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arXiv:2007.11602 · PRX Quantum

Many-Body Physics in the NISQ Era: Quantum Programming a Discrete Time Crystal

Matteo Ippoliti, Kostyantyn Kechedzhi, Roderich Moessner, Shivaji L. Sondhi, Vedika Khemani

Published Sep 20, 2021• 100 citations
arXivHTMLPDF

Abstract

NISQ devices are shown to be exceptionally well-suited for simulating periodically driven quantum systems, offering key capabilities for the realization of novel non-equilibrium phases of matter such as the elusive discrete time crystal.
DOI
10.1103/prxquantum.2.030346

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Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.
Many-body physics and quantum optics have traditionally worked on opposite sides of the physics spectrum. Quantum optics deals with the precise quantum control of atomic, optical, and solid state systems with a small number of degrees of freedom. On the other hand, many-body physics is typically associated with the statistical behavior of condensed-matter systems containing an infinite number of constituents. However, we are now in an era where our level of control of quantum-optical systems is so precise, that we can apply it to the design of devices that implement many-body models in regimes traditionally inaccessible to condensed-matter systems, so-called quantum simulators. Here we provide evidence that the addition of particle-non-conserving processes (pumping and dissipation) to the toolbox of quantum simulators will allow them to reach elusive many-body phases such as supersolids or time crystals.
Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.
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Major technological advances of the past century are rooted in our understanding of quantum physics in the non-interacting limit. A central challenge today is to understand the behavior of complex quantum many-body systems, where interactions play an essential role. About four decades ago, Richard Feynman proposed using controllable quantum systems to efficiently simulate complex physics and chemistry problems, envisioning quantum orreries, highly tunable quantum devices built to emulate less understood quantum systems. Here we ask whether quantum simulators have already uncovered new physical phenomena-and, if so, in which areas and with what impact. We find that, in several notable instances, they have advanced our understanding of many-body quantum dynamics. Although many of these insights could in principle have been obtained theoretically or numerically, they were nevertheless first achieved using quantum processors. While a broad landscape of problems beyond non-equilibrium dynamics still awaits exploration, it is encouraging that quantum simulators are already beginning to challenge and refine our conventional wisdom.