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arXiv:2011.02113 · Physical review. B./Physical review. B

Quantum metamorphism

V. M. Bastidas, Marta P. Estarellas, Tomo Osada, Kae Nemoto, William J. Munro

Published Dec 21, 2020• 3 citations
arXivHTMLPDF

Abstract

Crystals are widely present in our daily life in the form of solid materials whose atoms self-organize in regular patterns, such as salt, diamonds, and ice. While these arrangements tend to be periodic in space, such regularities can also arise in time. By using common tools in condensed matter theory, the authors show here that time crystals can indeed metamorphose as normal crystals do, with the difference that now the structural transformation happens in the temporal and not spatial dimension.

DOI
10.1103/physrevb.102.224307

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Crystals are widely present in our daily life in the form of solid materials whose atoms self-organize in regular patterns, such as salt, diamonds, and ice. While these arrangements tend to be periodic in space, such regularities can also arise in time. By using common tools in condensed matter theory, the authors show here that time crystals can indeed metamorphose as normal crystals do, with the difference that now the structural transformation happens in the temporal and not spatial dimension.
Time crystals are quantum many-body systems that, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in condensed matter physics. In solid state physics properties of space crystals are often investigated with the help of external potentials that are spatially periodic and reflect various crystalline structures. A similar approach can be applied for time crystals, as periodically driven systems constitute counterparts of spatially periodic systems, but in the time domain. Here we show that condensed matter problems ranging from single particles in potentials of quasicrystal structure to many-body systems with exotic long-range interactions can be realized in the time domain with an appropriate periodic driving. Moreover, it is possible to create molecules where atoms are bound together due to destructive interference if the atomic scattering length is modulated in time.
Significance Crystals—an extremely common and important class of states of matter—have been studied intensely and fruitfully for many years. Recently, the possibility of “time crystals,” which self-organize into regular patterns of behavior in time, was proposed theoretically and has inspired important experimental discoveries. This qualitatively new class of states of matter plausibly will lead, among other things, to better clocks. New concepts are needed to describe time (or space-time) crystals, because the most straightforward attempts lead to mathematical singularities. Here, we show how an enriched version of the simplest proposed time-crystal model can be realized as a limiting case of a conventional, fully nonsingular physical system. This firmer foundation predicts characteristic behavior and should support wide-ranging generalizations.
The article presents a short history of time crystals – systems which, like the formation of spatial crystals,self-organize spontaneously into periodic behavior but over time. Research on condensed matter in the time dimension is also described. It turns out that phenomena such as Anderson’s localization, multi-body localization or topological phases can be investigated in the time domain. In the future, one can expect time-tronics, that is, construction of useful devices that use crystalline structures in time.
Abstract Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research.
Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research.
Traditional condensed matter physics relies heavily on spatial periodicity to classify states of matter using crystal lattices and momentum space. In recent years, the paradigm has expanded to include temporal dimensions, notably through the theoretical and experimental exploration of discrete time crystals. However, searching strictly for discrete time crystals imposes rigid constraints on phase rigidity and symmetry breaking. In this paper, we propose a broader and more fundamental paradigm: Quantum Material Temporal Lattice Spectroscopy (QMTLS). Rather than seeking an isolated time crystal phase, QMTLS focuses on identifying internal temporal structures characterized by periodic sequences t_n = nT formed spontaneously or under driving within quantum materials. We formalize the theoretical foundation of temporal lattices in condensed matter, define the spectral density function S(omega) containing discrete temporal lattice peaks, and outline the microscopic mechanisms driving these phenomena. By avoiding traditional experimental validation sections and focusing on rigorous theoretical foundations, this framework opens a promising pathway toward discovering novel non-equilibrium states of matter with potential profound implications for fundamental physics.