The spontaneous breaking of time-translation symmetry has led to the discovery of a new
phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic …

The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously
breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the …

We present the first experimental realization of a time crystal stabilized by dissipation. The
central signature in our implementation in a driven open atom-cavity system is a period …

Spin–orbit coupling is an essential mechanism underlying quantum phenomena such as the
spin Hall effect and topological insulators. It has been widely studied in well-isolated …

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-
independent or periodically-driven quantum many-body systems. Spontaneous modification …

Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator
algebraic theory of dynamics in locally interacting systems in any dimension is provided …

Synchronization is a phenomenon where interacting particles lock their motion and display
non-trivial dynamics. Despite intense efforts studying synchronization in systems without …

Systems subject to a high-frequency drive can spend an exponentially long time in a
prethermal regime, in which novel phases of matter with no equilibrium counterpart can be …

A boundary time crystal is a quantum many-body system whose dynamics is governed by
the competition between coherent driving and collective dissipation. It is composed of N two …

We set out a general protocol for steering the state of a quantum system from an arbitrary
initial state toward a chosen target state by coupling it to auxiliary quantum degrees of …