Optical detection of radio waves through a nanomechanical transducer

Low frequency signal detection via correlated Ramsey measurements

The low frequency region of the spectrum is a challenging regime for quantum probes. We support the idea that, in this regime, performing Ramsey measurements carefully controlling the time at which each measurement is initiated is an excellent signal detection strategy. We use the Fisher information to demonstrate a high quality performance in the low frequency regime, compared to more elaborated measurement sequences, and to optimize the correlated Ramsey sequence according to any given experimental parameters, showing that correlated Ramsey rivals with state-of-the-art protocols, and can even outperform commonly employed sequences such as dynamical decoupling in the detection of low frequency signals. Contrary to typical quantum detection protocols for oscillating signals, which require adjusting the time separation between pulses to match the half period of the target signal, and consequently see their scope limited to signals whose period is shorter than the characteristic decoherence time of the probe, or to those protocols whose target is primarily static signals, the time-tagged correlated Ramsey sequence simultaneously tracks the amplitude and the phase information of the target signal, regardless of its frequency, which crucially permits correlating measurements in post-processing, leading to efficient spectral reconstruction.

Acoustic Resonance Tuning by High-Order Lorentzian Mixing

Nanoscale mechanical resonators have attracted a great deal of attention for signal processing, sensors, and quantum applications. Recent progress in ultrahigh-Q acoustic cavities in nanostructures allows strong interactions with various physical systems and advanced functional devices. Those acoustic cavities are highly sensitive to external perturbations, and it is hard to control those resonance properties since those responses are determined by the geometry and material. In this paper, we demonstrate a novel acoustic resonance tuning method by mixing high-order Lorentzian responses in an optomechanical system. Using weakly coupled phononic-crystal acoustic cavities, we achieve coherent mixing of second- and third-order Lorentzian responses, which is capable of the fine-tunability of the bandwidth and peak frequency of the resonance with a tuning range comparable to the acoustic dissipation rate of the device. This novel resonance tuning method can be widely applied to Lorentzian-response systems and optomechanics, especially active compensation for environmental fluctuation and fabrication errors.

Optomechanical Microwave-to-Optical Photon Transducer Chips: Empowering the Quantum Internet Revolution

The first quantum revolution has brought us the classical Internet and information technology. Today, as technology advances rapidly, the second quantum revolution quietly arrives, with a crucial moment for quantum technology to establish large-scale quantum networks. However, solid-state quantum bits (such as superconducting and semiconductor qubits) typically operate in the microwave frequency range, making it challenging to transmit signals over long distances. Therefore, there is an urgent need to develop quantum transducer chips capable of converting microwaves into optical photons in the communication band, since the thermal noise of optical photons at room temperature is negligible, rendering them an ideal information carrier for large-scale spatial communication. Such devices are important for connecting different physical platforms and efficiently transmitting quantum information. This paper focuses on the fast-developing field of optomechanical quantum transducers, which has flourished over the past decade, yielding numerous advanced achievements. We categorize transducers based on various mechanical resonators and discuss their principles of operation and their achievements. Based on existing research on optomechanical transducers, we compare the parameters of several mechanical resonators and analyze their advantages and limitations, as well as provide prospects for the future development of quantum transducers.

Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging 'dissipation dilution'-where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.

Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

High-Strength Amorphous Silicon Carbide for Nanomechanics

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 108 at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

Tunable Optical Display of Multilayer Graphene through Lithium Intercalation

The tunable optical display is vital for many application fields in telecommunications, sensors, and military devices. However, most optical materials have a strong wavelength dependence, which limits their spectral operation range. In this work, we develop an electrically reconfigurable optical medium based on graphene, demonstrating a cycle-controlled display covering the electromagnetic spectrum from the visible to the infrared wavelength. Through an electro-intercalation method, the graphene-based surface enables rich colors from gray to dark blue to dark red to yellow, and the response time is about 1 min from the start gray color to the final yellow color. Simultaneously, it exhibits a remarkable change in infrared emissivity (from 0.63 to 0.80 reduction to 0.20) with a response time of 1 s. This modification of optical properties of lithiated multilayer graphene (MLG) is the increase of Fermi energy (Ef) due to the charge transfer from lithium (Li) to graphene layers, which causes changes in interband and intraband electronic transitions. Our findings imply potential value in fabricating multispectral optical materials with high tunability.

