Multiple Mechanical Resonators Research Articles

Domino cooling of a coupled mechanical-resonator chain via cold-damping feedback

We propose a domino-cooling method to realize simultaneous ground-state cooling of a coupled mechanical-resonator chain through an optomechanical cavity working in the unresolved-sideband regime. This domino-effect cooling is realized by combining the cold-damping feedback on the first mechanical resonator with nearest neighbor couplings between other neighboring mechanical resonators. We obtain analytical results for the effective susceptibilities, noise spectra, final mean phonon numbers, and cooling rates of these mechanical resonators, and find the optimal cooling condition for these resonators. In particular, we analyze a two-mechanical-resonator case and find that by appropriately engineering either the laser power or the feedback, a flexible switch between symmetric and asymmetric ground-state cooling can be achieved. This could be used for preparing symmetric quantum states in multimode mechanical systems. We also simulate the cooling performance of a coupled $N$-mechanical-resonator chain and confirm that these resonators can be simultaneously cooled to their quantum ground states in the unresolved-sideband regime. Under proper parameter conditions, the cooling of the mechanical-resonator chain shows a temperature gradient along the chain. This study opens a route to quantum manipulation of multiple mechanical resonators in the bad-cavity regime.

Ground-state cooling of mechanical resonators by quantum reservoir engineering

Ground-state cooling of multiple mechanical resonators becomes vital to employ them in various applications ranging from ultra-precise sensing to quantum information processing. Here we propose a scheme for simultaneous cooling of multiple degenerate or near-degenerate mechanical resonators to their quantum ground-state, which is otherwise a challenging goal to achieve. As opposed to standard laser cooling schemes where coherence renders the motion of a resonator to its ground-state, we consider an incoherent thermal source to achieve the same aim. The underlying physical mechanism of cooling is explained by investigating a direct connection between the laser sideband cooling and “cooling by heating”. Our advantageous scheme of cooling enabled by quantum reservoir engineering can be realized in various setups, employing parametric coupling of a cooling agent with the target systems. We also discuss using non-thermal baths to simulate ultra-high temperature thermal baths for cooling.

Multimode cold-damping optomechanics with delayed feedback

We investigate the role of time delay in cold-damping optomechanics with multiple mechanical resonances. For instantaneous electronic response, it was recently shown in \textit{Phys. Rev. Lett. \textbf{123}, 203605 (2019)}, that a single feedback loop is sufficient to simultaneously remove thermal noise from many mechanical modes. While the intrinsic delayed response of the electronics can induce single mode and mutual heating between adjacent modes, we propose to counteract such detrimental effects by introducing an additional time delay to the feedback loop. For lossy cavities and broadband feedback, we derive analytical results for the final occupancies of the mechanical modes within the formalism of quantum Langevin equations. For modes that are frequency degenerate collective effects dominate, mimicking behavior similar to Dicke super- and subradiance. These analytical results, corroborated with numerical simulations of both transient and steady state dynamics, allow to find suitable conditions and strategies for efficient single or multimode feedback optomechanics.

Nonreciprocal ground-state cooling of multiple mechanical resonators

The simultaneous ground-state cooling of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity-field mode has become an outstanding challenge in cavity optomechanics. This is because the dark modes formed by these mechanical modes decouple from the cavity mode and prevent extracting energy from the dark modes through the cooling channel of the cavity mode. Here we propose a universal and reliable dark-mode-breaking method to realize the simultaneous ground-state cooling of two degenerate or nondegenerate mechanical modes by introducing a phasedependent phonon-exchange interaction, which is used to form a loop-coupled configuration. We find an asymmetrical cooling performance for the two mechanical modes and expound this phenomenon based on the nonreciprocal energy transfer mechanism, which leads to the directional flow of phonons between the two mechanical modes. We also generalize this method to cool multiple mechanical modes. The physical mechanism in this cooling scheme has general validity and this method can be extended to break other dark-mode and dark-state effects in physics.

