dynamics of two specific systems following a quantum quench: 3d Rb85 resonant Bose gas and 1d spin-imbalanced Fermi-Hubbard model. Using self-consistent Bogoliubov theory and Bosonization formalism, I identify rich post quench dynamics, which lead to thermal or prethermal states that depend strongly on initial state properties. My finding helps better understand the intriguing physics of unitary Bose gas as well as the elusive inhomogeneous superconductivity.
The coherence and tunability of Feshbach-resonant gasses enable the experimental studies of highly nonequiblirum quantum many-body states, with a particular focus on the dynamics following a quantum Hamiltonian quench Hi to Hf. These have raised numerous fundamental questions on thermalization under unitary time evolution of a closed quantum system. In my dissertation, I studied the dynamics of two specific systems following a quantum quench: 3d Rb85 resonant Bose gas and 1d spin-imbalanced Fermi-Hubbard model. Using self-consistent Bogoliubov theory and Bosonization formalism, I identify rich post quench dynamics, which lead to thermal or prethermal states that depend strongly on initial state properties. My finding helps better understand the intriguing physics of unitary Bose gas as well as the elusive inhomogeneous superconductivity.
We explore the dynamics of a resonant Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. For such deep quenches, we utilize a self-consistent dynamic field approximation and find that after an initial regime of many-body Rabi-type oscillations between the condensate and finite-momentum quasiparticle pairs, at long times, the gas reaches a prethermalized nonequilibrium steady state. We explore the resulting state through its broad stationary momentum distribution function, that exhibits a power-law high-momentum tail. We study the dynamics and steady-state form of the associated enhanced depletion, quench-rate-dependent excitation energy, Tan's contact, structure function, and radio-frequency spectroscopy. We find these predictions to be in a qualitative agreement with recent experiments.
The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We develop a conserving many-body theory capable of capturing these effects, allowing us to model the postquench dynamics in the previously inaccessible time regime where the gas departs from the universal prethermal stage. Our results show that this departure is driven by the growth of strong lossless three-body correlations, rather than atomic losses, thus framing the heating of the gas in this regime as a fully coherent phenomenon. We uncover the specific few-body scattering processes that affect this heating and show that the expected connection between the two-body and three-body contacts and the tail of the momentum distribution is obscured following the prethermal stage, explaining the absence of this connection in experiments. Our general framework, which reframes the dynamics of unitary quantum systems in terms of explicit connections to microscopic physics, can be broadly applied to any quantum system containing strong few-body correlations. Published by the American Physical Society 2024
We explore the dynamics of a Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. Within a self-consistent Bogoliubov analysis we find that after the initial condensate-quasiparticle Rabi oscillations, at long time scales the gas is characterized by a nonequilibrium steady-state momentum distribution function, with depletion, condensate density, and contact that deviate strongly from their corresponding equilibrium values. These are in a qualitative agreement with recent experiments on 85Rb by Makotyn et al. Our analysis also suggests that for sufficiently deep quenches close to the resonance the nonequilibrium state undergoes a phase transition to a fully depleted state, characterized by a vanishing condensate density.
