Nonlinear Optomechanics Research Articles

Higher-Order Optomechanical Nonlinearity Based on the Mechanical Effect of Light

Nonlinear cavity optomechanics based on the mechanical effect of light has recently received considerable attention due to its potential applications in high-precision metrology. In this work, we theoretically studied the third-order optomechanical nonlinearity by using a perturbative approach, and an analytical solution is given, which can be extended to cases of higher-order optomechanical nonlinearity. Furthermore, the generation of a third-order sideband is analyzed in detail, and the results show that the amplitude of the third-order sideband shows a high dependence on the control field detuning, suggesting that the high-order nonlinear intensity can be enhanced by properly adjusting the detuning of the laser field rather than by a strong laser drive. In addition to providing insight into optomechanical nonlinearity, the analytical description of third-order optomechanical nonlinearity based on the mechanical effects of light may find applications in ultra-high precision measurement under low power conditions.

Polaromechanics: polaritonics meets optomechanics

Cavity exciton polariton physics and cavity optomechanics have evolved into mature and active domains with, so far, very little connections between them. We argue here that there are strong reasons to bridge the two fields, opening interesting opportunities. Polaritons are entities sharing the properties of photons and excitons in a controllable way. They can lead to tunable and strongly enhanced optomechanical couplings and, through them, to single-particle cooperativies C0 > 1 as well as ultra-strong optomechanical coupling in the many-particle regime. Besides, exciton-exciton Coulomb interactions define a new regime of non-linear many-body optomechanics with notable and largely unexplored consequences. Conversely, coherent vibrations can add a qualitatively distinct ingredient to the field of polaritonics by introducing the variable of time. Indeed, the mechanics built-in in polariton resonators allows for controllable time-modulation up to frequencies of tens of GHz with important consequences for the control of quantum emitters and bidirectional optical-to-microwave conversion. Most interestingly, it also enables polaritons to access Floquet physics, Landau-Zenner-Stückelberg state preparation, spinor pseudo-magnetic resonance, as well as optomechanically induced non-reciprocal phenomena. This guest-editorial addresses the opportunities and challenges in these emerging field.

Enhanced nonlinear optomechanics in a coupled-mode photonic crystal device

The nonlinear component of the optomechanical interaction between light and mechanical vibration promises many exciting classical and quantum mechanical applications, but is generally weak. Here we demonstrate enhancement of nonlinear optomechanical measurement of mechanical motion by using pairs of coupled optical and mechanical modes in a photonic crystal device. In the same device we show linear optomechanical measurement with a strongly reduced input power and reveal how both enhancements are related. Our design exploits anisotropic mechanical elasticity to create strong coupling between mechanical modes while not changing optical properties. Additional thermo-optic tuning of the optical modes is performed with an auxiliary laser and a thermally-optimised device design. We envision broad use of this enhancement scheme in multimode phonon lasing, two-phonon heralding and eventually nonlinear quantum optomechanics.

Light as a quantum back-action nullifying meter

We propose a new, to the best of our knowledge, method to overcome quantum back-action in a measurement process using oscillators. An optical oscillator is used as a meter to measure the parameters of another open oscillator. The optical oscillator is synthesized such that the optical restoring force counters any perturbations induced by the quantum back-action phenomena. As a result, it is shown that the quantum back-action in continuous measurement is suppressed in the low frequency regime, i.e., for frequencies much smaller than the resonance frequency of the open oscillator. As the meter plays the role of measuring parameters as well as suppressing the quantum back-action, we call it a quantum back-action nullifying meter. As an application of this method, synthesis of the quantum back-action nullifying optical oscillator for suppressing radiation pressure force noise in linear and non-linear optomechanics is described.