Revealing the Velocity Uncertainties of a Levitated Particle in the Quantum Ground State

We demonstrate time-of-flight measurements for an ultracold levitated nanoparticle and reveal its velocity for the translational motion brought to the quantum ground state. We discover that the velocity distributions obtained with repeated release-and-recapture measurements are significantly broadened via librational motions of the nanoparticle. Under feedback cooling on all the librational motions, we recover the velocity distributions in reasonable agreement with an expectation from the occupation number, with approximately twice the width of the quantum limit. The strong impact of librational motions on the translational motions is understood as a result of the deviation between the libration center and the center of mass, induced by the asymmetry of the nanoparticle. Our results elucidate the importance of the control over librational motions and establish the basis for exploring quantum mechanical properties of levitated nanoparticles in terms of their velocity.

Entanglement enhancement and EPR steering based on a PT-symmetric-like cavity-opto-magnomechanical hybrid system

We investigate the enhancement of entanglement and EPR steering in a parity-time(PT-) symmetric-like cavity-opto-magnomechanical system. The system consists of an optical cavity, a magnon mode in a ferromagnetic crystal, a phonon mode, and a microwave cavity. Our findings demonstrate that microwave-cavity gain significantly boosts distant quantum entanglement and greatly improves the robustness of bipartite entanglement against environment temperature. Additionally, we observe an enhancement of tripartite entanglement within the system and uncover the phenomenon of entanglement transfer. Notably, we also achieve one-way steering and two-way asymmetric steering in the system. This study offers insights into the integration of traditional optomechanics and cavity magnomechanics, presenting a novel approach to manipulate asymmetric quantum steering between two distant macroscopic objects. The implications of our research extend to the fields of quantum state preparation and quantum information.

Low Noise Opto-Electro-Mechanical Modulator for RF-to-Optical Transduction in Quantum Communications

In this work, we present an Opto-Electro-Mechanical Modulator (OEMM) for RF-to-optical transduction realized via an ultra-coherent nanomembrane resonator capacitively coupled to an rf injection circuit made of a microfabricated read-out able to improve the electro-optomechanical interaction. This device configuration can be embedded in a Fabry-Perot cavity for electromagnetic cooling of the LC circuit in a dilution refrigerator exploiting the opto-electro-mechanical interaction. To this aim, an optically measured steady-state frequency shift of 380 Hz was seen with a polarization voltage of 30 V and a Q-factor of the assembled device above 106 at room temperature. The rf-sputtered titanium nitride layer can be made superconductive to develop efficient quantum transducers.

Ultra-low-noise microwave to optics conversion in gallium phosphide

Mechanical resonators can act as excellent intermediaries to interface single photons in the microwave and optical domains due to their high quality factors. Nevertheless, the optical pump required to overcome the large energy difference between the frequencies can add significant noise to the transduced signal. Here we exploit the remarkable properties of thin-film gallium phosphide to demonstrate bi-directional on-chip conversion between microwave and optical frequencies, realized by piezoelectric actuation of a Gigahertz-frequency optomechanical resonator. The large optomechanical coupling and the suppression of two-photon absorption in the material allows us to operate the device at optomechanical cooperativities greatly exceeding one. Alternatively, when using a pulsed upconversion pump, we demonstrate that we induce less than one thermal noise phonon. We include a high-impedance on-chip matching resonator to mediate the mechanical load with the 50-Ω source. Our results establish gallium phosphide as a versatile platform for ultra-low-noise conversion of photons between microwave and optical frequencies.

Sequential Measurements for Quantum-Enhanced Magnetometry in Spin Chain Probes

Quantum sensors outperform their classical counterparts in their estimation precision, given the same amount of resources. So far, quantum-enhanced sensitivity has been achieved by exploiting the superposition principle. This enhancement has been obtained for particular forms of entangled states, adaptive measurement basis change, critical many-body systems, and steady state of periodically driven systems. Here, we introduce a different approach to obtain quantum-enhanced sensitivity in a many-body probe through utilizing the nature of quantum measurement and its subsequent wave function collapse without demanding prior entanglement. Our protocol consists of a sequence of local measurements, without reinitialization, performed regularly during the evolution of a many-body probe. As the number of sequences increases, the sensing precision is enhanced beyond the standard limit, reaching the Heisenberg bound asymptotically. The benefits of the protocol are multifold as it uses a product initial state and avoids complex initialization (e.g., prior entangled states or critical ground states) and allows for remote quantum sensing.

