Measurement-Induced Continuous Time Crystals

Quantum Origin of Limit Cycles, Fixed Points, and Critical Slowing Down

Among the most iconic features of classical dissipative dynamics are persistent limit-cycle oscillations and critical slowing down at the onset of such oscillations, where the system relaxes purely algebraically in time. On the other hand, quantum systems subject to generic Markovian dissipation decohere exponentially in time, approaching a unique steady state. Here we show how coherent limit-cycle oscillations and algebraic decay can emerge in a quantum system governed by a Markovian master equation as one approaches the classical limit, illustrating general mechanisms using a single-spin model and a two-site lossy Bose-Hubbard model. In particular, we demonstrate that the fingerprint of a limit cycle is a slow-decaying branch with vanishing decoherence rates in the Liouville spectrum, while a power-law decay is realized by a spectral collapse at the bifurcation point. We also show how these are distinct from the case of a classical fixed point, for which the quantum spectrum is gapped and can be generated from the linearized classical dynamics.

Exotic Synchronization in Continuous Time Crystals Outside the Symmetric Subspace

Exploring continuous time crystals (CTCs) within the symmetric subspace of spin systems has been a subject of intensive research in recent times. Thus far, the stability of the time-crystal phase outside the symmetric subspace in such spin systems has gone largely unexplored. Here, we investigate the effect of including the asymmetric subspaces on the dynamics of CTCs in a driven dissipative spin model. This results in multistability, and the dynamics becomes dependent on the initial state. Remarkably, this multistability leads to exotic synchronization regimes such as chimera states and cluster synchronization in an ensemble of coupled identical CTCs. Interestingly, it leads to other nonlinear phenomena such as oscillation death and signature of chaos.

Time Crystal in a Single-Mode Nonlinear Cavity

Time crystal is a class of nonequilibrium phases with broken time-translational symmetry. Here, we demonstrate the time crystal in a single-mode nonlinear cavity. The time crystal originates from the self-oscillation induced by a linear gain and is stabilized by a nonlinear damping. We show in the time crystal phase there are sharp dissipative gap closing and pure imaginary eigenvalues of the Liouvillian spectrum in the thermodynamic limit. Dynamically, we observe a metastable regime with the emergence of quantum oscillation, followed by a dissipative evolution with a timescale much longer than the oscillating period. Moreover, we show there is a dissipative phase transition at the Hopf bifurcation, which can be characterized by the photon number fluctuation in the steady state. These results pave a new promising way for further experiments and deepen our understanding of time crystals.

Continuous Sensing and Parameter Estimation with the Boundary Time Crystal

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-level systems and features a transition between a stationary phase and an oscillatory one. The fact that the system is open allows one to continuously monitor its quantum trajectories and to analyze their dependence on parameter changes. This enables the realization of a sensing device whose performance we investigate as a function of the monitoring time T and of the system size N. We find that the best achievable sensitivity is proportional to sqrt[T]N, i.e., it follows the standard quantum limit in time and Heisenberg scaling in the particle number. This theoretical scaling can be achieved in the oscillatory time-crystal phase and it is rooted in emergent quantum correlations. The main challenge is, however, to tap this capability in a measurement protocol that is experimentally feasible. We demonstrate that the standard quantum limit can be surpassed by cascading two time crystals, where the quantum trajectories of one time crystal are used as input for the other one.