arXiv subjects

H. B. Chan

Publications and source records attributed to H. B. Chan.

At least 19 recordsLinked to original sources

arXiv2026

Multibranched parametric resonance and swallowtail catastrophe in electromechanical oscillators with nonlinear friction

Parametric resonance underpins the operation of a wide range of physical systems, from nanomechanical resonators to quantum-information systems and Ising machines. As an archetypal class of driven-dissipative systems, parametric oscillators are generally expected to exhibit a single pair of stable period-two states with opposite phases. This bistable behavior enables both the simulation of spin Hamiltonians and the preparation of superconducting cat states. Whether multiple pairs of such states can coexist in a single oscillator, however, remains an open question. Here, we show experimentally and theoretically that conventional controlled nonlinear friction can induce the coexistence of two distinct pairs of period-two states in a micromechanical oscillator. The friction is implemented via a canonical approach, utilizing a drive-induced resonant coupling that transfers two vibrational quanta from the oscillatory mode to a faster decaying mode. We demonstrate that the onset of multistability is governed by a swallowtail catastrophe and quantitatively map the associated bifurcation structure. Our results broaden the understanding of parametric resonance and establish micro- and nano-mechanical oscillators as a versatile platform for studying catastrophe theory and multistable nonequilibrium dynamics.

physics.class-ph↗

arXiv2024

Casimir-Lifshitz force for graphene-covered gratings

We study the Casimir-Lifshitz force (CLF) between a gold plate and a graphene-covered dielectric grating. Using a scattering matrix (S-matrix) approach derived from the Fourier Modal Method (FMM), we find a significant enhancement in the CLF as compared to a mere dielectric slab coated with graphene, over a wide range of temperatures. Additionally, we demonstrate that the CLF depends strongly on the chemical potential of graphene, with maximal effects observed at lower filling fractions. Finally, we analyse the Casimir force gradient between a gold sphere and a graphene-coated dielectric grating, highlighting potential avenues for experimental measurements.

cond-mat.mes-hall↗

arXiv2024

Frequency stabilization of self-sustained oscillations in a sideband-driven electromechanical resonator

We present a method to stabilize the frequency of self-sustained vibrations in micro- and nanomechanical resonators. The method refers to a two-mode system with the vibrations at significantly different frequencies. The signal from one mode is used to control the other mode. In the experiment, self-sustained oscillations of micromechanical modes are excited by pumping at the blue-detuned sideband of the higher-frequency mode. Phase fluctuations of the two modes show near perfect anti-correlation. They can be compensated in either one of the modes by a stepwise change of the pump phase. The phase change of the controlled mode is proportional to the pump phase change, with the proportionality constant independent of the pump amplitude and frequency. This finding allows us to stabilize the phase of one mode against phase diffusion using the measured phase of the other mode. We demonstrate that phase fluctuations of either the high or low frequency mode can be significantly reduced. The results open new opportunities in generating stable vibrations in a broad frequency range via parametric downconversion in nonlinear resonators.

eess.SY↗

arXiv2023

Tunable non-additivity in Casimir-Lifshitz force between graphene gratings

We investigate the Casimir-Lifshitz force (CLF) between two identical graphene strip gratings, laid on finite dielectric substrates, by using the scattering matrix (S-matrix) approach derived from the Fourier Modal Method with Local Basis Functions (FMM-LBF). We fully take into account the high-order electromagnetic diffractions, the multiple scattering and the exact 2D feature of the graphene strips. We show that the non-additivity, which is one of the most interesting features of the CLF in general, is significantly high and can be modulated in situ, without any change in the actual material geometry and this by varying the graphene chemical potential. We discuss the nature of the geometrical effects and show the relevance of the geometric parameter d/D (i.e. the ratio between separation and grating period), which allows to explore the regions of parameters where the additive result is fully acceptable or where the full calculation is needed. This study can open to deeper experimental exploration of the non-additive features of the CLF with micro- or nano-electromechanical graphene-based systems.

cond-mat.mes-hall↗

arXiv2023

Casimir-Lifshitz force between graphene-based structures out of thermal equilibrium

We study the non equilibrium Casimir-Lifshitz force between graphene-based parallel structures held at different temperatures and in presence of an external thermal bath at a third temperature. The graphene conductivity, which is itself a function of temperature, as well as of chemical potential, allows us to tune in situ the Casimir-Lifshitz force. We explore different non equilibrium configurations while considering different values of the graphene chemical potential. Particularly interesting cases are investigated, where the force can change sign going from attractive to repulsive or where the force becomes non monotonic with respect to chemical potential variations, contrary to the behaviour under thermal equilibrium.