Random number generation with a chaotic electromechanical resonator

Chaos enables the emergence of randomness in deterministic physical systems. Therefore it can be exploited for the conception of true random number generators mandatory in classical cryptography applications. Meanwhile, nanomechanical oscillators, at the core of many on-board functionalities such as sensing, reveal as excellent candidates to behave chaotically. This is made possible thanks to intrinsic mechanical nonlinearities emerging at the nanoscale. Here we present a platform gathering a nanomechanical oscillator and its integrated capacitive actuation. Using a modulation of the resonant force induced by the electrodes, we demonstrate chaotic dynamics and study how it depends on the dissipation of the system. The randomness of a binary sequence generated from a chaotic time trace is evaluated and discussed such that the generic parameters enabling successful random number generation can be established. This demonstration makes use of concepts which are sufficiently general to be applied to the next generation of nano-electro-optomechanical systems.

Soft-Clamped Silicon Nitride String Resonators at Millikelvin Temperatures

We demonstrate that soft-clamped silicon nitride strings with a large aspect ratio can be operated at mK temperatures. The quality factors (Q) of two measured devices show consistent dependency on the cryostat temperature, with soft-clamped mechanical modes reaching Q>10^{9} at roughly 46 mK. For low optical readout power, Q is found to saturate, indicating good thermalization between the sample and the stage it is mounted on. Our best device exhibits a calculated force sensitivity of 9.6  zN/sqrt[Hz] and a thermal decoherence time of 0.38 s, which bode well for future applications such as nanomechanical force sensing.

Structural Optimization of Graphene Triangular Lattice Phononic Crystal Based on Dissipation Dilution Theory

Nanomechanical resonators offer brilliant mass and force sensitivity applied in many fields, owing to a low mass m and high-quality factor Q. However, in vibrating process, resonant energy is inevitably dissipated. Typically, quality factor does not surpass the inverse of the material loss angle φ. Recently, some exceptions emerged in the use of highly stressed silicon nitride material. As yet, it is interpreted that the pre-stress seems to "dilute" the intrinsic energy dissipation according to the Zener model. Is there any other material that could further break the 1/φ limit and achieve higher quality factors? In our previous research, through theoretical calculation and finite element simulation, we have proved that graphene's quality factor is two orders of magnitude larger than silicon nitride, on account of the extremely thin thickness of graphene. Based on this, we further optimize the structure of phononic crystals to achieve higher quality factors, in terms of duty cycle and cell size. Through simulation analysis, the quality factor could improve with a larger duty cycle and bigger cell size of triangular lattice phononic crystal. Unexpectedly, the Q amplification coefficient of the 3 × 5-cell structure, which is the least number to compose a phononic crystal with a central defect area, is the highest. In contrast, the minimal cell-number structure in hexagonal lattice could not achieve the brilliant dissipation dilution effect as well as the triangular one. Then we consider how overall size and stress influence quality factor and, furthermore, compare theoretical calculation and finite simulation. Lastly, we start from the primitive 3 × 5 cells, constantly adding cells to the periphery. Through simulation, to our surprise, the largest Q amplification coefficient does not belong to the largest structure, instead originating from the moderate one consisting of 7 × 13 cells.

Photothermal Responsivity of van der Waals Material-Based Nanomechanical Resonators

Nanomechanical resonators made from van der Waals materials (vdW NMRs) provide a new tool for sensing absorbed laser power. The photothermal response of vdW NMRs, quantified from the resonant frequency shifts induced by optical absorption, is enhanced when incorporated in a Fabry–Pérot (FP) interferometer. Along with the enhancement comes the dependence of the photothermal response on NMR displacement, which lacks investigation. Here, we address the knowledge gap by studying electromotively driven niobium diselenide drumheads fabricated on highly reflective substrates. We use a FP-mediated absorptive heating model to explain the measured variations of the photothermal response. The model predicts a higher magnitude and tuning range of photothermal responses on few-layer and monolayer NbSe₂ drumheads, which outperform other clamped vdW drum-type NMRs at a laser wavelength of 532 nm. Further analysis of the model shows that both the magnitude and tuning range of NbSe₂ drumheads scale with thickness, establishing a displacement-based framework for building bolometers using FP-mediated vdW NMRs.

