Session A13: Non-Equilibrium Physics with Ultracold Atoms I

Ultrafast many-body interferometry of impurities coupled to a Fermi sea

The fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed matter systems, the time scale for such “ultrafast” processes is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we observed nonequilibrium dynamics of $^{40}$K impurities coupled to a Fermi sea of $^6$Li atoms [Cetina {\it et al.}, Science {\bf 354}, 96 (2016)]. Our interferometric measurements track the nonperturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasi-particles and the quantum interference between attractive and repulsive states throughout the full depth of the Fermi sea. Ultrafast time-domain methods applied to strongly interacting quantum gases enable the study of the dynamics of quantum matter under extreme nonequilibrium conditions. We also report on new results, where we replace the fermionic $^{40}$K impurities with bosonic $^{41}$K atoms. In this case, a small BEC is formed in the center of the large Fermi sea. Close to an interspecies Feshbach resonance we observe striking nonequilibrium dynamics in the collective behavior of the BEC.   

Dynamics of a single hole in the $t-J$ model

The realization of quantum-gas microscopes for ultracold fermions in optical lattices allows to investigate the dynamics of a single hole in an anti-ferromagnetic environment in-situ. We study this problem theoretically using exact numerical methods and semi-analytical approaches. In one dimension the coupling of the hole to the spin-environment is extremely weak -- a manifestation of spin-charge separation -- and we show that the dispersion relation of the magnetic polaron is closely related to the spinon dispersion. In two dimensions, in contrast, the dynamics of the hole is strongly modified by the surrounding spins. To describe this case analytically, we introduce a strong-coupling theory, valid in the limit when the hole-hopping is dominant, and show that a simple picture of the magnetic polaron dispersion can be obtained.   

Continuous time dissipation-assisted quantum walks on a finite lattice

We consider a possible dissipative quantum state transport scheme which makes use of a system which is moving on an $N$-site 1-dimensional lattice, coupled to an environment. The time-evolved interaction Hamiltonian for this system is similar in form to the Hamiltonian for a system undergoing a quantum walk, so the system is said to be undergoing a dissipation-assisted quantum walk. We then derive the master equation describing the dynamics of the system, making use of the Redfield equation in doing so. Numerical evaluation of the resulting master equation shows that it is possible for this quantum state transport scheme to be used to transport excited states to the end of the lattice, so long as the coupling between the system and the environment is weak. Furthermore, the resulting state will be a pure state, making it ideal as well for dissipative preparation of pure quantum states.   

Dynamic impurities coupled to two host Fermi Seas

We propose an ultracold atom setup, analogous to a spintronics device, which allows one to study non-equilibrium spin transport and statistics of fluctuations. This setup can be realized in the currently available experiments by using quantum impurities to induce tunneling between two imbalanced host fermion gases. Non-equilibrium spin accumulation, full counting statistics and the waiting time distributions are discussed in various regimes. Moreover, by employing the Ramsey interferometry, one can reach the dynamic impurity response for full times, which could not be accessed in solid-state systems. This impurity response exhibits a non-trivial exponential decay, different from the standard power-law decay of Anderson's orthogonality catastrophe, which is expected in the case of single host fermions. By mapping this system to a multi-Fermi edge problem, we provide analytical expressions for the impurity response for long time dynamics. Our scheme paves a way for controlling and harnessing fermionic many-body states in atomtronics.   

Towards exact results for spectral functions of quantum impurity models in the long-time limit of the multiple-quench time-dependent numerical renormalization group approach

We develop a new multiple-quench time dependent numerical renormalization group (TDNRG) approach to study the time-evolution of strongly correlated quantum impurities in response to quantum quenches, pulses and periodic driving fields with potential application to a number of fields, including cold atom systems, non-equilibrium transport in nanoscale devices, and the theory of pump-probe spectroscopies of correlated materials within the non-equilibrium dynamical mean field theory. While the single-quench TDNRG suffers from sizeable errors for spectral functions and thermodynamic observables in the long-time limit, we show that our new mutiple-quench TDNRG approach systematically reduces these errors to negligible values. Precise results are presented for local observables of the Anderson model, both static (local occupation and double occupancy) and dynamic (spectral function), in the long-time limit. Significant Improvements are also demonstrated at finite times for periodic driving fields, by comparison with our previous multiple-quench TDNRG approach (H. T. M. Nghiem $\&$ T. A. Costi, Phys. Rev. B89, 075118 (2014) and Phys. Rev. B90, 035129 (2014)).   