Two-mode Schrödinger-cat states with nonlinear optomechanics: generation and verification of non-Gaussian mechanical entanglement

Cavity quantum optomechanics has emerged as a new platform for quantum science and technology with applications ranging from quantum-information processing to tests of the foundations of physics. Of crucial importance for optomechanics is the generation and verification of non-Gaussian states of motion and a key outstanding challenge is the observation of a canonical two-mode Schrödinger-cat state in the displacement of two mechanical oscillators. In this work, we introduce a pulsed approach that utilizes the nonlinearity of the radiation–pressure interaction combined with photon-counting measurements to generate this entangled non-Gaussian mechanical state, and, importantly, describe a protocol using subsequent pulsed interactions to verify the non-Gaussian entanglement generated. Our pulsed verification protocol allows quadrature moments of the two mechanical oscillators to be measured up to any finite order providing a toolset for experimental characterisation of bipartite mechanical quantum states and allowing a broad range of inseparability criteria to be evaluated. Key experimental factors, such as optical loss and open-system dynamics, are carefully analyzed and we show that the scheme is feasible with only minor improvements to current experiments that operate outside the resolved-sideband regime. Our scheme provides a new avenue for quantum experiments with entangled mechanical oscillators and offers significant potential for further research and development that utilizes such non-Gaussian states for quantum-information and sensing applications, and for studying the quantum-to-classical transition.

Single-mode, single-polarization and dispersion-flattened waveguides based on silicon carbide and diamond

Fundamental properties of an optical waveguide are mainly related to its guided modes and associated loss, dispersion, polarization and nonlinearity. Single-mode and single-polarization waveguiding has long been of interest, i.e., so-called truly single mode. We propose SiC- and diamond-based waveguides, which are truly single-mode and simultaneously dispersion-flattened. This is preferred for broadband nonlinear applications, such as octave-spanning supercontinuum and frequency comb generation. An ultra-low and flat dispersion profile with four zero-dispersion wavelengths (ZDWs) can be obtained over an octave-spanning bandwidth from 1.8 to 3.6 μm. Meanwhile, only TE00 mode is supported in the proposed waveguide over the low-dispersion bandwidth. Scattering loss of the waveguide is greatly reduced by 8.6 times, compared to a standard strip waveguide. Fabrication of the proposed waveguide is easier than previous dispersion-tailored waveguides, without dry etching SiC and diamond. It is expected that the proposed waveguides can find applications in nonlinear photonics, optomechanics and quantum optics.

Enhancement of charge sensitivity by nonlinear optomechanics

Quantum estimation of electrical charge is investigated by using nonlinear optomechanical interaction. Due to the light-matter decoupling at one mechanical period, we need to consider only the cavity state, meaning that no direct access to the oscillator state is required. It is shown that the charge sensitivity can be greatly improved by enhancing optomechanical coupling. Further, we find that our theoretical result can surpass the sensitivity obtained from electrical measurements.

Estimation of heavy tails in optical non-linear processes

In optical non-linear processes, rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special since the probability of registering extremely high intensities is significantly higher than for the exponential distribution, which is most commonly observed in statistical and quantum optics. Our work provides a practical overview of the generic statistics toolkit concerning heavy-tailed distributions and proposes methods to deal with issues specific to non-linear optics. We take a closer look at supercontinuum generation, where rogue waves were already observed. We propose modifications to the Hill estimator to deal with detector saturation as well as corrections introduced by pumping the process by bright squeezed vacuum. The suggested methodology facilitates statistically reliable observation of heavy-tailed distribution in non-linear optics, nano-optics, atomic, solid-state processes, and optomechanics.

Sideband-resolved resonator electromechanics based on a nonlinear Josephson inductance probed on the single-photon level

Light-matter interaction in optomechanical systems is the foundation for ultra-sensitive detection schemes as well as the generation of phononic and photonic quantum states. Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280 Hz. Complementary, early proposals and experiments suggest that inductive coupling schemes are tunable and have the potential to reach the single-photon strong-coupling regime. Here, we follow the latter approach by integrating a partly suspended superconducting quantum interference device (SQUID) into a microwave resonator. The mechanical displacement translates into a time varying flux in the SQUID loop, thereby providing an inductive electromechanical coupling. We demonstrate a sideband-resolved electromechanical system with a tunable vacuum coupling rate of up to 1.62 kHz, realizing sub-aN Hz−1/2 force sensitivities. The presented inductive coupling scheme shows the high potential of SQUID-based electromechanics for targeting the full wealth of the intrinsically nonlinear optomechanics Hamiltonian.

