Classical many-body time crystals

Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a many-body state, alongside several experimental realizations. In this work, we provide a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators. In our analysis, we use classical period-doubling bifurcation theory and present a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition. We experimentally demonstrate this paradigm using coupled mechanical oscillators, thus providing a clear route for time crystals realizations in real materials.Comment: 23 pages, 5 figures, comments are welcom

The role of fluctuations in quantum and classical time crystals

Discrete time crystals (DTCs) are a many-body state of matter whose dynamics are slower than the forces acting on it. The same is true for classical systems with period-doubling bifurcations. Hence, the question naturally arises what differentiates classical from quantum DTCs. Here, we analyze a variant of the Bose-Hubbard model, which describes a plethora of physical phenomena and has both a classical and a quantum time-crystalline limit. We study the role of fluctuations on the stability of the system and find no distinction between quantum and classical DTCs. This allows us to probe the fluctuations in an experiment using two strongly coupled parametric resonators subject to classical noise.Comment: 11 pages, 5 figure

Rapid flipping of parametric phase states

Since the invention of the solid-state transistor, the overwhelming majority of computers followed the von Neumann architecture that strictly separates logic operations and memory. Today, there is a revived interest in alternative computation models accompanied by the necessity to develop corresponding hardware architectures. The Ising machine, for example, is a variant of the celebrated Hopfield network based on the Ising model. It can be realized with artifcial spins such as the `parametron' that arises in driven nonlinear resonators. The parametron encodes binary information in the phase state of its oscillation. It enables, in principle, logic operations without energy transfer and the corresponding speed limitations. In this work, we experimentally demonstrate flipping of parametron phase states on a timescale of an oscillation period, much faster than the ringdown time \tau that is often (erroneously) deemed a fundamental limit for resonator operations. Our work establishes a new paradigm for resonator-based logic architectures.Comment: 6 pages, 3 figure

Ghost in the Ising machine

Coupled nonlinear systems have promise for parallel computing architectures. En route to realizing complex networks for Ising machines, we report an experimental and theoretical study of two coupled parametric resonators (parametrons). The coupling severely impacts the bifurcation topology and the number of available solutions of the system; in part of the stability diagram, we can access fewer solutions than expected. When applying noise to probe the stability of the states, we find that the switching rates and the phase-space trajectories of the system depend on the detuning in surprising ways. We present a theoretical framework that heralds the existence of 'ghost bifurcations'. These bifurcations involve only unstable solutions and lead to avoided zones in phase space. The emergence of such ghost bifurcations is an important feature of parametron networks that can influence their application for parallel logic operations

A parametric symmetry breaking transducer

Force detectors rely on resonators to transduce forces into a readable signal. Usually these resonators operate in the linear regime and their signal appears amidst a competing background comprising thermal or quantum fluctuations as well as readout noise. Here, we demonstrate that a parametric symmetry breaking transduction leads to a novel and robust nonlinear force detection in the presence of noise. The force signal is encoded in the frequency at which the system jumps between two phase states which are inherently protected against phase noise. Consequently, the transduction effectively decouples from readout noise channels. For a controlled demonstration of the method, we experiment with a macroscopic doubly-clamped string. Our method provides a promising new paradigm for high-precision force detection.Comment: 7 pages, 5 figure