Continuous time crystal in an electron-nuclear spin system: stability and melting of periodic auto-oscillations (2303.15989v1)

Abstract: Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time. Originally suggested for closed thermodynamic systems in equilibrium, no-go theorems prevent the existence of time crystals. Proposals for open systems out of equilibrium led to the observation of discrete time crystals subject to external periodic driving to which they respond with a sub-harmonic response. A continuous time crystal is an autonomous system that develops periodic auto-oscillations when exposed to a continuous, time-independent driving, as recently demonstrated for the density in an atomic Bose-Einstein condensate with a crystal lifetime of a few ms. Here we demonstrate an ultra-robust continuous time crystal in the nonlinear electron-nuclear spin system of a tailored semiconductor with a coherence time exceeding hours. Varying the experimental parameters reveals huge stability ranges of this time crystal, but allows one also to enter chaotic regimes, where aperiodic behavior appears corresponding to melting of the crystal. This novel phase of matter opens the possibility to study systems with nonlinear interactions in an unprecedented way.

Continuous Time Crystal in an Electron-Nuclear Spin System: Stability and Melting of Periodic Auto-Oscillations

The paper under consideration addresses the advancement of continuous time crystal (CTC) behavior within semiconductor electron-nuclear spin systems (ENSS) and proposes an experimental framework for the establishment and analysis of this phenomenon. The research delineates the emergence of robust periodic auto-oscillations in ENSS under continuous optical pumping, illustrating both the stability and "melting" of these states.

The authors focus on an ENSS within a semiconductor structure composed of an In$_{0.03}$Ga$_{0.97}$As epilayer doped with silicon (Si) donors. This system is designed to exhibit non-linear interactions conducive to establishing a CTC with coherence exceeding several hours. A distinctive aspect of the paper is the intentional introduction of lattice distortions through indium doping, leading to quadrupole splitting that influences the nuclear level structure and effectively promotes the formation of the CTC. This tailored environment showcases periodic auto-oscillations recognizable as CTC states given their undamped oscillatory behavior over extended periods.

Experimental conditions such as laser power, magnetic field orientation, and sample temperature were iteratively varied to map the stability regime of the CTC and determine regions where linear and chaos-like behaviors might manifest. Notable findings include the identification of parameter spaces where the CTC sustains its periodicity, demonstrated by the narrow, equidistant frequency spectrum peaks. These observations corroborated through time-series analysis confirm the presence of behavior typical of periodic nonlinear systems.

The paper also explores the instability introduced through specific parameter manipulations, causing what is referred to as the "melting" of the CTC. This transition predominantly occurs as chaotic oscillations marked by non-integer correlation dimensions and positive Lyapunov exponents, indicative of a shift from orderly periodic behavior to chaotic dynamics. As an example, the increase in magnetic field misalignment from the traditional Voigt arrangement promotes instability in the periodic nature of the oscillations, suggesting the dynamic sensitivity of the ENSS.

The practical implications of these findings extend into areas such as computational and quantum information processing, where CTCs could serve as precise timekeeping and signal modulation devices due to their inherent stability and tunable periods. Theoretically, the research provides insight into the dynamic coupling of electron and nuclear spins, backed by I.E. D'yakonov's theoretical model, revealing opportunities for further exploration in fundamental spin dynamics and quantum state manipulation.

An interesting dimension for future exploration lies in the controlled modulation of external CTC parameters, potentially leading to engineered periodic auto-oscillations, thereby paving the way for highly reliable, application-oriented quantum devices. Given the quantum nature of the interactions and the macroscopic manifestation of a CTC, exploring the crossover to other quantum phases can serve as a rich vein for further research.

In conclusion, this work provides a substantial leap in understanding ENSS dynamics within reduced-symmetry semiconductor systems and opens new paths both in the experimental realization of CTCs and their practical deployment across various fields of physics and technology.