cond-mat.mes-hall↗

arXiv2023

Controlled asymmetric Ising model implemented with parametric micromechanical oscillators

Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a well-controlled and fully characterizable physical system to implement the model. Such oscillators are bistable. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. Our experiment on two coupled micromechanical resonators reveals unusual features of asymmetric Ising systems, including the onset of a probability current that circulates in the stationary state. We relate the asymmetry to the exponentially strong effect of a periodic force on the switching rates of an individual parametric oscillator, which we measure. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity.

cond-mat.mes-hall↗

arXiv2023

Superfluid $^3$He-B Surface States in a Confined Geometry Probed by a Microelectromechanical Oscillator

A microelectromechanical oscillator with a 0.73 $μ$m gap structure is employed to probe the surface Andreev bound states in superfluid $^3$He-B. The surface specularity of the oscillator is increased by preplating it with 1.6 monolayers of $^4$He. In the linear regime, the temperature dependence of the damping coefficient is measured at various pressures, and the normalized energy gap is extracted. The damping coefficient increases after preplating at lower pressures, which is attributed to the decreased energy minigap of the surface bound states. The device is also driven into the nonlinear regime, where the temperature independent critical velocity at each pressure is measured. The critical velocity is observed to increase after preplating at all pressures, which might be related to the increased average energy gap. The observed behavior warrants a microscopic theory beyond a single parameter characterization of the surface.

cond-mat.other↗

arXiv2022

Energy Transfer into Period-Tripled States in Coupled Electromechanical Modes at Internal Resonance

Efficient energy transfer often occurs between oscillation modes in a resonator when they are tuned to internal resonance. We design the eigenfrequencies of two vibrational modes of an electromechanical resonator to be close to a ratio of 3:1 and demonstrate that the energy supplied to the upper mode can be controllably transferred to the lower mode. With the lower mode vibrating with a period tripled that of the upper mode, the discrete time-translation symmetry imposed by the periodic drive is broken. The lower mode settles into one of three stable period-tripled states with different phases. This channel for energy transfer from the upper mode can be turned on or off without changing system parameters. When the upper mode itself becomes multistable under strong resonant or parametric drive, additional sets of coexisting period-tripled states emerge in the lower mode. In the latter case, we measure a total of 6 coexisting vibration states with identical amplitude but phases differing by $π$/3. Excitation of coexisting states with three different phases could open new opportunities in designing mechanical memory based on ternary logic. Coupled resonators with period-tripled states can also be used to model complex interacting systems with spin equals one.

cond-mat.mes-hall↗

arXiv2021

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular gratings in regimes not accessible before. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

quant-ph↗

arXiv2020

Damping of a micro-electromechanical oscillator in turbulent superfluid $^4$He: A novel probe of quantized vorticity in the ultra-low temperature regime

We report a comprehensive investigation of the effects of quantum turbulence and quantized vorticity in superfluid $^4$He on the motion of a micro-electromechanical systems (MEMS) resonator. We find that the MEMS is uniquely sensitive to quantum turbulence present in the fluid. To generate turbulence in the fluid, a quartz tuning fork (TF) is placed in proximity to the MEMS and driven at large amplitude. We observe that at low velocity, the MEMS is damped by the turbulence, and that above a critical velocity, $v_c \simeq 5\,$mm\,s$^{-1}$, the turbulent damping is greatly reduced. We find that above $v_c$, the damping of the MEMS is reduced further for increasing velocity, indicating a velocity dependent coupling between the surface of the MEMS and the quantized vortices constituting the turbulence. We propose a model of the interaction between vortices in the fluid and the surface of the MEMS. The sensitivity of these devices to a small number of vortices and the almost unlimited customization of MEMS open the door to a more complete understanding of the interaction between quantized vortices and oscillating structures, which in turn provides a new route for the investigation of the dynamics of single vortices.

cond-mat.other↗

arXiv2019

Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion

Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the resonator to noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the frequency of eigenoscillations on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large vibration amplitudes. The spectral peak undergoes counter-intuitive narrowing when the noise intensity is increased. With the resonator serving as the frequency determining element in a feedback loop, the phase noise at the extremum amplitude is three times smaller than the conventional nonlinear regime. Zero dispersion phenomena open new opportunities for improving resonant sensors and frequency references.

cond-mat.mes-hall↗

arXiv2019

Giant Casimir torque between rotated gratings and the $θ=0$ anomaly

We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle $θ$ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at $θ=0$, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of the system. We show that for finite gratings with only 10 period repetitions, the maximum torque is already 60 times larger than the one predicted in the case of infinite gratings. These findings pave the way to the design of a contactless quantum vacuum torsional spring, with possible relevance to micro- and nano-mechanical devices.

