Observation of discrete time-crystalline order in a disordered dipolar many-body system (1610.08057v1)

Abstract: Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions; this order is remarkably stable against perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.

• The paper experimentally demonstrates stable discrete time-crystalline order in a disordered dipolar many-body system using NV centers in diamond.
• The study employs periodic microwave driving and spin rotation sequences to probe the interplay of disorder and interactions in a million-spin ensemble.
• Findings challenge conventional localization paradigms and suggest potential for advancing robust quantum information processing.

Observation of Discrete Time-Crystalline Order in a Disordered Dipolar Many-Body System

This paper presents a detailed exploration and experimental observation of discrete time-crystalline (DTC) order within a disordered dipolar many-body quantum system. Time crystals represent a novel phase of matter where the system exhibits temporal periodicity that breaks time-translation symmetry, raising significant interest in the paper of non-equilibrium quantum systems.

The investigation utilizes an ensemble of nitrogen vacancy (NV) spin impurities in diamond, which are subjected to periodic driving under a strong microwave field. These ensembles, consisting of approximately $10^6$ dipolar coupled spins, provide an ideal platform for studying such states due to the interplay of disorder and interactions. Encounters with strong disorder and non-equilibrium conditions lead to dynamic phase transitions and the unique emergence of DTC order that is characterized by periods longer than the fundamental driving period.

Key Experimental Observations

• Experimental Setup and Procedure: The paper focuses on NV centers in diamond, where spins are initially aligned and subsequently evolved using a combination of dipolar interaction and global spin rotation sequences. By varying rotation angles and interaction times while maintaining periodic driving, the authors effectively probe the presence and stability of DTC order.
• Phase Stability and Disorder: The observation reveals that the DTC order remains stable even in the presence of slow thermalization, emphasizing the robustness imparted by strong interactions. Interestingly, this stability showcases a diminishing dependency on the conventional localization paradigm.
• Impact of Perturbations: It is noted that the temporal order in the system can endure significant perturbations in rotation angles, up to approximately $17\%$, without the immediate loss of subharmonic response, underlining the stability and resilience of such order against external fluctuations and imperfections.

Theoretical Implications and Development

The experimental results of this work challenge the conventional views on disorder and localization phenomena within driven systems. The results incline towards the conclusion that the robustness of the observed time-crystalline phase does not strictly rely on many-body localization (MBL). The system demonstrates a phase boundary that is dictated not solely by disorder-induced localization, but also by interaction-driven stabilization mechanisms.

Through a self-consistent approach, the dynamics and stability of the DTC phase are theoretically modeled by considering the effective Floquet Hamiltonian over discrete cycles. The analysis explores the emergent long-range order and the associated eigenstates that demonstrate periodic doubling, unravelling a nuanced understanding of the critical behavior in non-equilibrium quantum systems.

Practical and Theoretical Ramifications

The proposed work opens numerous pathways for further research in dynamical quantum phases and enhancing the control over interacting disordered systems. With potential relevance to quantum information processing and quantum computing, these findings could pave the way for using non-equilibrium phases for storing and manipulating quantum information robustly against decoherence and perturbations. Furthermore, it invites discussion on the potential emergence of new, pre-thermal phases of matter which can further illuminate the underlying principles governing time-dependent quantum systems.

Conclusion and Future Directions

This paper not only experimentally validates the presence of discrete time-crystalline order in a system where localization is not a guaranteed outcome but also highlights the critical role of strong interactions in stabilizing such phases. Future research could explore the mechanisms of interaction-induced stabilization and exploit these insights in expanding the repertoire of quantum phase manipulation and control.

The synergy between theoretical predictions and experimental validation as depicted in this paper underscores the evolving landscape of quantum dynamical phase orderings, motivating further theoretical studies that complement emerging experimental capabilities in quantum many-body physics.