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Nonreciprocal nonequilibrium process are attracting growing interest in sociology, animal behaviour, chemistry, and nanotechnology, and may have played a role in the origin of life. It is less widely recognized, however, that in open systems light can induce nonreciprocal predator-prey like forces between nanoparticles. Such forces provide access to the continuous time crystal state of matter, which has been demonstrated in a plasmonic metamaterial array of nanowires wherein light triggers a spontaneous mobilization transition to the robust oscillatory state, breaking time translation symmetry. Here, we report on the first experimental study of the transient dynamics of light-induced mobilization and demobilization in a time crystal. By analysing time resolved phase trajectories of the system of nanowires, we show that the mobilization transition is accompanied by breaking of continuous time translation symmetry and ergodicity, and a decrease in the entropy of motion. This insight into the transient dynamics of a nonreciprocity-driven time crystal is relevant to optical timetronics, an information and communications technology paradigm relying on the unique functionalities of time crystals, and applications of the interacting nanowire oscillator platform to modelling a wide range of nonreciprocal processes from many-body dynamics to the early stages of matter-to-life transitions., Comment: 9 pages, 4 figures

Continuous time crystals (CTCs) - media with broken continuous time translation symmetry - are an eagerly sought state of matter that spontaneously transition from a time-independent state to one of periodic motion in response to a small perturbation. The state has been realized recently in an array of nanowires decorated with plasmonic metamolecules illuminated with light. Here we show that this as-yet-unexplained CTC state can be understood as arising from a nonreciprocal phase transition induced by nonconservative radiation pressure forces among plasmonic metamolecules: above a certain intensity threshold, light drives the inhomogeneously broadened array of thermally-driven noisy nanowire oscillators to a synchronized coherent space-time crystal state and ergodicity of the system is broken. At the onset of synchronization, this mechanism does not require nonlinearity in the oscillators but depends instead on nonreciprocal forces. As such it is fundamentally different from the regimes of synchronization that depend on nonlinearity., Comment: 7 pages, 5 figures

Time crystals are an eagerly sought phase of matter with broken time-translation symmetry. Quantum time crystals with discretely broken time-translation symmetry have been demonstrated in trapped ions, atoms and spins while continuously broken time-translation symmetry has been observed in an atomic condensate inside an optical cavity. Here we report that a classical metamaterial nanostructure, a two-dimensional array of plasmonic metamolecules supported on flexible nanowires, can be driven to a state possessing all of the key features of a continuous time crystal: continuous coherent illumination by light resonant with the metamolecules' plasmonic mode triggers a spontaneous phase transition to a superradiant-like state of transmissivity oscillations, resulting from many-body interactions among the metamolecules, characterized by long-range order in space and time. The phenomenon is of interest to the study of dynamic classical many-body states in the strongly correlated regime and applications in all-optical modulation, frequency conversion and timing., Comment: 10 pages, 6 figures

Flexural oscillations of free-standing films, nano-membranes and nano-wires are attracting growing attention for their importance to the thermal, electrical and mechanical properties of 2D materials. Here we report on the observation of short-timescale ballistic motion in the flexural mode of a nano-membrane cantilever, driven by thermal fluctuation of flexural phonons, including measurements of ballistic velocities and displacements performed with sub-atomic resolution, using a new free electron edge-scattering technique. Within intervals <10 {\mu}s, the membrane moves ballistically at a constant velocity, typically ~300 {\mu}m/s, while Brownian-like dynamics emerge for longer observation periods. Access to the ballistic regime provides verification of the equipartition theorem and Maxwell-Boltzmann statistics for flexural modes, and can be used in fast thermometry and mass sensing during atomic absorption/desorption processes on the membrane. We argue that the ballistic regime should be accounted for in understanding the electrical, optical, thermal and mechanical properties of 2D materials., Comment: 7 pages, 4 figures

Despite recent tremendous progress in optical imaging and metrology, the resolution gap between atomic scale transmission electron microscopy and optical techniques has not been closed. Is optical imaging and metrology of nanostructures exhibiting Brownian motion possible with resolution beyond thermal fluctuations? Here we report on an experiment in which the average position of a nanowire with a thermal oscillation amplitude of ~150 pm is resolved in single-shot measurements with precision of 92 pm using light at a wavelength of {\lambda} = 488 nm, providing the first example of such sub-Brownian metrology with ~{\lambda}/5,300 precision. To localize the nanowire, we employ a deep learning analysis of the scattering of topologically structured light, which is highly sensitive to the nanowire's position. As a non-invasive optical metrology with sub-Brownian absolute errors, down to a fraction of the typical size of an atom (Si: 220 pm diameter), it opens the exciting field of picophotonics., Comment: 11 pages, 4 figures

Nanomechanical photonic metamaterials provide a wealth of active switching, nonlinear and enhanced light-matter interaction functionalities by coupling optically and mechanically resonant subsystems. Thermal (Brownian) motion of the nanostructural components of such metamaterials leads to fluctuations in optical properties, which may manifest as noise, but which also present opportunity to characterize performance and thereby optimize design at the level of individual nanomechanical elements. We show that Brownian motion in an all-dielectric metamaterial ensemble of silicon-on-silicon-nitride nanowires can be controlled by light at sub-{\mu}W/{\mu}m2 intensities. Induced changes in nanowire temperature of just a few Kelvin, dependent upon nanowire dimensions, material composition, and the direction of light propagation, yield proportional changes of several percent in the few-MHz Eigenfrequencies and picometric displacement amplitudes of Brownian motion. The tuning mechanism can provide active control of frequency response in photonic metadevices and may serve as a basis for bolometric, mass and micro/nanostructural stress sensing., Comment: 11 pages, 5 figures