Microwave-to-optical conversion with a gallium phosphide photonic crystal cavity

Electrically actuated optomechanical resonators provide a route to quantum-coherent, bidirectional conversion of microwave and optical photons. Such devices could enable optical interconnection of quantum computers based on qubits operating at microwave frequencies. Here we present a platform for microwave-to-optical conversion comprising a photonic crystal cavity made of single-crystal, piezoelectric gallium phosphide integrated on pre-fabricated niobium circuits on an intrinsic silicon substrate. The devices exploit spatially extended, sideband-resolved mechanical breathing modes at ~3.2 GHz, with vacuum optomechanical coupling rates of up to g₀/2π ≈ 300 kHz. The mechanical modes are driven by integrated microwave electrodes via the inverse piezoelectric effect. We estimate that the system could achieve an electromechanical coupling rate to a superconducting transmon qubit of ~200 kHz. Our work represents a decisive step towards integration of piezoelectro-optomechanical interfaces with superconducting quantum processors.

A route to scalability for superconducting quantum computation is the modular approach, which however requires coherent microwave-to-optical conversion. Here the authors use gallium phosphide optomechanical crystal cavities for this task, exploiting their high refractive index and large OM coupling rate.

Ground state cooling of an ultracoherent electromechanical system

Cavity electromechanics relies on parametric coupling between microwave and mechanical modes to manipulate the mechanical quantum state, and provide a coherent interface between different parts of hybrid quantum systems. High coherence of the mechanical mode is of key importance in such applications, in order to protect the quantum states it hosts from thermal decoherence. Here, we introduce an electromechanical system based around a soft-clamped mechanical resonator with an extremely high Q-factor (>10⁹) held at very low (30 mK) temperatures. This ultracoherent mechanical resonator is capacitively coupled to a microwave mode, strong enough to enable ground-state-cooling of the mechanics (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{n}}_{\min }=0.76\pm 0.16$$\end{document}n¯min=0.76±0.16). This paves the way towards exploiting the extremely long coherence times (t_coh > 100 ms) offered by such systems for quantum information processing and state conversion.

’Systems with long coherence times are extremely important for the processing of quantum information. To this end the authors present a system able to cool down a resonator to its quantum mechanical ground state harnessing the large coupling between an ultra-coherent mechanical resonator and a superconducting circuit.’

Tunable microwave-optical entanglement and conversion in multimode electro-opto-mechanics

We study tunable double-channel microwave-optical (M-O) entanglement and coherent conversion by controlling the quantum interference effect. This is realized in a two-mechanical-mode electro-opto-mechanical (EOM) system, in which two mechanical resonators (MRs) are coupled with each other by phase-dependent phonon-phonon interaction, and link the interaction between the microwave and optical cavity. It's demonstrated that the mechanical coupling between two MRs leads to the interference of two pathways of electro-opto-mechanical interaction, which can generate the tunable double-channel phenomena in comparison with a typical three-mode EOM system. In particular, by tuning of phonon-phonon interaction and couplings between cavities with MRs, we can not only steer the switch from the M-O interaction with a single channel to that of the double-channel, but also modulate the entanglement and conversion characteristics in each channel. Moreover, our scheme can be extended to an N-mechanical-mode EOM system, in which N discrete channels will be observed and controlled. This study opens up prospects for quantum information transduction and storage with a wide bandwidth and multichannel quantum interface.

Quantum-enabled operation of a microwave-optical interface

Solid-state microwave systems offer strong interactions for fast quantum logic and sensing but photons at telecom wavelength are the ideal choice for high-density low-loss quantum interconnects. A general-purpose interface that can make use of single photon effects requires < 1 input noise quanta, which has remained elusive due to either low efficiency or pump induced heating. Here we demonstrate coherent electro-optic modulation on nanosecond-timescales with only [Formula: see text] microwave input noise photons with a total bidirectional transduction efficiency of 8.7% (or up to 15% with [Formula: see text]), as required for near-term heralded quantum network protocols. The use of short and high-power optical pump pulses also enables near-unity cooperativity of the electro-optic interaction leading to an internal pure conversion efficiency of up to 99.5%. Together with the low mode occupancy this provides evidence for electro-optic laser cooling and vacuum amplification as predicted a decade ago.

Strong Parametric Coupling between Two Ultracoherent Membrane Modes

We demonstrate parametric coupling between two modes of a silicon nitride membrane. We achieve the coupling by applying an oscillating voltage to a sharp metal tip that approaches the membrane surface to within a few 100 nm. When the voltage oscillation frequency is equal to the mode frequency difference, the modes exchange energy periodically and faster than their free energy decay rate. This flexible method can potentially be useful for rapid state control and transfer between modes, and is an important step toward parametric spin sensing experiments with membrane resonators.

