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Register a new userCoexisting attractors and chaotic canard explosions in a slow-fast optomechanical system
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The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system.
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We study the nonreciprocal transmission and the fast-slow light effects in a cavity optomechanical system, in which the cavity supports a clockwise and a counter-clockwise circulating optical modes, both the two modes are driven simultaneously by a strong pump field and a weak signal field. We find that when the intrinsic photon loss of the cavity is equal to the external coupling loss of the cavity, the system reveals a nonreciprocal transmission of the signal fields. However, when the intrinsic photon loss is much less than the external coupling loss, the nonreciprocity about the transmission properties almost disappears, and the nonreciprocity is shown in the group delay properties of the signal fields, and the system exhibits a nonreciprocal fast-slow light propagation phenomenon.
Nanomechanical resonators have demonstrated great potential for use as versatile tools in a number of emerging quantum technologies. For such applications, the performance of these systems is restricted by the decoherence of their fragile quantum states, necessitating a thorough understanding of their dissipative coupling to the surrounding environment. In bulk amorphous solids, these dissipation channels are dominated at low temperatures by parasitic coupling to intrinsic two-level system (TLS) defects, however, there remains a disconnect between theory and experiment on how this damping manifests in dimensionally-reduced nanomechanical resonators. Here, we present an optomechanically-mediated thermal ringdown technique, which we use to perform simultaneous measurements of the dissipation in four mechanical modes of a cryogenically-cooled silicon nanoresonator, with resonant frequencies ranging from 3 - 19 MHz. Analyzing the devices mechanical damping rate at fridge temperatures between 10 mK - 10 K, we demonstrate quantitative agreement with the standard tunneling model for TLS ensembles confined to one dimension. From these fits, we extract the defect density of states ($P_0 sim$ 1 - 4 $times$ 10$^{44}$ J$^{-1}$ m$^{-3}$) and deformation potentials ($gamma sim$ 1 - 2 eV), showing that each mechanical mode couples on average to less than a single thermally-active defect at 10 mK.
We study the problem of preservation of canard connections for time discretized fast-slow systems with canard fold points. In order to ensure such preservation, certain favorable structure preserving properties of the discretization scheme are required. Conventional schemes do not possess such properties. We perform a detailed analysis for an unconventional discretization scheme due to Kahan. The analysis uses the blow-up method to deal with the loss of normal hyperbolicity at the canard point. We show that the structure preserving properties of the Kahan discretization imply a similar result as in continuous time, guaranteeing the occurrence of canard connections between attracting and repelling slow manifolds upon variation of a bifurcation parameter. The proof is based on a non-canonical Melnikov computation along an invariant separating curve, which organizes the dynamics of the map similarly to the ODE problem.
The kinetics of a periodically driven nonlinear oscillator, bistable in a nearly resonant field, has been investigated theoretically and through analogue experiments. An activation dependence of the probabilities of fluctuational transitions between the coexisting attractors has been observed, and the activation energies of the transitions have been calculated and measured for a wide range of parameters. The position of the kinetic phase transition (KPT), at which the populations of the attractors are equal, has been established. A range of critical phenomena is shown to arise in the vicinity of the KPT including, in particular, the appearance of a supernarrow peak in the spectral density of the fluctuations, and the occurrence of high-frequency stochastic resonance (HFSR). The experimental measurements of the transition probabilities, the KPT line, the multipeaked spectral densities, the strength of the supernarrow spectral peak, and of the HFSR effect are shown to be in good agreement with the theoretical predictions.
A theoretical study of delayed feedback in spin-torque nano-oscillators is presented. A macrospin geometry is considered, where self-sustained oscillations are made possible by spin transfer torques associated with spin currents flowing perpendicular to the film plane. By tuning the delay and amplification of the self-injected signal, we identify dynamical regimes in this system such as chaos, switching between precession modes with complex transients, and oscillator death. Such delayed feedback schemes open up a new field of exploration for such oscillators, where the complex transient states might find important applications in information processing.
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