Finite temperature quenches of fermions in an optical lattice

Although interaction quenches are known to drive interesting dynamics, much prior work has focused on quenches initiated from states that are well below the system's ordering temperature. Motivated by experiments with ultracold fermions in optical lattices, which are currently outside this regime, as well as recent work with condensed matter out of equilibrium, we study interaction quenches in the Fermi-Hubbard model starting from finite-temperature initial states. We show that interesting dynamics occur even under these conditions. In particular, we study quenches to noninteracting systems, which despite their simplicity have been the focus of recent work concerning integrability and prethermalization. Even in the limit where the initial temperature $T$ is much greater than the tunneling $t$, we find that there is transient growth of intertwined two-site spin and charge correlations. We also study a case in which the initial system contains a single hole defect, and show that the propagation of this defect affects spin correlations even in the absence of interactions.   

Entanglement and Confinement in a two dimensional system of interacting fermions.

In light of recent results on the effect of confinement in quantum quenches in 1D, we examine the out-of-equilibrium dynamics of a system of interacting fermions in two spatial dimensions. Using numerical simulations with chain array matrix product states, and a Bethe-Salpeter analysis, we explore the role of bound states in this system, and their contribution to the post quench correlations and entanglement. In particular we see marked differences in the behaviour of these quantities between quenches in the ordered phase and quenches in the disordered phase of the 2D quantum Ising model.   

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

We study the static and dynamical properties of isolated spin 1/2 systems as prototypes of many-body quantum systems and compare the results to those of full random matrices from a Gaussian orthogonal ensemble. Full random matrices do not represent realistic systems, because they imply that all particles interact at the same time, as opposed to realistic Hamiltonians, which are sparse and have only few-body interactions. Nevertheless, with full random matrices we can derive analytical results that can be used as references and bounds for the corresponding properties of realistic systems. In particular, we show that the results for the Shannon information entropy are very similar to those for the von Neumann entanglement entropy, with the former being computationally less expensive. We also discuss the behavior of the survival probability of the initial state at different time scales and show that it contains more information about the system than the entropies.   

Numerical linked cluster expansions for quantum quenches in one-dimensional Lattices

We discuss the application of two complementary numerical linked cluster expansions (NLCEs) -- a site expansion and a maximally connected expansion -- to the study of quantum quenches in one-dimensional systems of hard-core bosons. We compare the NLCE results with those of exact diagonalization in finite systems with periodic boundary conditions. We show that NLCE results converge faster than exact diagonalization ones to the thermodynamic limit result. Furthermore, we discuss the effectiveness of resummation techniques in extending the region of convergence of NLCEs.   

Transient entanglement generation and control in few-photon bidirectional multiqubit chiral waveguide QED

By driving and applying few-photon Fock state master equation, we investigate the generation and manipulation of multiqubit entanglement in bidirectional waveguide QED. In particular, we focus on how preferential photonic emission directions in the waveguide (chirality) can maximize the generated transient entanglement as compared to the non-chiral settings [Imran M. Mirza and John C. Schotland, Phys. Rev. A 94, 012302 and 012309 (2016)].   

Steady States in Interacting Dissipative Fermionic Floquet Systems

The possibility to drive quantum systems periodically in time offers unique ways to deeply modify their fundamental properties, as exemplified by Floquet topological insulators. It also opens the door to a variety of non-equilibrium effects. Resonant driving fields, in particular, lead to excitations which can expose the system to heating. We previously demonstrated that the analog of thermal states can be achieved and controlled in a fermionic Floquet system in the presence of phonon scattering, spontaneous emission, and an energy filtered fermionic bath. Interactions contribute both to thermalization and heating, and to coherent oscillatory behavior of the long-time state. We analyze the effects of perturbative interactions in the presence of dissipation and the role of coherences in determining the long-time state of the driven system.