Vibrational Kerr Solitons in an Optomechanical Microresonator

Kerr soliton microcombs in microresonators have been a prominent miniaturized coherent light source. Here, for the first time, we demonstrate the existence of Kerr solitons in an optomechanical microresonator, for which a nonlinear model is built by incorporating a single mechanical mode and multiple optical modes. Interestingly, an exotic vibrational Kerr soliton state is found, which is modulated by a self-sustained mechanical oscillation. Besides, the soliton provides extra mechanical gain through the optical spring effect, and results in phonon lasing with a red-detuned pump. Various nonlinear dynamics is also observed, including limit cycle, higher periodicity, and transient chaos. This work provides a guidance for not only exploring many-body nonlinear interactions, but also promoting precision measurements by featuring superiority of both frequency combs and optomechanics.

Mid-infrared-perturbed molecular vibrational signatures in plasmonic nanocavities

Recent developments in surface-enhanced Raman scattering (SERS) enable observation of single-bond vibrations in real time at room temperature. By contrast, mid-infrared (MIR) vibrational spectroscopy is limited to inefficient slow detection. Here we develop a new method for MIR sensing using SERS. This method utilizes nanoparticle-on-foil (NPoF) nanocavities supporting both visible and MIR plasmonic hotspots in the same nanogap formed by a monolayer of molecules. Molecular SERS signals from individual NPoF nanocavities are modulated in the presence of MIR photons. The strength of this modulation depends on the MIR wavelength, and is maximized at the 6-12 μm absorption bands of SiO₂ or polystyrene placed under the foil. Using a single-photon lock-in detection scheme we time-resolve the rise and decay of the signal in a few 100 ns. Our observations reveal that the phonon resonances of SiO₂ can trap intense MIR surface plasmons within the Reststrahlen band, tuning the visible-wavelength localized plasmons by reversibly perturbing the localized few-nm-thick water shell trapped in the nanostructure crevices. This suggests new ways to couple nanoscale bond vibrations for optomechanics, with potential to push detection limits down to single-photon and single-molecule regimes.

Fabry-Perot interferometric calibration of van der Waals material-based nanomechanical resonators

One of the challenges in integrating nanomechanical resonators made from van der Waals materials in optoelectromechanical technologies is characterizing their dynamic properties from vibrational displacement. Multiple calibration schemes using optical interferometry have tackled this challenge. However, these techniques are limited only to optically thin resonators with an optimal vacuum gap height and substrate for interferometric detection. Here, we address this limitation by implementing a modeling-based approach via multilayer thin-film interference for in situ, non-invasive determination of the resonator thickness, gap height, and motional amplitude. This method is demonstrated on niobium diselenide drumheads that are electromotively driven in their linear regime of motion. The laser scanning confocal configuration enables a resolution of hundreds of picometers in motional amplitude for circular and elliptical devices. The measured thickness and spacer height, determined to be in the order of tens and hundreds of nanometers, respectively, are in excellent agreement with profilometric measurements. Moreover, the transduction factor estimated from our method agrees with the result of other studies that resolved Brownian motion. This characterization method, which applies to both flexural and acoustic wave nanomechanical resonators, is robust because of its scalability to thickness and gap height, and any form of reflecting substrate.

An electro-mechano-optical NMR probe for 1H–13C double resonance in a superconducting magnet

A compact nanomembrane radiofrequency-to-light transducer brings the emerging Electro-Mechano-Optical (EMO) NMR technique into the realm of practical NMR in chemistry using a superconducting magnet.

Continuous-wave frequency upconversion with a molecular optomechanical nanocavity

[Figure: see text].

Optically Heralded Entanglement of Superconducting Systems in Quantum Networks

Networking superconducting quantum computers is a longstanding challenge in quantum science. The typical approach has been to cascade transducers: converting to optical frequencies at the transmitter and to microwave frequencies at the receiver. However, the small microwave-optical coupling and added noise have proven formidable obstacles. Instead, we propose optical networking via heralding end-to-end entanglement with one detected photon and teleportation. This new protocol can be implemented on standard transduction hardware while providing significant performance improvements over transduction. In contrast to cascaded direct transduction, our scheme absorbs the low optical-microwave coupling efficiency into the heralding step, thus breaking the rate-fidelity trade-off. Moreover, this technique unifies and simplifies entanglement generation between superconducting devices and other physical modalities in quantum networks.

