Quantum systems engineering

Abstract:

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.

Abstract:

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit "Doob-transformed" dynamics that optimally realizes rare dynamical events.

Abstract:

We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady states with long-range correlations between η pairs. We induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal η correlations. These correlations were first recognized in the superconducting eigenstates described in Yang’s seminal Letter [Phys. Rev. Lett. 63, 2144 (1989)], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.

Abstract:

We show that strong electron-electron interactions in quantum materials can give rise to electronic transitions that couple strongly to cavity fields, and collective enhancement of these interactions can result in ultrastrong effective coupling strengths. As a paradigmatic example we consider a Fermi-Hubbard model coupled to a single-mode cavity and find that resonant electron-cavity interactions result in the formation of a quasi-continuum of polariton branches. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and scales with USD g_{\text{eff}}\propto\sqrt{2L} USD, where USD L USD is the number of electronic sites, and the maximal achievable value for USD g_{\text{eff}} USD is determined by the volume of the unit cell of the crystal. We find that USD g_{\text{eff}} USD for existing quantum materials can by far exceed the width of the first excited Hubbard band. This effect can be experimentally observed via measurements of the optical conductivity and does not require ultrastrong coupling on the single-electron level. Quantum correlations in the electronic ground state as well as the microscopic nature of the light-matter interaction enhance the collective light-matter interaction compared to an ensemble of independent two-level atoms interacting with a cavity mode.