Quantum optomechanics of a two-dimensional atomic array

We demonstrate that a two-dimensional (2D) atomic array can be used as a novel platform for quantum optomechanics. Such arrays feature both nearly-perfect reflectivity and ultra-light mass, leading to significantly-enhanced optomechanical phenomena. Considering the collective atom-array motion under continuous laser illumination, we study the nonlinear optical response of the array. We find that the spectrum of light scattered by the array develops multiple sidebands, corresponding to collective mechanical resonances, and exhibits nearly perfect quantum-noise squeezing. Possible extensions and applications for quantum nonlinear optomechanics are discussed.

Berry-Hannay relation in nonlinear optomechanics

We address the quantum-classical comparison of phase measurements in optomechanics in the general framework of Berry phases for composite systems. While the relation between Berry phase and Hannay angle has been proven for a large set of quadratic Hamiltonians, such correspondence has not been shown so far in the case of non-linear interactions (e.g. when three or more operators are involved). Remarkably, considering the full optomechanical interaction we recover the aforementioned mathematical relation with the Hannay angle obtained from classical equations of motion. Our results link at a fundamental level previous proposals to measure decoherence, such as the one expressed by Marshall et al., with the no-go theorem shown by Armata et al., which provides boundaries to understand the quantum-to-classical transition in optomechanics.

Quantum sensing with nanoparticles for gravimetry: when bigger is better

Abstract Following the first demonstration of a levitated nanosphere cooled to the quantum ground state in 2020 (U. Delić, et al. Science, vol. 367, p. 892, 2020), macroscopic quantum sensors are seemingly on the horizon. The nanosphere’s large mass as compared to other quantum systems enhances the susceptibility of the nanoparticle to gravitational and inertial forces. In this viewpoint, we describe the features of experiments with optically levitated nanoparticles (J. Millen, T. S. Monteiro, R. Pettit, and A. N. Vamivakas, “Optomechanics with levitated particles,” Rep. Prog. Phys., vol. 83, 2020, Art no. 026401) and their proposed utility for acceleration sensing. Unique to the levitated nanoparticle platform is the ability to implement not only quantum noise limited transduction, predicted by quantum metrology to reach sensitivities on the order of 10−15 ms−2 (S. Qvarfort, A. Serafini, P. F. Barker, and S. Bose, “Gravimetry through non-linear optomechanics,” Nat. Commun., vol. 9, 2018, Art no. 3690) but also long-lived quantum spatial superpositions for enhanced gravimetry. This follows a global trend in developing sensors, such as cold-atom interferometers, that exploit superposition or entanglement. Thanks to significant commercial development of these existing quantum technologies, we discuss the feasibility of translating levitated nanoparticle research into applications.

Gravimetry through non-linear optomechanics

Precision gravimetry is key to a number of scientific and industrial applications, including climate change research, space exploration, geological surveys and fundamental investigations into the nature of gravity. A variety of quantum systems, such as atom interferometry and on-chip-Bose–Einstein condensates have thus far been investigated to this aim. Here, we propose a new method which involves using a quantum optomechanical system for measurements of gravitational acceleration. As a proof-of-concept, we investigate the fundamental sensitivity for gravitational accelerometry of a cavity optomechanical system with a trilinear radiation pressure light-matter interaction. The phase of the optical output encodes the gravitational acceleration g and is the only component which needs to be measured. We prove analytically that homodyne detection is the optimal readout method and we predict an ideal fundamental sensitivity of Δg = 10−15 ms−2 for state-of-the-art parameters of optomechanical systems, showing that they could, in principle, surpass the best atomic interferometers even for low optical intensities. Further, we show that the scheme is strikingly robust to the initial thermal state of the oscillator.

Method of Higher-order Operators for Quantum Optomechanics

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.

All-optical control of ultrahigh-Q silica microcavities with iron oxide nanoparticles.