Topological phase induced by distinguishing parameter regimes in a cavity optomechanical system with multiple mechanical resonators

We propose two kinds of distinguishing parameter regimes to induce a topological Su-Schrieffer-Heeger (SSH) phase in a one-dimensional (1D) multiresonator cavity optomechanical system via modulation of the frequencies of both cavity fields and resonators. The introduction of frequency modulations allows us to eliminate the Stokes heating process for mapping of the tight-binding Hamiltonian without the usual rotating-wave approximation, which is totally different from the traditional mapping of the topological tight-binding model. We find that the tight-binding Hamiltonian can be mapped into a topological SSH phase via modification of the Bessel function originating from the frequency modulations of cavity fields and resonators, and the induced SSH phase is independent of the effective optomechanical coupling strength. On the other hand, the insensitivity of the system to the effective optomechanical coupling provides us another new path to induce the topological SSH phase based on the present 1D cavity optomechanical system. And we show that the system can exhibit a topological SSH phase via variation of the effective optomechanical coupling strength in an alternative way, which is much easier to achieve in experiments. Furthermore, we also construct an analogous bosonic Kitaev model with trivial topology by keeping the Stokes heating processes. Our scheme provides a steerable platform for investigation of the effects of next-nearest-neighbor interactions on the topology of the system.

Optomechanically induced transparency, amplification, and fast–slow light transitions in an optomechanical system with multiple mechanical driving phases

We investigate the change in width of transparency windows and the amplification of the probe output spectra in an optomechanical system with multiple mechanical resonators. Each mechanical resonator is driven by a mechanical driving field, and the phases of these mechanical driving fields are different. Via exhibiting the probe output spectra of the system, we find that the number of transparency windows is explicitly decided by the number of mechanical resonators with different frequencies. Meanwhile, we discuss the effect of cavity decay rate on the width of the transparency windows. Moreover, we also investigate the absorption and amplification phenomena with the different phase differences among the pump field, probe field, and mechanical driving fields. By adjusting the phase differences, the fast–slow light transitions can occur. These interesting phenomena can also be exploited to investigate the optical switch and frequency comb generation.

Time evolution of coupled multimode and multiresonator optomechanical systems

We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanicallike interactions. We find the analytical expression for the full time evolution of the system and compute the expectation value of relevant quantities of interest. Among the most interesting ones, we are able to compute the first-order quantum bipartite coherence between pairs of subsystems, and the analytical expression for the mixedness induced by the nonlinear interaction in the reduced state of the mechanical oscillators. Finally, we also compare our results with a linearized version of the system, and we find a regime where there are qualitative and quantitative differences in the behavior of some measurable quantities. Our results can, therefore, be used to describe the full time-evolution of the system to characterize its nonlinear character and explore the validity of the linearization approach.

Selective activation of localized mechanical resonators via a phonon waveguide

An electromechanical phonon waveguide that is weakly connected to three localized mechanical resonators is developed. A nonlinear elastic effect induced by intense piezoelectric excitation enables acoustic waves in the waveguide to be transferred to the spatially distinct resonators. Adjusting the frequency of the nonlinear modulation enables a target resonator to be selectively driven by switching the acoustic wave from the waveguide to it. The ability to remotely control multiple mechanical resonators via the phonon waveguide opens up the possibility of a phonon network in which acoustic waves can be guided to distributed sub-systems.

Parallel Transduction of Nanomechanical Motion Using Plasmonic Resonators.

We demonstrate parallel transduction of thermally driven mechanical motion of an array of gold-coated silicon nitride nanomechanical beams, by using near-field confinement in plasmonic metal–insulator–metal resonators supported in the gap between the gold layers. The free-space optical readout, enabled by the plasmonic resonances, allows for addressing multiple mechanical resonators in a single measurement. Light absorbed in the metal layer of the beams modifies their mechanical properties, allowing photothermal tuning of the eigenfrequencies. The appearance of photothermally driven parametric amplification indicates the possibility of plasmonic mechanical actuation.

