Observation of a Discrete Time Crystal (1609.08684v1)

Abstract: Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed, but later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency. This new phase of matter has been dubbed a "discrete time crystal" (DTC). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbations. Such a time crystal opens the door for studying systems with long-range spatial-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

• The paper reports the first experimental observation of a discrete time crystal, a novel non-equilibrium phase of matter, in a system of trapped ytterbium ions.
• Using a periodically driven system of trapped 171 Yb + ions, the authors implemented a specific Floquet Hamiltonian protocol to induce and control the time crystal state.
• The experiment observed robust sub-harmonic oscillations resistant to perturbations, demonstrating the stability of this phase and suggesting potential for future quantum technologies like robust memories.

Observation of a Discrete Time Crystal

The paper "Observation of a Discrete Time Crystal" presents the first experimental observation of a discrete time crystal (DTC), contributing significantly to the paper of non-equilibrium quantum systems. It focuses on the robust sub-harmonic temporal response of a many-body localized (MBL) system of interacting spin chains under periodic driving, showcasing a novel phase of matter that breaks discrete time translation symmetry.

Overview

Spontaneous symmetry breaking is a well-known phenomenon in physics, underlying various phase transitions. Traditionally, time-crystals were considered impossible in thermal equilibrium systems. However, recent theoretical developments suggest that non-equilibrium Floquet systems, subject to periodic driving, can exhibit persistent time-correlations at sub-harmonic frequencies, enabling the realization of discrete time crystals.

The authors report the successful realization of a DTC in a spin chain of trapped $^{171}$Yb$^+$ ions. They employ a periodic Hamiltonian protocol that combines a global spin flip, long-range Ising interactions, and strong disorder to control the system, leading to a sub-harmonic response that is impervious to moderate perturbations.

Methodology

The experimental setup includes 10 $^{171}$Yb$^+$ ions trapped in a linear configuration, where each ion represents a spin-1/2 particle encoded in hyperfine states. The paper utilizes global Raman transitions to manipulate individual spin rotations and spin-dependent optical dipole forces to induce interactions. Disorder is introduced via site-specific ac Stark shifts. The process employs a Floquet Hamiltonian consisting of a series of operations: a nearly $\pi$ global spin flip ($H_1$), long-range Ising interactions ($H_2$), and disordered fields ($H_3$).

Results and Implications

The experiment observes time crystal behavior by measuring magnetization dynamics over 100 Floquet periods, demonstrating robust oscillations at twice the Floquet period even amidst moderate perturbations in drive amplitude. The authors investigate the phase boundary between the DTC and a symmetry-unbroken phase, identifying critical values of perturbation and interaction strength that delineate the transition.

Variations in the sub-harmonic peak's amplitude across different strengths illustrate dynamics linked to the presence or absence of a DTC phase. These fluctuations imply the emergence of entangled states within the system, resonating with theoretical predictions of Floquet time crystal structures.

Discussion

The experimental realization of a discrete time crystal opens avenues for exploring novel quantum phases with long-range temporal correlations. This work also provides a testing ground for theoretical models concerning DTC stability boundaries and dynamics in non-equilibrium conditions.

The existence of DTCs suggests intriguing possibilities for developing new quantum technologies, such as robust quantum memories or systems capable of operating outside of equilibrium, potentially tapping into new functionalities for quantum information processing.

Future Prospects

Future research might aim to extend this observation to larger systems, test other Floquet driving protocols, or explore interactions beyond long-range Ising models. Additionally, theoretical frameworks might further elucidate the role of disorder and interactions in stabilizing or transitioning from the DTC phase.

Overall, this experimental demonstration is a significant stride in understanding non-equilibrium physics and time-dependent phases of matter, unlocking new experimental and theoretical pathways for quantum science.