Time Crystals Break the Rules of Repetition with a Novel, Persistent Rhythm

Researchers are now demonstrating the emergence of time quasicrystals within driven quantum systems, offering a new avenue for exploring non-equilibrium physics. Sk Anisur and Sayan Choudhury, both from Harish-Chandra Research Institute, alongside Sk Anisur et al., detail how a quasi-periodic ‘Fibonacci’ drive applied to an open Dicke model generates these time quasicrystals, characterised by a unique sub-harmonic response differing from the initial stimulus. This work is significant because it establishes the existence of this ordered phase across a broad range of parameters and, crucially, confirms its persistence even in minimal systems containing only two qubits. The team systematically shows that the lifetime of these time quasicrystals increases with system size, suggesting quasi-periodically driven dissipative systems represent a promising platform for realising previously unseen phases of matter.

Dissipative Fibonacci driving induces time quasicrystal phases in small quantum systems

Scientists have uncovered a novel state of matter, termed a time quasicrystal, within a specially designed quantum system. This breakthrough demonstrates the emergence of stable, non-equilibrium order driven by a unique combination of dissipation and quasi-periodic modulation. The research centers on the open Dicke model, a system of interacting qubits within a cavity, subjected to a Fibonacci-based driving force.
Remarkably, this work establishes that these time quasicrystals can exist even in systems as small as two qubits, challenging conventional expectations for the emergence of such phases. The study directly analyzes the system’s dynamics to confirm the existence of time quasicrystal order across a broad range of parameters.

A key finding is the monotonic increase in the lifetime of the time quasicrystal, denoted as τ ∗, with increasing system size. This suggests the potential for creating increasingly stable and robust time quasicrystals by scaling up the number of qubits. Researchers computed the decorrelator and the quasicrystal fraction to rigorously establish the existence of this novel phase in the thermodynamic limit.

Furthermore, the investigation reveals a robust sub-harmonic quasi-periodic response, qualitatively different from the external Fibonacci drive, which is the defining characteristic of these time quasicrystals. By employing a quasi-periodic Fibonacci drive, the team demonstrated a stable, shifted response in the system, confirming the presence of a distinct non-equilibrium phase.

The interplay between dissipation, the loss of energy from the system, and the aperiodic driving protocol is crucial for stabilizing this time quasicrystal state. This work demonstrates that quasi-periodically driven dissipative quantum systems offer a promising platform for realizing previously unattainable non-equilibrium phases of matter.

The findings open avenues for exploring new quantum technologies and potentially impacting fields such as quantum sensing and information processing, where stable, non-equilibrium states are highly desirable. The observed linear relationship between the time quasicrystal lifetime and system size suggests a pathway towards building larger, more resilient quantum systems exhibiting this unique temporal order.

Numerical integration of the open Dicke model with Fibonacci driving for time quasicrystal dynamics

A fourth-order Runge, Kutta method numerically integrates the coupled nonlinear differential equations governing the system’s dynamics. These equations, derived from considerations of the open Dicke model subjected to a quasi-periodic Fibonacci drive, describe the time evolution of the collective operators j = {jx, jy, jz}.

The integration procedure precisely calculates the temporal behaviour of these operators, which are central to characterizing the emergence of time quasicrystals. This numerical approach allows for detailed analysis of the system’s response across a wide range of parameters. The study investigates time quasicrystals, focusing on a robust sub-harmonic quasi-periodic response distinct from the external drive.

Researchers directly analysed the system dynamics in the limit to establish the existence of time quasicrystal order, demonstrating its persistence even with only two qubits. To quantify this behaviour, the lifetime, of the time quasicrystal was systematically studied as a function of the number of qubits.

Measurements reveal that increases monotonically with system size, indicating a strengthening of the time quasicrystal phase with increasing complexity. The work employs a quasi-periodic Fibonacci drive to induce these novel non-equilibrium phases of matter. This specific drive, combined with the numerical integration scheme, facilitates the observation and characterization of the emergent time quasicrystal order, providing a platform for exploring novel states beyond conventional equilibrium systems.

Emergence and scaling of time quasicrystals in the open Dicke model

Scientists demonstrate the emergence of time quasicrystals (TQCs) within the open Dicke model, driven by a quasi-periodic Fibonacci sequence. The research establishes TQC order across a wide parameter range, notably persisting even with only two qubits present in the system. Investigations reveal that the TQC lifetime increases monotonically with system size, indicating a scalable pathway for realizing these novel phases of matter.

Analysis of the system in the thermodynamic limit, through computation of the decorrelator and quasicrystal fraction, confirms the robust existence of a TQC. The study further examines the dynamics in the deep quantum regime, observing transient TQC behaviour even within a two-qubit system. Specifically, the TQC lifetime was found to increase linearly with the number of qubits, demonstrating a clear relationship between system scale and TQC stability.

The work employs mean-field semiclassical equations to model the system’s evolution, tracking quadratures x and p, alongside normalized collective spin components jx, jy, and jz. Initial collective spin configurations were set near a steady state solution, with jx(0) = 1/2√(1 − λ2c/λ2), jy(0) = 0, and jz(0) = −1/2λ2c/λ2.

Throughout the experiments, the photon-loss rate, κ, was maintained at 0.03, and the light-matter coupling strength, λ, at 1. To distinguish TQC phases from chaotic behaviour, the quasi-crystalline fraction, f(ε), was calculated using the formula |S(ν0)| / Σ[|S(ν)|] from ν0−δ to ν0+δ, where ν0 represents the subharmonic peak frequency at ε = 0 and δ = 1/20.

Results, as shown in figures, demonstrate a robust TQC parameter regime. The decorrelator, ⟨d⟩, was also computed to identify chaotic regions, revealing that the TQC regime is characterized by low decorrelator values and high quasi-crystalline fractions.

Fibonacci Driving Stabilises Extended Lifetime Time Quasicrystals

Scientists have demonstrated the emergence of time quasicrystals within a driven, dissipative quantum system, specifically the open Dicke model subjected to a quasi-periodic Fibonacci drive. These time quasicrystals exhibit a distinct sub-harmonic response differing qualitatively from the external drive, indicating a novel non-equilibrium phase of matter.

The research establishes the existence of this ordered phase across a broad range of system parameters and, notably, even with only two qubits, suggesting robustness at small scales. Systematic investigation revealed that the lifetime of the time quasicrystal order increases with the number of qubits in the system, implying that larger systems sustain this phase for extended durations.

This work confirms that combining quasi-periodic driving with dissipation offers a viable pathway for realizing stable, non-equilibrium states. However, the analysis primarily focuses on the semi-classical limit and the behaviour of the system is investigated using mean-field equations, which may not fully capture all quantum effects.

Future research directions include exploring the impact of stronger quantum effects and investigating the potential for observing similar phenomena in other physical systems. The authors acknowledge the limitations of the mean-field approach and suggest that further study is needed to fully understand the behaviour of the system in the deep quantum regime. These findings contribute to the growing field of non-equilibrium physics and may inform the development of new quantum technologies based on driven, dissipative systems.