Quantum systems engineering

Abstract:

Under the action of coherent periodic driving a generic quantum system will undergo Floquet heating and continuously absorb energy until it reaches a featureless thermal state. The phase-space constraints induced by certain symmetries can, however, prevent this and allow the system to dynamically form robust steady states with off-diagonal long-range order. In this work, we take the Hubbard model on an arbitrary lattice with arbitrary filling and, by simultaneously diagonalizing the two possible SU(2) symmetries of the system, we analytically construct the correlated steady states for different symmetry classes of driving. This construction allows us to make verifiable, quantitative predictions about the long-range particle-hole and spin-exchange correlations that these states can possess. In the case when both SU(2) symmetries are preserved in the thermodynamic limit we show how the driving can be used to form a unique condensate which simultaneously hosts particle-hole and spin-wave order.

Abstract:

Coherent driving has established itself as a powerful tool for guiding a many-body quantum system into a desirable, coherent non-equilibrium state. A thermodynamically large system will, however, almost always saturate to a featureless infinite temperature state under continuous driving and so the optical manipulation of many-body systems is considered feasible only if a transient, prethermal regime exists, where heating is suppressed. Here we show that, counterintuitively, in a broad class of lattices Floquet heating can actually be an advantageous effect. Specifically, we prove that the maximum entropy steady states which form upon driving the ground state of the Hubbard model on unbalanced bi-partite lattices possess uniform off-diagonal long-range order which remains finite even in the thermodynamic limit. This creation of a 'hot' condensate can occur on any driven unbalanced lattice and provides an understanding of how heating can, at the macroscopic level, expose and alter the order in a quantum system. We discuss implications for recent experiments observing emergent superconductivity in photoexcited materials.

Abstract:

We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.