We propose and experimentally demonstrate, to the best of our knowledge, the first all-optical control scheme of ultrahigh-quality (Q)-factor silica microcavities, which can maintain their Q factors over 108 during the tuning process. For silica microcavities, the resonance tunability is very important and is also challenging for many applications. However, almost all previous works on resonance tuning deteriorate the Q factors of silica microcavities at different levels, and evidently these schemes are not suitable for applications in which ultrahigh Q factors are required. In this work, based on the proposed silica microbottle cavity and iron oxide nanoparticles, we realize all-optical control of the silica microcavity and maintain its Q factor of around 1.2×108 during the tuning process. A tuning range of 85.9GHz (0.68nm) and a tuning sensitivity of 13.6GHz/mW are obtained, and it is possible to realize full tunability by bridging the azimuthal free spectral range using six adjacent q-series modes. Moreover, all-optical control of the reflection spectrum is also carried out. This work will broaden the applications of ultrahigh-Q silica microcavities in nonlinear optics, microwave photonics, cavity optomechanics, and cavity quantum electrodynamics.

Nonlinear optomechanics with gain and loss: amplifying higher-order sideband and group delay

We study the nonlinear optomechanically induced transparency (OMIT) with gain and loss. We find that (i) for a single active cavity, significant enhancement can be achieved for the higher-order sidebands, including the transmission rate and the group delay; (ii) for active–passive-coupled cavities, hundreds of microsecond of optical delay or advance are attainable for the nonlinear sideband pulses in the parity-time-symmetric regime. The active higher-order OMIT effects, as firstly revealed here, open up the way to make a low-power optomechaical amplifier, which can amplify both the strength and group delay of not only the probe light but also its higher-order sidebands.

Design and experimental demonstration of optomechanical paddle nanocavities

We present the design, fabrication, and initial characterization of a paddle nanocavity consisting of a suspended sub-picogram nanomechanical resonator optomechanically coupled to a photonic crystal nanocavity. The optical and mechanical properties of the paddle nanocavity can be systematically designed and optimized, and the key characteristics including mechanical frequency can be easily tailored. Measurements under ambient conditions of a silicon paddle nanocavity demonstrate an optical mode with a quality factor Qo∼6000 near 1550 nm and optomechanical coupling to several mechanical resonances with frequencies ωm/2π∼ 12−64 MHz, effective masses meff∼350−650 fg, and mechanical quality factors Qm∼ 44−327. Paddle nanocavities are promising for optomechanical sensing and nonlinear optomechanics experiments.

Cavity optomechanics mediated by a quantum two-level system.

Coupling electromagnetic waves in a cavity and mechanical vibrations via the radiation pressure of photons is a promising platform for investigations of quantum–mechanical properties of motion. A drawback is that the effect of one photon tends to be tiny, and hence one of the pressing challenges is to substantially increase the interaction strength. A novel scenario is to introduce into the setup a quantum two-level system (qubit), which, besides strengthening the coupling, allows for rich physics via strongly enhanced nonlinearities. Here we present a design of cavity optomechanics in the microwave frequency regime involving a Josephson junction qubit. We demonstrate boosting of the radiation–pressure interaction by six orders of magnitude, allowing to approach the strong coupling regime. We observe nonlinear phenomena at single-photon energies, such as an enhanced damping attributed to the qubit. This work opens up nonlinear cavity optomechanics as a plausible tool for the study of quantum properties of motion.

Cavity optomechanics

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion. This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments. In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices.

Ultrahigh-Q TE/TM dual-polarized photonic crystal holey fishbone-like nanobeam cavities

We propose and theoretically investigate a one-dimensional photonic crystal holey fishbone-like silicon nanobeam cavity that simultaneously supports both fundamental transverse-electric (TE) and second-order transverse-magnetic (TM) modes, and modes. Three-dimensional finite-difference time-domain simulations show that with thin cavity thickness and compact cavity size, the cavity possesses ultrahigh Q (, ), along with small mode volume and high confinement factor, for both and modes. We believe our proposed cavity could be beneficial for nonlinear frequency conversion, optomechanics and other applications where dual-polarized TE/TM modes are needed.