Synchronization in a mechanical resonator array coupled quadratically to a common electromagnetic field mode.

Optomechanical systems are based on the nonlinear coupling between the electromagnetic (EM) field in a resonator and one or more bulk mechanical resonators such that the frequency of the EM field resonator depends on the displacement coordinates of each of the mechanical resonators. In this paper we consider the case of multiple mechanical resonators interacting with a common field for which the frequency of the EM resonance is tuned to depend quadratically (to lowest order) on the displacement of the resonators. By using the method of amplitude equations around a critical point, it is shown that groups of near-identical bulk mechanical resonators with low driving fail to synchronize unless their natural frequencies are identical, in which case the resulting system can exhibit multistability.

Multiple broadband magnetoelectric response in thickness-controlled Ni/[011] Pb(Mg1/3Nb2/3)O3-Pb(Zr,Ti)O3 single crystal/Ni laminates

We report the realization of a multiple, broadband, magnetoelectric (ME) response using Ni/[011]-Pb(Mg1/3Nb2/3)O3-Pb(Zr,Ti)O3 (PMN-PZT) single crystal/Ni laminates that take advantage of the multiple mechanical resonances inherent to laminates with anisotropic piezoelectric properties. The ME voltage coefficient of the laminates showed three distinct resonance frequencies and large in-plane anisotropy in its sign and magnitude owing to the anisotropic planar piezoelectric coefficient of [011]-oriented PMN-PZT single crystals. Upon serially connecting three such laminates with different thickness ratios between the Ni and PMN-PZT layers, we observed two distinct frequency windows with bandwidths of ∼60 kHz showing flat, giant ME responses of over 16 V/cm Oe, which suggests that these ME laminates are good candidates for application in broadband field sensors or energy harvesters.

A Full-Wave Rectifier With Integrated Peak Selection for Multiple Electrode Piezoelectric Energy Harvesters

Piezoelectric transducers are a viable way of harvesting vibrational energy for low power embedded systems such as wireless sensors. A proposed disk-shaped piezoelectric transducer with several electrodes enables increased energy harvesting from multiple mechanical resonances. To rectify the low-frequency AC voltage from harvested vibrational energy, a full-wave rectifier has been fabricated in 0.35 mum CMOS. Integrated peak selection circuitry allows input signals with 90deg relative phase shift from the multiple-electrode piezoelectric transducer to be rectified with reduced output ripple. The rectifier has a measured power efficiency of 98.3% while delivering 90 muW and occupying an area of 0.007 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This high efficiency further enables energy harvesters to power wireless devices for extended durations.

Limits on the sensitivity of spherical gravitational wave detectors and on the accuracy of reconstructed signals

A spherical geometry for a resonant-mass gravitational wave antenna offers significant improvements over traditional cylindrical antennas. However, completing a detector requires breaking the bare antenna's spherical symmetry by attaching multiple mechanical resonators and transducers. To fully assess the merits of such detectors, it is essential to be able to calculate the detector's sensitivity and the accuracy of the extractable signal information without relying on exact mathematical transducer or resonator symmetries to simplify the analysis, as has been done in previous work. Without making such assumptions, this paper generalizes the fundamental sensitivity limits, known for cylindrical detectors, that arise from the back-action noise present in any linear amplifier, and from thermal Brownian motion noise when detection bandwidth is limited. Optimal signal detection and estimation methods are derived by generalizing techniques used for one-dimensional detectors to the case of multiple interacting transducers. Formulas for the optimized signal-to-noise ratio are derived which generalize the connection between bandwidth and sensitivity known for one-dimensional detectors. A demand for isotropic sensitivity then gives requirements on transducer placement and matching. Comparing bandwidth anisotropies, the detector design proposed by Johnson and Merkowitz is found to be superior to an alternative proposal by Lobo and Serrano, and to be reasonably robust against asymmetries. In addition to sensitivity limits and optimal data analysis methods, limits are derived for the accuracy of reconstructed signal parameters such as direction, polarization, phase, and arrival time.