Imaging Off-Resonance Nanomechanical Motion as Modal Superposition

Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion can be obtained by also looking at modal responses at frequencies in between resonances. Here, an imaging of the modal responses for a nanomechanical drum driven off resonance is presented. By using the frequency modal analysis, these shapes are described as a superposition of resonance modes. It is found that the spatial distribution of the oscillating component of the driving force, which is affected by both the shape of the actuating electrode and inherent device properties such as asymmetry and initial slack, greatly influences the modal weight or participation. This modal superposition analysis elucidates the dynamics of any nanomechanical system through modal weights. This aids in optimizing mode-specific designs for force sensing and integration with other systems.

Quantum control of a nanoparticle optically levitated in cryogenic free space

Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence^1-3. Quantum control of mechanical motion has been achieved by engineering the radiation-pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator^4-7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states⁸. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects^9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10^-15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales¹¹.

Efficient microwave-to-optical single-photon conversion with a single flying circular Rydberg atom

We propose a scheme for converting a microwave (mw) single photon in a mw cavity to a flying optical photon. The conversion is realized by using a flying circular Rydberg atom, which plays a role of the "data bus" as an excellent memory to connect the mw and optical cavities. To link the energy levels of atom in optical domain and mw domain, we use fast decircularization method and three-photon Raman transition method. Thank to these low loss processes and the super long lifetime of circular Rydberg states, this scheme can efficiently convert single mw photons into the optical domain. Based on existing experiments and data, the conversion efficiency is simulated as 60%. The theoretical limit of the conversion efficiency is about 87%.

High-frequency broadband laser phase noise cancellation using a delay line

Laser phase noise remains a limiting factor in many experimental settings, including metrology, time-keeping, as well as quantum optics. Hitherto this issue was addressed at low frequencies ranging from well below 1 Hz to maximally 100 kHz. However, a wide range of experiments, such as, e.g., those involving nanomechanical membrane resonators, are highly sensitive to noise at higher frequencies in the range of 100 kHz to 10 MHz, such as nanomechanical membrane resonators. Here we employ a fiber-loop delay line interferometer optimized to cancel laser phase noise at frequencies around 1.5 MHz. We achieve noise reduction in 300 kHz-wide bands with a peak reduction of more than 10 dB at desired frequencies, reaching phase noise of less than -160 dB(rad²/Hz) with a Ti:Al₂O₃ laser. These results provide a convenient noise reduction technique to achieve deep ground-state cooling of mechanical motion.

Rare-Earth-Mediated Optomechanical System in the Reversed Dissipation Regime

Strain-mediated interaction between phonons and telecom photons is demonstrated using excited states of erbium ions embedded in a mechanical resonator. Owing to the extremely long-lived nature of rare-earth ions, the dissipation rate of the optical resonance falls below that of the mechanical one. Thus, a "reversed dissipation regime" is achieved in the optical frequency region. We experimentally demonstrate an optomechanical coupling rate g_{0}=2π×21.7  Hz, and numerically reveal that the interaction causes stimulated excitation of erbium ions. Numerical analyses further indicate the possibility of g_{0} exceeding the dissipation rates of erbium and mechanical systems, thereby leading to single-photon strong coupling. This strain-mediated interaction, moreover, involves the spin degree of freedom, and has a potential to be extended to highly coherent opto-electro-mechanical hybrid systems in the reversed dissipation regime.

Impact of the central frequency of environment on non-Markovian dynamics in piezoelectric optomechanical devices

The piezoelectric optomechanical devices supply a promising experimental platform to realize the coherent and effective control and measurement of optical circuits working in Terahertz (THz) frequencies via superconducting electron devices typically working in Radio (MHz) frequencies. However, quantum fluctuations are unavoidable when the size of mechanical oscillators enter into the nanoscale. The consequences of the noisy environment are still challenging due to the lack of analytical tools. In this paper, a semi-classical and full-quantum model of piezoelectric optomechanical systems coupled to a noisy bosonic quantum environment are introduced and solved in terms of quantum-state diffusion (QSD) trajectories in the non-Markovian regime. We show that the noisy environment, particularly the central frequency of the environment, can enhance the entanglement generation between optical cavities and LC circuits in some parameter regimes. Moreover, we observe the critical points in the coefficient functions, which can lead the different behaviors in the system. Besides, we also witness the entanglement transfers between macroscopic objects due to the memory effect of the environment. Our work can be applied in the fields of electric/ optical switches, and long-distance distribution in a large-scale quantum network.

