Complex coherent quantum many-body dynamics through dissipation
Nature Communications Springer Nature 10 (2019) 1730
Abstract:
The assumption that physical systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies. These have been studied for systems with a few degrees of freedom only. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationary dynamics typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.Isolated Heisenberg magnet as a quantum time crystal
Physical Review B American Physical Society 102:4 (2020) 041117(R)
Abstract:
We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not equilibrate. It constitutes an example of persistent nonstationarity in a quantum many-body system that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries. We discuss how the ensuing persistent oscillations that seemingly violate one of the most fundamental laws of physics could be observed experimentally.Out-of-time-ordered crystals and fragmentation
Physical Review Letters American Physical Society 128 (2021) 100601
Abstract:
Is a spontaneous perpetual reversal of the arrow of time possible? The out-of-time-ordered correlator (OTOC) is a standard measure of irreversibility, quantum scrambling, and the arrow of time. The question may be thus formulated more precisely and conveniently: can spatially ordered perpetual OTOC oscillations exist in many-body systems? Here we give a rigorous lower bound on the amplitude of OTOC oscillations in terms of a strictly local dynamical algebra allowing for identification of systems that are out-of-time-ordered (OTO) crystals. While OTOC oscillations are possible for few-body systems, due to the spatial order requirement OTO crystals cannot be achieved by effective single or few body dynamics, e.g., a pendulum or a condensate. Rather they signal perpetual motion of quantum scrambling. It is likewise shown that if a Hamiltonian satisfies this novel algebra, it has an exponentially large number of local invariant subspaces, i.e., Hilbert space fragmentation. Crucially, the algebra, and hence the OTO crystal, are stable to local unitary and dissipative perturbations. A Creutz ladder is shown to be an OTO crystal, which thus perpetually reverses its arrow of time.Algebraic theory of quantum synchronization and limit cycles under dissipation
SciPost Physics SciPost 12 (2022) 097
Abstract:
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.Unified theory of local quantum many-body dynamics: eigenoperator thermalization theorems
Physical Review X American Physical Society 13:3 (2023) 31013