Quantum systems engineering

Abstract:

The existence of multistability in quantum systems beyond the mean-field approximation remains an intensely debated open question. Quantum fluctuations are finite-size corrections to the mean-field as the full exact solution is unobtainable and they usually destroy the multistability present on the mean-field level. Here, by identifying and using exact modulated dynamical symmetries in a driven-dissipative fermionic chain we exactly prove multistability in the presence of quantum fluctuations. Further, unlike common cases in our model, rather than destroying multistability, the quantum fluctuations themselves exhibit multistability, which is absent on the mean-field level for our systems. Moreover, the studied model acquires additional thermodynamic dynamical symmetries that imply persistent periodic oscillations, constituting the first case of a boundary time crystal,to the best of our knowledge, a genuine extended many-body quantum system with the previous cases being only in emergent single- or few-body models. The model can be made into a dissipative time crystal in the limit of large dissipation (i.e. the persistent oscillations are stabilized by the dissipation) making it both a boundary and dissipative time crystal.

Abstract:

Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small fraction of the pairs of the constituents directly interact. Motivated by advances in control over the pairwise interactions in many-body simulators, we determine the fate of spin systems on more general, arbitrary graphs. Placing the minimum possible constraints on the underlying graph, we prove how, with certainty in the thermodynamic limit, such systems behave like a single collective spin. We thus understand the emergence of complex many-body physics as dependent on 'exceptional', geometrically constrained structures such as the low-dimensional, regular ones found in nature. Within the space of dense graphs we identify hitherto unknown exceptions via their inhomogeneity and observe how complexity is heralded in these systems by entanglement and highly non-uniform correlation functions. Our work paves the way for the discovery and exploitation of a whole class of geometries which can host uniquely complex phases of matter.

Abstract:

Stark many-body localized (SMBL) systems have been shown both numerically and experimentally to have Bloch many-body oscillations, quantum many-body scars, and fragmentation in the large field tilt limit, but these observations have not been fundamentally understood. We explain and analytically prove all these observations by rigorously perturbatively showing the existence of novel algebraic structures that are exponentially stable in time, which we call dynamical l-bits. In particular, we show that many-body Bloch oscillations persist even at infinite temperature for exponentially long-times using a new type of dynamical algebra and provide a bound on the tilt strength for this non-ergodic transition. We numerically confirm our results by studying the prototypical Stark MBL model of a tilted XXZ spin chain. Our work explains why thermalization was observed in a recent 2D tilted experiment. As dynamical l-bits represent stable, localized, and quantum coherent excitations, our work opens new possibilities for quantum information processing in Stark MBL systems even at high temperature.