There are many ways to characterize quantum systems, for example, by measuring system-specific observables or probing their response to external perturbations. A complementary approach is based on quantum information measures. Independent of the microscopic details, it offers a universal perspective on quantum systems and enables a unified characterization of diverse quantum systems. Central, in this regard, is the determination of the quantum entanglement within a quantum system. Recently, in the interest of studying genuine nonequilibrium properties of a quantum system, the dynamics of the quantum entanglement have been established as a powerful approach to gain deep insights into the structure of quantum matter. In this Thesis, we investigate the entanglement dynamics in one-dimensional non-interacting fermionic chains following a quantum quench, i.e. after a sudden change of the system parameters. We propose a new and generic setting for the analysis of entanglement spreading in complex inhomogeneous systems, which we call a hybrid quench-probe setup. The key feature of this new approach is a separation between the quenched part of the system and a static probe region, where the quench induced entanglement spreading is measured. This separation allows a spatial and energy-resolved analysis of the entanglement dynamics. We demonstrate the capability of our protocol by identifying fractionally quantized entanglement jumps of log(2)/2 as a signature of fractionalized topological quasi-particles, such as isolated Majorana modes, that appear at the edges of an open-boundary Kitaev chain in the topological phase. In addition, we observe in this setup an interesting nonequilibrium effect: a static and a propagating contribution to the entanglement dynamics. To understand the origin of this effect, a local perspective on the entanglement structure is necessary. For this purpose, we employ the information lattice, which offers a local scale-resolved decomposition of the correlations present in a quantum state. In nonequilibrium systems with unitary dynamics, this framework enables a hydrodynamic description of the information flow through local densities and currents. Using the information lattice, we analyze three quantum quenches in one-dimensional fermionic systems and identify spatiotemporal features of the local information flow, such as information interfaces and long-range transport from topological edge modes. This analysis enables us to derive an analytical description of the nonequilibrium effect observed in the quenched Kitaev chain.
We study the nonadiabatic dynamics of a two-dimensional
p+ip superfluid following an instantaneous quantum quench of the BCS coupling constant. The model describes a topological superconductor with a nontrivial BCS (trivial BEC) phase appearing at weak- (strong-) coupling strengths. We extract the exact long-time asymptotics of the order parameter $\ensuremath{\Delta}(t)$ by exploiting the integrability of the classical
p-wave Hamiltonian, which we establish via a Lax construction. Three different types of asymptotic behavior can occur depending upon the strength and direction of the interaction quench. We refer to these as the nonequilibrium phases {I, II, III}, characterized as follows. In phase I, the order parameter asymptotes to zero due to dephasing. In phase II, $\ensuremath{\Delta}\ensuremath{\rightarrow}{\ensuremath{\Delta}}_{\ensuremath{\infty}}$, a nonzero constant. Phase III is characterized by persistent oscillations of $\ensuremath{\Delta}(t)$. For quenches within phases I and II, we determine the topological character of the asymptotic states. We show that two different formulations of the bulk topological winding number, although equivalent in the BCS or BEC ground states, must be regarded as independent out of equilibrium. The first winding number
Q characterizes the Anderson pseudospin texture of the initial state; we show that
Q is generically conserved. For $Q\ensuremath{\ne}0$, this leads to the prediction of a ``gapless topological'' state when $\ensuremath{\Delta}$ asymptotes to zero. The presence or absence of Majorana edge modes in a sample with a boundary is encoded in the second winding number
W, which is formulated in terms of the retarded Green's function. We establish that
W can change following a quench across the quantum critical point. When the order parameter asymptotes to a nonzero constant, the final value of
W is well defined and quantized. We discuss the implications for the (dis)appearance of Majorana edge modes. Finally, we show that the parity of zeros in the bulk out-of-equilibrium Cooper-pair distribution function constitutes a
Z2-valued quantum number, which is nonzero whenever $W\ensuremath{\ne}Q$. The pair distribution can in principle be measured using rf spectroscopy in an ultracold-atom realization, allowing direct experimental detection of the
Z2 number. This has the following interesting implication: topological information that is experimentally inaccessible in the bulk ground state can be transferred to an observable distribution function when the system is driven far from equilibrium.
We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.
We study the sudden quench of a one-dimensional p-wave superconductor through its topological signature in the entanglement spectrum. The long-time evolution of the system and its topological characterization depend on a pseudomagnetic field ${\bs R}_{\mbox{\text eff}}(k)$, which connects both the initial and the final Hamiltonians, hence exhibiting a memory effect. In particular, we explore the robustness of the Majorana zero-mode associated with the entanglement cut in the topologically nontrivial phase and identify the parameter space in which the mode can survive in the infinite-time limit.
The fermionic and Majorana edge mode dynamics of various topological systems are compared, after a sudden global quench of the Hamiltonian parameters takes place. Attention is focused on the regimes where the survival probability of an edge state has oscillations either due to critical or off-critical quenches. The nature of the wave functions and the overlaps between the eigenstates of different points in parameter space determine the various types of behaviors, and the distinction due to the Majorana nature of the excitations plays a lesser role. Performing a sequence of quenches, it is shown that the edge states, including Majorana modes, may be switched off and on. Also, the generation of Majoranas due to quenching from a trivial phase is discussed.