Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain.

The construction of the generalized Gibbs ensemble, to which isolated integrable quantum many-body systems relax after a quantum quench, is based upon the principle of maximum entropy. In contrast, there are no universal and model-independent laws that govern the relaxation dynamics and stationary states of open quantum systems, which are subjected to Markovian drive and dissipation. Yet, as we show, relaxation of driven-dissipative systems after a quantum quench can, in fact, be determined by a maximum entropy ensemble, if the Liouvillian that generates the dynamics of the system has parity-time symmetry. Focusing on the specific example of a driven-dissipative Kitaev chain, we show that, similar to isolated integrable systems, the approach to a parity-time symmetric generalized Gibbs ensemble becomes manifest in the relaxation of local observables and the dynamics of subsystem entropies. In contrast, the directional pumping of fermion parity, which is induced by nontrivial non-Hermitian topology of the Kitaev chain, represents a phenomenon that is unique to relaxation dynamics in driven-dissipative systems. Upon increasing the strength of dissipation, parity-time symmetry is broken at a finite critical value, which thus constitutes a sharp dynamical transition that delimits the applicability of the principle of maximum entropy. We show that these results, which we obtain for the specific example of the Kitaev chain, apply to broad classes of noninteracting fermionic models, and we discuss their generalization to a noninteracting bosonic model and an interacting spin chain.

Quantized Floquet Topology with Temporal Noise.

Time-periodic (Floquet) drive is a powerful method to engineer quantum phases of matter, including fundamentally nonequilibrium states that are impossible in static Hamiltonian systems. One characteristic example is the anomalous Floquet insulator, which exhibits topologically quantized chiral edge states similar to a Chern insulator, yet is amenable to bulk localization. We study the response of this topological system to time-dependent noise, which breaks the topologically protecting Floquet symmetry. Surprisingly, we find that the quantized response, given by partially filling the fermionic system and measuring charge pumped per cycle, remains quantized up to finite noise amplitude. We trace this robust topology to an interplay between diffusion and Pauli blocking of edge state decay, which we expect should be robust against interactions. We determine the boundaries of the topological phase for a system with spatial disorder numerically through level statistics, and corroborate our results in the limit of vanishing disorder through an analytical Floquet superoperator approach. This approach suggests an interpretation of the state of the system as a non-Hermitian Floquet topological phase. We comment on quantization of other topological responses in the absence of Floquet symmetry and potential experimental realizations.

Quantum non-demolition measurement of a many-body Hamiltonian.

In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.

Space-Time Vortex Driven Crossover and Vortex Turbulence Phase Transition in One-Dimensional Driven Open Condensates.

We find a first-order transition driven by the strength of nonequilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable nonequilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly nonthermal behavior. Below the transition, we identify a new time scale associated with noise-activated unbound space-time vortices, beyond which, the temporal coherence function changes from a Kardar-Parisi-Zhang-type subexponential to a disordered exponential decay. Experimental realization of the nonequilibrium vortex turbulent phase is facilitated in driven open condensates with a large diffusion rate.