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Physical Review A

Spontaneous breaking of time translation symmetry via spatially inhomogeneous many-body interactions

Tingmei Li, Pai Zhou, Yu‐Hui Chen, Xiangdong Zhang

Published Jun 16, 2026• 0 citations
Publisher
DOI
10.1103/4m5r-z4bz

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Spontaneous emergence of temporal structures in a continuously driven many-body system

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Abstract The spontaneous emergence of temporal structures challenges the conventional understanding that systems governed by time-invariant laws remain unchanged over time. Recent experiments have observed this time translation symmetry breaking in quantum atomic systems that either exhibit strong atom-atom interactions or have low dissipation rates. While current theoretical frameworks reveal the importance of strong atom-atom interactions, they fall short in explaining this phenomenon observed in low-dissipation atomic systems. Here, we present a theoretical study on the spontaneous breaking of time translation symmetry in materials with low dissipation rates. By constructing phase diagrams for a system of four-level atoms driven by a continuous-wave optical field, we identify the essential requirements for self-sustained temporal motions. These include a driven open system, nonlinear interactions, and sufficient degrees of freedom that facilitate competing processes. Our findings contribute to a better understanding of the emergence of spontaneous time translation symmetry breaking in these materials.

Europhysics Letters (EPL)•Aug 12, 2024•4 citations
We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry. In many-body simulations, we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time-translation symmetry.
The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.
Abstract The spontaneous emergence of temporal structures challenges the conventional understanding that systems governed by time-invariant laws remain unchanged over time. Recent experiments have observed this time translation symmetry breaking in quantum atomic systems that either exhibit strong atom-atom interactions or have low dissipation rates. While current theoretical frameworks reveal the importance of strong atom-atom interactions, they fall short in explaining this phenomenon observed in low-dissipation atomic systems. Here, we present a theoretical study on the spontaneous breaking of time translation symmetry in materials with low dissipation rates. By constructing phase diagrams for a system of four-level atoms driven by a continuous-wave optical field, we identify the essential requirements for self-sustained temporal motions. These include a driven open system, nonlinear interactions, and sufficient degrees of freedom that facilitate competing processes. Our findings contribute to a better understanding of the emergence of spontaneous time translation symmetry breaking in these materials.