cond-mat.mes-hall↗

arXiv2018

Measurement of mechanical deformations induced by enhanced electromagnetic stress on a parallel metallic-plate system

We measured the electromagnetic stress-induced local strain distribution on a centimeter-sized parallel-plate metallic resonant unit illuminated with microwave. Using a fiber interferometer, we found that the strain changes sign across the resonant unit, in agreement with theoretical predictions that the attractive electric and repulsive magnetic forces act at different locations. The enhancement of the corresponding maximum local electromagnetic stress is stronger than the enhancement of the net force, reaching a factor of >600 compared to the ordinary radiation pressure.

physics.app-ph↗

arXiv2018

Strong negative nonlinear friction from induced two-phonon processes in vibrational systems

Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative [1,2]. The runaway of the vibration amplitude is prevented by positive nonlinear friction that increases rapidly with the amplitude. Here we use a modulated electromechanical resonator to show that nonlinear friction can be made negative and sufficiently strong to overcome positive linear friction at large vibration amplitudes. The experiment involves applying a drive that simultaneously excites two phonons of the studied mode and a phonon of a faster decaying high-frequency mode. We study generic features of the oscillator dynamics with negative nonlinear friction. Remarkably, self-sustained vibrations of the oscillator need to be activated in this case. When, in addition, a resonant force is applied, a branch of large-amplitude forced vibrations can emerge, isolated from the branch of the ordinary small-amplitude response. Isolated branches of self-sustained and forced vibrations are advantageous for applications in sensing and control.

quant-ph↗

arXiv2017

Critical Velocity in the Presence of Surface Bound States in Superfluid $^3$He-B

A microelectromechanical oscillator with a gap of 1.25 $μ$m was immersed in superfluid $^3$He-B and cooled below 250 $μ$K at various pressures. Mechanical resonances of its shear motion were measured at various levels of driving force. The oscillator enters into a nonlinear regime above a certain threshold velocity. The damping increases rapidly in the nonlinear region and eventually prevents the velocity of the oscillator from increasing beyond the critical velocity which is much lower than the Landau critical velocity. We propose that this peculiar nonlinear behavior stems from the escape of quasiparticles from the surface bound states into the bulk fluid.

cond-mat.supr-con↗

arXiv2017

Measurement of non-monotonic Casimir forces between silicon nanostructures

Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field. Apart from controlling the Casimir force via the optical properties of the materials, a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps. Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators, we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the Casimir force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.

quant-ph↗

arXiv2016

Anomalous Damping of a Micro-electro-mechanical Oscillator in Superfluid $^3$He-B

The mechanical resonance properties of a micro-electro-mechanical oscillator with a gap of 1.25 $μ$m was studied in superfluid $^3$He-B at various pressures. The oscillator was driven in the linear damping regime where the damping coefficient is independent of the oscillator velocity. The quality factor of the oscillator remains low ($Q\approx 80$) down to 0.1 $T_c$, 4 orders of magnitude less than the intrinsic quality factor measured in vacuum at 4 K. In addition to the Boltzmann temperature dependent contribution to the damping, a damping proportional to temperature was found to dominate at low temperatures. We propose a multiple scattering mechanism of the surface Andreev bound states to be a possible cause for the anomalous damping.

cond-mat.supr-con↗

arXiv2016

Correlated anomalous phase diffusion of coupled phononic modes in a side-band driven resonator

The dynamical backaction from a periodically driven optical or microwave cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Fundamentally, the driving breaks the continuous time-translation symmetry and replaces it with the symmetry with respect to time translation by the driving period. This discrete symmetry should be reflected in the character of the oscillations. Here, we perform experimental and theoretical study of new aspects of the backaction and the discrete time-translation symmetry using a micromechanical resonator designed to have two nonlinearly coupled vibrational modes with strongly differing frequencies and decay rates. We find that self-sustained oscillations are induced not only in the low frequency mode as measured in previous experiments, but also in the high frequency mode. The vibration frequencies and amplitudes are determined by the system nonlinearity, which also leads to bistability and hysteresis. A remarkable consequence of the discrete time-translation symmetry is revealed by studying the vibration phases. We find that the phase fluctuations of the two modes are nearly perfectly anti-correlated. At the same time, in each mode the phase undergoes anomalous diffusion, where the time dependence of the phase variance follows a superlinear rather than the standard linear power law. Our analysis shows that the exponent of the power law is determined by the exponent of the 1/f-type intrinsic frequency noise of the resonator. We demonstrate the possibility of compensating for these fluctuations using a feedback scheme to generate stable oscillations that could prove useful in frequency standards and resonant detection.

cond-mat.mes-hall↗