Tunable intertwining via collective excitations

TL;DR

This paper demonstrates how collective excitations in a driven-dissipative quantum system can be used to stabilize and explore a variety of intertwined orders, including novel out-of-equilibrium phases like time crystals, in a controllable experimental platform.

Contribution

It introduces a minimal quantum-engineered platform to study intertwined orders and shows how periodic drives can stabilize complex out-of-equilibrium phases beyond traditional Landau orders.

Findings

Collective excitations stabilize diverse intertwined orders.

Out-of-equilibrium phases include time crystals and their combinations.

Results are experimentally observable in current setups.

Abstract

The intertwining of multiple order parameters is a widespread phenomenon in equilibrium condensed matter systems, yet its exploration is often hindered by the complexity of real materials. Here, we present a controlled study of intertwined orders in a minimal and versatile driven-dissipative quantum-engineered platform. We consider a Bose-Einstein condensate at the intersection of two optical cavities, realizing two competing copies of a $\mathbb{Z}_2$ symmetry-breaking superradiant phase transition characterized by density wave orders. Using periodic drives that exploit dynamical symmetry reduction, we show that collective excitations can be harnessed to stabilize a variety of novel intertwined orders. Going beyond the conventional phenomenology involving Landau orders, we show the emergence of a larger class of out-of-equilibrium intertwined phases, including intertwining of purely time-crystalline orders, as well as between Landau and time crystal orders. These results should be observable in state of the art experimental setups.