Robust Stability of Discrete Time Crystals in Non-Interacting Systems Enabled by Environmental Dissipation

The quest to create materials that break the fundamental symmetry of time has led researchers to explore discrete time crystals, phases of matter exhibiting a robust, repeating response at intervals less than that of the driving force. Gourab Das from the Indian Institute of Science Education and Research Kolkata, Saptarshi Saha from Technische Universität Berlin, and Rangeet Bhattacharyya, also from the Indian Institute of Science Education and Research Kolkata, now demonstrate a surprisingly stable form of these time crystals within systems that do not require interactions between their constituent parts. This achievement overcomes a key limitation of previous designs, which proved vulnerable to environmental disturbances, and reveals a pathway to creating time crystals whose lifespan remains consistent regardless of initial conditions or system size. The team experimentally confirms this behaviour using Nuclear Magnetic Resonance spectroscopy, opening new avenues for exploring non-equilibrium phases of matter and potentially harnessing their unique properties.

and settle into a discrete time crystalline (DTC) phase, an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust subharmonic response, yet the DTC phase is fragile when exposed to environmental dissipation. This work proposes and exemplifies a DTC phase in a noninteracting system, the stability of which arises from environmental dissipation. The lifetime of this DTC is independent of initial conditions and the size of the system, although it depends on the frequency of the external driver. Discrete time crystals were proposed as periodically driven systems exhibiting spontaneous symmetry breaking, and they represent a novel phase of matter distinct from conventional equilibrium phases.

Discrete Time Crystals and Ground State Order

This research explores the creation and properties of Discrete Time Crystals (DTCs). Traditionally, crystals exhibit spatial order, with atoms arranged in repeating patterns. Time crystals, however, display repeating patterns in time, even in their ground state, their lowest energy state, without needing external forces. This breaks the expected symmetry of time. Discrete Time Crystals are a specific type of time crystal created by applying a periodic driving force, a repeating signal.

These DTCs are not isolated systems; they are driven by the periodic signal and dissipative, meaning they lose energy to their surroundings. This dissipation is crucial, as it allows for a stable, repeating pattern despite energy loss. The driving force compensates for this loss, maintaining the time-crystalline order. The research also considers ‘prethermalization’, where a system initially driven far from equilibrium reaches a quasi-stable state before reaching true equilibrium. This prethermal state can act as a precursor to the DTC phase.

The team focused on using systems of interacting dipoles, like tiny magnets, to create DTCs. The interactions between the dipoles and the periodic driving are carefully tuned to induce the time-crystalline behavior. The mathematical framework developed describes the dynamics of the dipolar system and the emergence of the DTC phase, analyzing the resulting magnetization patterns.

Environment Sustains Discrete Time Crystalline Phase

Scientists demonstrate a novel discrete time crystalline (DTC) phase in a two-level system, achieving stability through interaction with its environment, rather than relying on isolation. This work reveals that environmental dissipation, typically detrimental to quantum coherence, can actually sustain the DTC phase under specific conditions. The research centers on a pulse sequence where the system interacts with its environment for a specific time, τ, followed by a rotation.

Measurements confirm that when the relaxation timescale, T1, is significantly longer than the decoherence timescale, T2, the system exhibits behavior characteristic of a DTC. Specifically, the magnetization component, Mz, relaxes slowly, similar to a spin-locking pulse, enabling the emergence of the DTC phase. After the τ time delay, the components Mx and My approach zero, while Mz retains its value, setting the stage for the periodic behavior essential for time crystallinity. Further experiments with a rotation pulse demonstrate that the system achieves 2T-periodicity, a hallmark of DTCs, with Mz reversing its sign after time T and returning near its initial value after 2T.

The lifetime of this DTC is independent of the number of particles in the system, a significant departure from previously reported DTCs. Introducing a small perturbation, δ, to the rotation, scientists found that the period doubling of Mz is absent, but the DTC phase can be retrieved if δ approaches zero or T2 is less than τ. Measurements of the Fourier spectrum of Mz reveal peaks around a frequency of 0. 5, confirming the 2T-periodicity. The lifetime of the DTC phase, determined by the width of the Mz peak in the frequency domain, vanishes as δ squared, demonstrating the sensitivity of the phase to perturbations.

Dissipation Stabilizes Novel Discrete Time Crystal

Researchers have demonstrated a novel phase of matter, termed an environment-assisted discrete time crystal (EDTC), which exhibits robust, periodic behavior without relying on interactions between its constituent parts. This achievement expands the understanding of time crystals, previously thought to require many-body interactions for stability, by showing that environmental dissipation can instead provide the necessary robustness. The team experimentally realized this EDTC phase using nuclear magnetic resonance spectroscopy, confirming its existence and characteristics. Notably, this newly discovered phase differs from previously identified time crystals, as it is neither a Floquet nor a prethermal DTC, and its dynamics are governed by a dissipator rather than a traditional Hamiltonian description. The lifetime of the EDTC is independent of system size, a significant departure from many other time crystal realizations, and is determined by the timescales of decoherence and relaxation within the system. Future research may explore the potential for manipulating and controlling these environment-assisted time crystals, potentially opening new avenues for precision measurement and quantum technologies.