Light-Driven Quantum Systems Exhibit Novel Time-Crystal Phase Transitions.

Researchers demonstrate that rapid, parametrically driven systems exhibit a transition into a time-crystalline phase, achieved through nonlinear scattering that effectively pumps energy into long-wavelength fluctuations within O(N) models, commonly used to describe ordering in condensed matter physics. This establishes a pathway to induce novel, non-equilibrium states of matter.

The pursuit of states of matter far from equilibrium represents a significant challenge in contemporary condensed matter physics, with potential implications for novel materials and devices. Researchers are increasingly exploring the use of external, time-periodic drives, such as coherent light, to induce and control these non-equilibrium phases. A new theoretical framework, detailed in a recent publication, demonstrates how rapid, parametric driving of interacting quantum systems can generate a previously unobserved transition into a time-crystalline phase, a state exhibiting spontaneous breaking of time-translation symmetry. This work, undertaken by Carl Philipp Zelle, Romain Daviet, and Sebastian Diehl of the Institut für Theoretische Physik, Universität zu Köln, in collaboration with Andrew J. Millis from the Center for Computational Quantum Physics at the Flatiron Institute, is presented in their article, “Nonequilibrium orders in parametrically driven field theories”. The study utilises O(N) models, a class of theoretical frameworks describing the collective behaviour of ordering fields commonly found in condensed matter systems, to elucidate the underlying mechanisms driving this transition.

Modern physics increasingly investigates non-equilibrium states of matter, and recent research details a theoretical framework for understanding the emergence of time-crystalline phases in systems subjected to rapid parametric driving, specifically within the context of O(N) models. These models are commonly employed to describe condensed matter systems, representing many-body systems with interactions between components. The study demonstrates that rapid, periodic modulation effectively induces a pumping mechanism at long wavelengths, triggering a transition into a time-crystalline state. This mechanism relies on nonlinear scattering processes within the system, providing a pathway for sustained oscillatory behaviour without external forcing.

Researchers investigate the emergence of time-crystalline phases through this rapid parametric driving, focusing on the long-wavelength fluctuations of ordering fields. Ordering fields describe the collective behaviour of particles within a material, such as their magnetic alignment. The findings reveal a pathway for creating sustained oscillations in material systems without relying on conventional external forces, offering a new approach to manipulating and controlling quantum phenomena.

The investigation differentiates between systems possessing full O(3) symmetry, such as Heisenberg antiferromagnets where spins align in opposing directions, and those exhibiting only SO(3) symmetry, like ferromagnets where spins align in the same direction. The transition to a time crystal proceeds via distinct universality classes depending on the system’s symmetry. Universality classes categorise systems based on their shared critical behaviour near phase transitions. Specifically, the transition in ferromagnets aligns with a noisy Hopf bifurcation or a complex Gross-Pitaevskii equation (cGPE) universality class. The ferromagnetic coupling, denoted as κ, plays a critical role in initiating this transition by inducing a finite frequency, preventing a first-order transition where the system abruptly changes its state.

The cGPE, originally developed to describe Bose-Einstein condensates – states of matter formed by bosons cooled to near absolute zero – provides a mathematical framework for understanding the dynamics of the time crystal in this context. This connection suggests that the underlying physics governing the emergence of time-translation symmetry breaking in parametrically driven ferromagnets shares similarities with the behaviour of these quantum fluids, and researchers therefore provide a theoretical basis for exploring and potentially realizing time crystals in a wider range of magnetic systems through controlled parametric driving.

The resulting time crystal exhibits a spontaneous breaking of time-translation symmetry, oscillating perpetually without requiring an external energy source. The research highlights the importance of nonlinear scattering in mediating the transition to the time-crystalline phase. The parametric drive excites fluctuations in the ordering field, and these fluctuations interact nonlinearly, leading to the amplification of specific modes and the emergence of sustained oscillations.

Understanding the limits of stability is crucial for assessing the potential for realizing these phases in real materials. Additionally, extending the theoretical framework to incorporate more complex interactions and symmetries could reveal new and exotic time-crystalline phases with tailored properties. Future work should also focus on identifying specific material systems where this mechanism could be experimentally verified, opening new avenues for exploring non-equilibrium states of matter and developing novel quantum technologies.