Hybrid Integration of Silicon Photonic Devices on Lithium Niobate for Optomechanical Wavelength Conversion

The rapid development of quantum information processors has accelerated the demand for technologies that enable quantum networking. One promising approach uses mechanical resonators as an intermediary between microwave and optical fields. Signals from a superconducting, topological, or spin qubit processor can then be converted coherently to optical states at telecom wavelengths. However, current devices built from homogeneous structures suffer from added noise and a small conversion efficiency. Combining advantageous properties of different materials into a heterogeneous design should allow for superior quantum transduction devices-so far these hybrid approaches have however been hampered by complex fabrication procedures. Here we present a novel integration method, based on previous pick-and-place ideas, that can combine independently fabricated device components of different materials into a single device. The method allows for a precision alignment by continuous optical monitoring during the process. Using our method, we assemble a hybrid silicon-lithium niobate device with state-of-the-art wavelength conversion characteristics.

Polariton-driven phonon laser

Efficient generation of phonons is an important ingredient for a prospective electrically-driven phonon laser. Hybrid quantum systems combining cavity quantum electrodynamics and optomechanics constitute a novel platform with potential for operation at the extremely high frequency range (30-300 GHz). We report on laser-like phonon emission in a hybrid system that optomechanically couples polariton Bose-Einstein condensates (BECs) with phonons in a semiconductor microcavity. The studied system comprises GaAs/AlAs quantum wells coupled to cavity-confined optical and vibrational modes. The non-resonant continuous wave laser excitation of a polariton BEC in an individual trap of a trap array, induces coherent mechanical self-oscillation, leading to the formation of spectral sidebands displaced by harmonics of the fundamental 20 GHz mode vibration frequency. This phonon "lasing" enhances the phonon occupation five orders of magnitude above the thermal value when tunable neighbor traps are red-shifted with respect to the pumped trap BEC emission at even harmonics of the vibration mode. These experiments, supported by a theoretical model, constitute the first demonstration of coherent cavity optomechanical phenomena with exciton polaritons, paving the way for new hybrid designs for quantum technologies, phonon lasers, and phonon-photon bidirectional translators.

Converting microwave and telecom photons with a silicon photonic nanomechanical interface

Practical quantum networks require low-loss and noise-resilient optical interconnects as well as non-Gaussian resources for entanglement distillation and distributed quantum computation. The latter could be provided by superconducting circuits but existing solutions to interface the microwave and optical domains lack either scalability or efficiency, and in most cases the conversion noise is not known. In this work we utilize the unique opportunities of silicon photonics, cavity optomechanics and superconducting circuits to demonstrate a fully integrated, coherent transducer interfacing the microwave X and the telecom S bands with a total (internal) bidirectional transduction efficiency of 1.2% (135%) at millikelvin temperatures. The coupling relies solely on the radiation pressure interaction mediated by the femtometer-scale motion of two silicon nanobeams reaching a Vπ as low as 16 μV for sub-nanowatt pump powers. Without the associated optomechanical gain, we achieve a total (internal) pure conversion efficiency of up to 0.019% (1.6%), relevant for future noise-free operation on this qubit-compatible platform.

Cavity piezo-mechanics for superconducting-nanophotonic quantum interface

Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10 GHz phonons are resonantly coupled with photons in a superconducting cavity and a nanophotonic cavity at the same time. Taking advantage of the large piezo-mechanical cooperativity (Cem ~7) and the enhanced optomechanical coupling boosted by a pulsed optical pump, we demonstrate coherent interactions at cryogenic temperatures via the observation of efficient microwave-optical photon conversion. This hybrid interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in microwave-optical photon entanglement and quantum sensing mediated by gigahertz phonons.

Impact of Transduction Scaling Laws on Nanoelectromechanical Systems

We study the electromechanical transduction in nanoelectromechanical actuators and show that the differences in scaling laws for electrical and mechanical effects lead to an overall nontrivial miniaturization behavior. In particular, the previously neglected fringing fields considerably increase electrical forces and improve the stability of nanoscale actuators. This shows that electrostatics does not pose any limitations to the miniaturization of electromechanical systems; in fact, in several respects, nanosystems outperform their microscale counterparts. As a specific example, we consider in-plane actuation of ultrathin slabs and show that devices consisting of a few layers of graphene are feasible, implying that electromechanical resonators operating beyond 40 GHz are possible with currently available technology.

