We experimentally and theoretically investigate the nonequilibrium phase structure of a well-controlled driven-dissipative quantum spin system governed by the interplay of coherent driving, spontaneous decay, and long-range spin-spin interactions.
Statistical mechanics provides a powerful framework for understanding and classifying states of matter close to thermal equilibrium – a seminal example being the transition between paramagnetic and ferromagnetic phases of Ising magnets and the liquid-gas transition in fluids. However, most systems found in nature are not in thermodynamic equilibrium, as for instance, their inevitable coupling to the environment leads to a continuous exchange of energy or information that can give rise to fundamentally new physics. For understanding quantum many-body systems, this poses a significant challenge, since theoretical methods capable of dealing with open many-body systems are less developed and it is experimentally difficult to devise observables capable of distinguishing their vastly different types of behavior. This is especially relevant now, due to the emergence of a new generation of experiments that that are genuinely non-equilibrium in nature, such as crystals of laser cooled ions, semiconductor exciton-polariton condensates, ensembles of nitrogen-vacancy centers in diamond, superconducting circuits, ultracold atomic gases in optical cavities and laser driven ensembles of Rydberg atoms.
We addressed this challenge by probing a prototypical driven-dissipative quantum system consisting of an ultracold atomic gas driven far from equilibrium by a laser field, thus creating a small number of (Rydberg) excitations. These excitations are short-lived, but exhibit strong and long-range interactions such that a single excitation strongly influences many nearby atoms resulting in complex non-equilibrium many-body dynamics. As a function of the driving strength and detuning from atomic resonance we discover that the rate of population loss obeys remarkably simple scaling laws over several orders of magnitude (in analogy with the scaling of thermodynamic properties often encountered in the vicinity of equilibrium phase transitions). The measured scaling exponents reflect the underlying non-equilibrium phase structure of the many-body system, which we use to distinguish the different regimes, including dissipation-dominated, paramagnetic and critical regimes as well as an instability which drives the system towards states with high excitation density. While some features of the system can be linked to corresponding equilibrium models, we also find genuinely non-equilibrium features such as the crossover from the dissipation-dominated regime to a critical regime governed by collectively enhanced atom-light interactions. These results show that scaling laws can provide a much needed tool for identifying universal and non-universal aspects of non-equilibrium quantum many-body systems and as a benchmark for state-of-the-art many-body theory. This opens up a new means to study and classify quantum systems out of equilibrium and extends the domain where scale-invariant behavior may be found in nature.