Theoretical treatments of nonequilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here we apply the cumulant expansion to study nonequilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance. Published by the American Physical Society 2024
The study of out-of-equilibrium dynamics in ultra-cold gases is a new and exciting field, driven largely by the recent experimental advances in controlling and imaging cold clouds. The experimental and theoretical work thus far has been somewhat exploratory and largely numerical in nature, as the very paradigms for thinking about these systems are not well established. In this thesis I consider several different scenarios of ultra-cold bosonic and fermionic gases driven out of equilibrium and study their properties. In Chapter 1, I provide an overview of the phenomenology of ultra-cold gases, highlighting the timescales governing these systems and how the experimentalist can tune them. I discuss how cold gases can be cooled and trapped and discuss the basic physics behind optical lattices. I also discuss experimental probes of these gases, in particular the new high resolution imaging techniques developed recently at Chicago, Munich and Harvard. In Chapter 2, I discuss an early experiment (circa. 2008) which observed long lived spin dynamics in a thermal spin-1/2 Fermi gas. This experiment is an nice illustration of interesting physics resulting from the separation of timescales between spin and collisional dynamics. In my opinion, it is an excellent example of why cold gases are naturally suited to studying non-equilibrium dynamics. I simulate the experiment numerically using a collisionless Boltzmann equation and explain the observed spin dynamics both qualitatively and quantitively. In Chapter 3, I continue the discussion of spin waves in thermal gases by extending previous works on spin-1/2 gases to spin-1 Bose gases. In contrast to Chapter 2, the bulk of the work in this Chapter is analytic in nature. In particular, I find a spin wave instability in the thermal spin-1 Bose gas, which is the high temperature analog of the polar to ferromagnetic transition in a spin-1 Bose Einstein condensate. In Chapter 3, I turn my attention to bosonic systems and briefly review the the Bogoliubov mean-field theory. I calculate the momentum distribution and density-density correlation function of an interacting Bose gas within the Bogoliubov framework. Then I consider bosons in an optical lattice, and introduce the Bose Hubbard model. I calculate the mean-field phase diagram of the Bose Hubbard model and then consider fluctuations about the mean field, and derive the excitation spectrum of the lattice gas in the superfluid and insulating regimes. In Chapter 4, I ask what we learn by studying the dynamics of correlation functions following a sudden change in the interactions in a superfluid. Using the Bogoliubov theory developed in Chapter 3, I will show how the underlying excitation spectrum influences the long and short time behavior of the correlation functions. By considering a lattice dispersion, I study the analogous problem in a weak optical lattice and discuss how the lattice dispersion leads to additional features in the correlation functions. I will also discuss the timescale governing the revival of the condensate fraction in a quantum depleted gas. In Chapter 5, I derive equations of motion governing the dynamics of one and two body correlation functions in the single-band Bose Hubbard model, applicable to bosons in deep lattices. I then consider a simple quench from a Mott insulating initial state to a weakly interacting final state and produce analytic expressions describing the dynamics of correlations following such a quench. I discuss the timescale for the development of long range order following such a quench. I study the problem of chapter 4 using an equations of motion approach. This approach complements the Bogoliubov approach of Chapter 4. First, I derive exact expressions for a quench to a non-interacting state. I then consider how interactions redistribute quasi-momentum to first order in perturbation theory in different dimensions. In Chapter 6, I calculate the relevant timescales for local and global dynamics in trapped lattice Bose gases, a work done in collaboration with Dr. Kaden R. A Hazzard. Using a time-dependent Gutzwiller mean-field theory, I show that the timescale for local equilibration in these systems is fast in experimental terms. I then show that due to the spatial inhomogeneities inherent to cold gases, achieving global equilibrium can be quite complicated, sometimes taking longer than the lifetime of the experiment, an issue of practical importance to current day experiments. I continue this discussion in Chapter 7 which is a collaborative work with experimentalists David McKay and Prof. Brian DeMarco from the University of Toronto and the University of Illinois, Urbana Champaign. Using experimental and numerical methods, we show that the rapid timescales for local dynamics in interacting systems invalidates a frequently used cold atom technique for mapping out the momentum distribution of atoms in an optical lattice.
We study a nonequilibrium dynamics of a one-dimensional spin-imbalanced Fermi-Hubbard model following a quantum quench of on-site interaction, realizable, for example, in Feshbach-resonant atomic Fermi gases. We focus on the post-quench evolution starting from the initial BCS and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) ground states and analyze the corresponding spin-singlet, spin-triplet, density-density, and magnetization-magnetization correlation functions. We find that beyond a light-cone crossover time, rich post-quench dynamics leads to thermalized and pre-thermalized stationary states that display strong dependence on the initial ground state. For initially gapped BCS state, the long-time stationary state resembles thermalization with the effective temperature set by the initial value of the Hubbard interaction. In contrast, while the initial gapless FFLO state reaches a stationary pre-thermalized form, it remains far from equilibrium. We suggest that such post-quench dynamics can be used as a fingerprint for identification and study of the FFLO phase.