Nonreciprocal and Geometric Frustration in Dissipative Quantum Spins

TL;DR

This paper explores how nonreciprocal interactions in dissipative quantum spins induce both nonreciprocal and geometric frustration, leading to novel phases like time crystals and chiral dynamics, with robustness against disorder.

Contribution

It reveals the interplay of nonreciprocal and geometric frustration in quantum spins mediated by a cavity, uncovering a nonreciprocal phase transition and time-crystalline order.

Findings

Identification of nonreciprocal frustration in quantum spins

Discovery of a nonreciprocal phase transition with chiral dynamics

Demonstration of robustness of degeneracy against disorder

Abstract

Nonreciprocal interactions often create conflicting dynamical objectives that cannot be simultaneously satisfied, leading to nonreciprocal frustration. On the other hand, geometric frustration arises when conflicting static objectives in energy minimization cannot be satisfied. In this work, we show that nonreciprocal interaction among three collective quantum spins, mediated by a damped cavity, induces not only nonreciprocal frustration, intrinsic to nonreciprocity, but also geometric frustration with a remarkable robustness against disorder. It therefore ensures that the accidental degeneracy for steady states remains intact even when the system is perturbed away from a fine-tuned point of enhanced symmetry, in sharp contrast to the equilibrium case. Leveraging this finding, we identify a nonreciprocal phase transition driven by both geometric and nonreciprocal frustration. It gives rise to a time-dependent state, which shows a chiral dynamics along a geometry shaped by the geometric frustration and dynamically restores the broken discrete symmetries. Moreover, it constitutes a time-crystalline order, with multiple harmonics set by an emergent time scale that exhibits critical slowing down. Our predictions have important physical implications for a three-component spinor BEC-cavity system, which manifest as a geometric frustration in the structural phase transition and chiral dynamics of the frustrated self-organized BECs. We demonstrate the feasibility of experimental observation despite the presence of disorder in the spin-cavity coupling strengths.