Time Crystals Now Possible in Interacting Atomic Systems

Haohang Zhou and colleagues at Shanghai Jiao Tong University have observed a superradiant continuous time crystal phase within a Rydberg-dressed Dicke system, showing that such a phase can emerge even in interacting spin-1/2 systems. The observation sharply advances the field by identifying an additional key coupling generated by Rydberg-dressed interactions, which influences dynamical phase transitions and provides experimentally measurable signatures via cavity emission photons. The resulting system offers a promising, flexible platform for exploring macroscopic temporal order in open quantum matter.

Engineering critical coupling via Rydberg-dressed interactions within an open Dicke model

Rydberg-dressed interactions proved key to this work, effectively modifying how atoms interact with each other. These interactions are created by coupling atoms to highly excited Rydberg states, resulting in a long-range, tunable interaction strength. Imagine atoms wearing special ‘coats’ that dramatically change how strongly they interact, like magnets attracting or repelling, but with the strength of that attraction or repulsion precisely controlled by laser fields. Within an open Dicke model, a simplified representation of light-matter interaction analogous to a musical instrument’s resonating body and strings, these interactions were utilised. The Dicke model traditionally describes the collective behaviour of N two-level atoms interacting with a single mode of the electromagnetic field, forming the basis for understanding superradiance. However, the standard Dicke model assumes nearest-neighbour interactions. This research extends this model to incorporate the all-to-all Rydberg-dressed interactions, significantly altering the system’s behaviour. Carefully tuning these Rydberg-dressed interactions generated an additional critical coupling, altering the system’s stability and enabling the observation of new quantum phases. A cavity-QED platform with N atoms coupled to a single optical cavity, driven by Raman and drive lasers, was employed, alongside an all-to-all approximation for interatomic interactions, simplifying complex many-body effects into a collective interaction parameter, V. The value of N was not specified in the abstract, but is crucial for understanding the scaling behaviour of the observed phenomena. The Raman and drive lasers are essential for preparing the initial state and driving the system away from equilibrium, respectively, creating the conditions necessary for observing the time crystal phase. The all-to-all approximation, while simplifying the calculations, assumes that each atom interacts equally with all other atoms, which may not be entirely accurate in a real physical system.

Many-body fluctuations establish a superradiant continuous time crystal phase

As system size, N, increased, the steady-state normalized variance, F2, experienced a four-fold increase, demonstrating a departure from independent-particle noise and confirming collective fluctuations crucial for persistent oscillation. Independent-particle models previously failed to predict such growth in variance, as they predicted finite fluctuations regardless of system size. This is because independent-particle models treat each atom as isolated, ignoring the crucial correlations arising from the many-body interactions. The observed four-fold increase in F2 indicates that the fluctuations are not simply additive, but rather exhibit a collective behaviour driven by the interactions between the atoms. This sublinear dependence of F2 on N signifies an intrinsically many-body feature, distinguishing this superradiant continuous time crystal (CTC) phase from simpler oscillating systems. A linear dependence would be expected for independent particles, whereas the sublinear behaviour confirms the emergence of collective phenomena. The concept of a continuous time crystal relies on the spontaneous breaking of time-translation symmetry, leading to persistent oscillations in the system’s observables without any external driving force. This is analogous to a conventional crystal, which breaks spatial translation symmetry, leading to a periodic structure in space.

Rydberg-dressed interactions generate an additional critical coupling, altering the stability of fixed points and determining dynamical phase transitions, as detailed analysis of system behaviour revealed. Monte Carlo wave-function simulations and second-order cumulant expansion consistently showed a sublinear dependence of steady-state normalized variance on the number of particles, N, diverging from the finite fluctuations predicted by simpler models. These computational methods allowed the researchers to explore the behaviour of the system for different values of N and interaction strengths, providing strong evidence for the emergence of the superradiant CTC phase. Furthermore, the dominant oscillation frequency of the spin order parameter and photon number exhibited a second-harmonic relation, with the photon number oscillating at approximately twice the frequency of the spin order parameter. This second-harmonic relation is a key signature of the superradiant CTC phase, indicating a specific type of collective oscillation. These findings demonstrate a superradiant continuous time crystal phase, proving such a phase can exist in an interacting spin-1/2 system. The superradiant nature of the time crystal implies that the collective emission of photons from the cavity plays a crucial role in sustaining the oscillations.

Superradiance unlocks persistent oscillation in a complex time crystal system

The focus of many scientists is increasingly on utilising nonequilibrium quantum phases, seeking to control matter far from its usual stable states. These states offer potential advantages for various applications, including quantum information processing and precision sensing. This work demonstrates a superradiant continuous time crystal phase within an interacting system, representing a significant advance. Previously, time crystals had largely been demonstrated in non-interacting or weakly interacting systems. This research demonstrates that robust time crystal behaviour can persist even in the presence of strong interactions, opening up new possibilities for realising these states in more complex and realistic materials. However, quantifying the durability and lifetime of the resulting superradiant oscillation remains an open question, potentially limiting practical applications. The lifetime of the oscillation is limited by various factors, including dissipation and decoherence, which can disrupt the delicate balance required to maintain the time crystal phase. Time crystals represent a new state of matter exhibiting persistent oscillation without energy input; previously observed in non-interacting systems, this expands the possibility of creating these structures in more complex, realistic materials, potentially unlocking new avenues for precision sensing and quantum information storage. The persistent oscillation could be used as a highly sensitive clock, while the collective quantum state could be used to store and process quantum information.

A striking advancement in understanding nonequilibrium quantum phenomena is the establishment of a superradiant continuous time crystal phase within an interacting system. Persistent oscillation can emerge even when atoms mutually interact, overcoming limitations of prior studies, as this research successfully demonstrated. By employing a Rydberg-dressed Dicke model, a new critical coupling influencing the system’s stability was identified. This system offers measurable signatures via cavity emission, providing a flexible platform for exploring active phase transitions, and raises questions regarding the scalability of these time crystals and the potential for utilising them in precision sensing or quantum information storage. Future research will likely focus on increasing the number of atoms in the system, improving the coherence time of the oscillations, and exploring potential applications of this novel quantum phase of matter.

The researchers successfully demonstrated a superradiant continuous time crystal phase in an interacting system of spin-1/2 atoms. This finding expands the possibility of creating time crystals, states of matter exhibiting persistent oscillation without energy input, beyond previously studied non-interacting systems. Using a Rydberg-dressed Dicke model, they identified a new critical coupling that influences the stability of the system and its resulting dynamics. The system’s measurable signatures, observed through cavity emission, offer a platform for exploring dynamical phase transitions, and the authors intend to investigate increasing the number of atoms within the system to further refine these observations.