Quantum limit cycles with continuous symmetries from coherent parametric driving: exact solutions and many-body extensions

TL;DR

This paper introduces a class of multi-mode bosonic quantum models with continuous symmetries driven coherently, allowing exact solutions of their steady states and revealing rich phenomena like entanglement and quantum limit tori.

Contribution

It presents a new framework for understanding quantum limit cycles with continuous symmetries under coherent parametric driving, including exact steady state solutions.

Findings

Exact quantum steady states can be derived for the models.

Models exhibit steady state entanglement and reduced phase diffusion.

Potential realization in quantum optical and superconducting platforms.

Abstract

There is widespread interest in many-body quantum systems that exhibit limit-cycle or time-crystalline behaviour. An ideal quantum limit cycle would be realized using fully coherent driving (to minimize noise) and also have a continuous internal symmetry (to ensure generation of monochromatic radiation). While these two requirements may seem incompatible, we introduce in this work a large class of multi-mode bosonic limit cycle models based on coherent parametric driving which possess an O(N) continuous symmetry. Surprisingly, the full quantum dissipative steady state of these models can be found exactly. They exhibit rich physics, including steady state entanglement, reduced phase diffusion and the possibility of realizing quantum limit tori. The basic mechanism we identify provides a unified way to understand how coherent parametric driving can yield symmetry-enriched limit cycles, and also helps us understand related models where the relevant symmetries are weakly broken. The models we study are compatible with a range of different experimental platforms, including quantum optical setups and superconducting quantum circuits.