Nonreciprocal Synchronization of Active Quantum Spins

TL;DR

This paper introduces a quantum spin model with nonreciprocal interactions, demonstrating a phase transition to time-crystalline states with broken parity-time symmetry, and proposes an experimental implementation using chiral waveguides.

Contribution

It presents the first quantum many-body model exhibiting nonreciprocal phase transitions and time-crystalline states, with a feasible implementation in atomic ensembles coupled via chiral waveguides.

Findings

Nonreciprocal interactions induce a phase transition to time-crystalline states.

Time-crystalline states exhibit spontaneous parity-time symmetry breaking.

Signatures of the phase can be observed in correlation functions for finite systems.

Abstract

Active agents are capable of exerting nonreciprocal forces upon one another. For instance, one agent, say $A$, may attract another agent $B$ while $B$ repels $A$. These antagonistic nonreciprocal interactions have been extensively studied in classical systems, revealing a wealth of exciting phenomena such as novel phase transitions and traveling-wave states. Whether these phenomena can originate in quantum many-body systems is an open issue, and proposals for their realization are lacking. In this work, we present a model of two species of quantum spins that interact in an antagonistic nonreciprocal way of the attraction-repulsion type. We propose an implementation based on two atomic ensembles coupled via chiral waveguides featuring both braided and non-braided geometries. The spins are active due to the presence of local gain, which allows them to synchronize. In the thermodynamic limit, we show that nonreciprocal interactions result in a nonreciprocal phase transition to time-crystalline traveling-wave states, associated with spontaneous breaking of parity-time symmetry. We establish how this symmetry emerges from the microscopic quantum model. For a finite number of spins, signatures of the time-crystal phase can still be identified by inspecting equal-time or two-time correlation functions. Remarkably, continuous monitoring of the output field of the waveguides induces a quantum traveling-wave state: a time-crystalline state of a finite-size quantum system, in which parity-time symmetry is spontaneously broken. Our work lays the foundation to explore nonreciprocal interactions in active quantum matter.