Time Crystals and Space Crystals in terms of Macroscopic Quantum Phenomena

Krzysztof Sacha

Wolfram Schommers

啓治 中津川

Giovanni Amelino-camelia A, Robert Brandenberger, Chong‐Sun Chu +9 more

Vedika Khemani, Roderich Moessner, Shivaji L. Sondhi

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.

Keith Schwab, Ulrich A. Johann, Markus Aspelmeyer

Quantum physics challenges our understanding of the nature of physical reality and of space-time and suggests the necessity of radical revisions of their underlying concepts. Experimental tests of quantum phenomena involving massive macroscopic objects would provide novel insights into these fundamental questions. Making use of the unique environment provided by space, MAQRO aims at investigating this largely unexplored realm of macroscopic quantum physics. MAQRO has originally been proposed as a medium-sized fundamental-science space mission for the 2010 call of Cosmic Vision. MAQRO unites two experiments: DECIDE (DECoherence In Double-Slit Experiments) and CASE (Comparative Acceleration Sensing Experiment). The main scientific objective of MAQRO, which is addressed by the experiment DECIDE, is to test the predictions of quantum theory for quantum superpositions of macroscopic objects containing more than 108 atoms. Under these conditions, deviations due to various suggested alternative models to quantum theory would become visible. These models have been suggested to harmonize the paradoxical quantum phenomena both with the classical macroscopic world and with our notion of Minkowski space-time. The second scientific objective of MAQRO, which is addressed by the experiment CASE, is to demonstrate the performance of a novel type of inertial sensor based on optically trapped microspheres. CASE is a technology demonstrator that shows how the modular design of DECIDE allows to easily incorporate it with other missions that have compatible requirements in terms of spacecraft and orbit. CASE can, at the same time, serve as a test bench for the weak equivalence principle, i.e., the universality of free fall with test-masses differing in their mass by 7 orders of magnitude. I.