A Brief History of Time Crystals (1910.10745v1)

Abstract: The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization. Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics --- that of an intrinsically out-of-equilibrium many-body phase of matter. We include a compendium of necessary background, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. We formalize the notion of a time-crystal as a stable, macroscopic, conservative clock --- explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. We also cover a range of related phenomena, including various types of long-lived prethermal time-crystals, and expose the roles played by symmetries -- exact and (emergent) approximate -- and their breaking. We clarify the distinctions between many-body time-crystals and other ostensibly similar phenomena dating as far back as the works of Faraday and Mathieu. En route, we encounter Wilczek's suggestion that macroscopic systems should exhibit TTSB in their ground states, together with a theorem ruling this out. We also analyze pioneering recent experiments detecting signatures of time crystallinity in a variety of different platforms, and provide a detailed theoretical explanation of the physics in each case. In all existing experiments, the system does not realize a `true' time-crystal phase, and we identify necessary ingredients for improvements in future experiments.

Overview of "A Brief History of Time Crystals"

The paper "A Brief History of Time Crystals" by Vedika Khemani, Roderich Moessner, and S. L. Sondhi provides a comprehensive review of the theoretical development and experimental pursuits of time crystals, a novel phase of matter in quantum statistical mechanics marked by time translation symmetry breaking (TTSB). The concept of time crystals has posed intriguing questions ever since Wilczek proposed the spontaneous breaking of time translation symmetry, sparking debates and subsequent explorations beyond traditional quantum phases.

The authors outline how the field has progressed from early theoretical constructs, such as those presenting time crystals in equilibrium, to experimentally viable non-equilibrium realizations in many-body systems. A distinctive feature of these developments is the shift towards realizing time-crystalline order in Floquet (periodically driven) systems, particularly when combined with many-body localization (MBL), which circumvents the thermalization that typically prevails in isolated quantum systems.

Key Contributions and Arguments

1. Introduction to Time Crystals and TTSB: The review starts by revisiting the thematic importance of symmetries and their spontaneous breaking in modern physics, drawing parallels to spatial symmetries in typical solid-state systems. Crystals break spatial translation symmetry, and magnets break spin rotational symmetry. Wilczek's notion of TTSB brings these concepts into the temporal domain, with the intriguing proposition of a system whose ground state repeats in time.
2. Floquet Time Crystals: The paper asserts that truly long-lived time-crystal phases exist not in static Hamiltonian systems but in periodically driven (Floquet) systems under certain conditions that prevent heating to equilibrium states. Here, the existence of many-body localized phases preserves order by inhibiting energy absorption, thereby maintaining a subharmonic response to the driving frequency—a haLLMark of time-crystalline behavior.
3. Spatiotemporal Order: Intriguingly, time-crystals exhibit spatiotemporal order, meaning that they not only break temporal translation symmetry but also exhibit unconventional spatial behavior, akin to traditional ordered phases like antiferromagnets. This dual nature stems from emergent symmetries within many-body localized contexts and contributes to the richness of the phenomenon.
4. Prethermal Time Crystals: Detailed discussions include the formulation of prethermal time-crystals where a phase exhibits time-crystalline order for exponentially long but finite durations before reaching equilibrium. This phenomenon expands the landscape of time crystals by positing scenarios where even systems not inherently many-body localized can show time-crystalline behavior transiently due to specific driving regimes.
5. Experimental Realizations and Challenges: The review highlights several experimental efforts across platforms such as trapped ions, nitrogen-vacancy centers, and NMR systems, each bringing unique advantages and challenges to realize time-crystalline behavior. Notably, these systems provide high precision in altering and measuring states, underscoring the complex interplay between theory and practice in this burgeoning field.

Numerical and Logistical Considerations

The paper methodically integrates numerical simulations with analytical frameworks to substantiate claims about the feasibility and characteristics of time crystals. Particularly, the resilience of subharmonic responses under varying conditions and parameters suggests promising avenues for technological advances and deeper understanding of non-equilibrium phases.

Future Directions

Looking forward, the paper suggests ongoing expansions of time-crystal research could offer insights into higher-order temporal symmetries, richer synchronization phenomena, and potential applications in quantum information and metrology. Moreover, exploring the limits of stability against perturbations remains a fertile ground for theoretical physics and experimental innovation.

This paper provides an authoritative and insightful guide through the theoretical evolutions and experimental milestones of time crystals. It poignantly balances the foundational principles with the cutting-edge methodologies pushing boundaries in contemporary quantum physics research. As the field progresses, time crystals may not only reshape our understanding of matter and time but also inspire novel applications in quantum technologies.