A Chip-Scale Oscillation-Mode Optomechanical Inertial Sensor Near the Thermodynamical Limits

Modern navigation systems integrate the global positioning system (GPS) with an inertial navigation system (INS), which complement each other for correct attitude and velocity determination. The core of the INS integrates accelerometers and gyroscopes used to measure forces and angular rate in the vehicular inertial reference frame. With the help of gyroscopes and by integrating the acceleration to compute velocity and distance, precision and compact accelerometers with sufficient accuracy can provide small-error location determination. Solid-state implementations, through coherent readout, can provide a platform for high performance acceleration detection. In contrast to prior accelerometers using piezoelectric or capacitive readout techniques, optical readout provides narrow-linewidth high-sensitivity laser detection along with low-noise resonant optomechanical transduction near the thermodynamical limits. Here an optomechanical inertial sensor with an 8.2 μg Hz-1/2 velocity random walk (VRW) at an acquisition rate of 100 Hz and 50.9 μg bias instability is demonstrated, suitable for applications, such as, inertial navigation, inclination sensing, platform stabilization, and/or wearable device motion detection. Driven into optomechanical sustained-oscillation, the slot photonic crystal cavity provides radio-frequency readout of the optically-driven transduction with an enhanced 625 μg Hz-1 sensitivity. Measuring the optomechanically-stiffened oscillation shift, instead of the optical transmission shift, provides a 220× VRW enhancement over pre-oscillation mode detection.

Spectrally broadband electro-optic modulation with nanoelectromechanical string resonators

In this paper, we present a shutter-based electro-optical modulator made of two parallel nanoelectromechanical silicon nitride string resonators. These strings are covered with electrically connected gold electrodes and actuated either by Lorentz or electrostatic forces. The in-plane string vibrations modulate the width of the gap between the strings. The gold electrodes on both sides of the gap act as a mobile mirror that modulate the laser light that is focused in the middle of this gap. These electro-optical modulators can achieve an optical modulation depth of almost 100% for a driving voltage lower than 1 mV at a frequency of 314 kHz. The frequency range is determined by the string resonance frequency, which can take values of the order of a few hundred kilohertz to several megahertz. The strings are driven in the strongly nonlinear regime, which allows a frequency tuning of several kilohertz without significant effect on the optical modulation depth.

Single particles as resonators for thermomechanical analysis

Thermal methods are indispensable for the characterization of most materials. However, the existing methods require bulk amounts for analysis and give an averaged response of a material. This can be especially challenging in a biomedical setting, where only very limited amounts of material are initially available. Nano- and microelectromechanical systems (NEMS/MEMS) offer the possibility of conducting thermal analysis on small amounts of materials in the nano-microgram range, but cleanroom fabricated resonators are required. Here, we report the use of single drug and collagen particles as micro mechanical resonators, thereby eliminating the need for cleanroom fabrication. Furthermore, the proposed method reveals additional thermal transitions that are undetected by standard thermal methods and provide the possibility of understanding fundamental changes in the mechanical properties of the materials during thermal cycling. This method is applicable to a variety of different materials and opens the door to fundamental mechanistic insights.

Efficient bidirectional piezo-optomechanical transduction between microwave and optical frequency

Efficient interconversion of both classical and quantum information between microwave and optical frequency is an important engineering challenge. The optomechanical approach with gigahertz-frequency mechanical devices has the potential to be extremely efficient due to the large optomechanical response of common materials, and the ability to localize mechanical energy into a micron-scale volume. However, existing demonstrations suffer from some combination of low optical quality factor, low electrical-to-mechanical transduction efficiency, and low optomechanical interaction rate. Here we demonstrate an on-chip piezo-optomechanical transducer that systematically addresses all these challenges to achieve nearly three orders of magnitude improvement in conversion efficiency over previous work. Our modulator demonstrates acousto-optic modulation with [Formula: see text] = 0.02 V. We show bidirectional conversion efficiency of [Formula: see text] with 3.3 μW  red-detuned optical pump, and [Formula: see text] with 323 μW blue-detuned pump. Further study of quantum transduction at millikelvin temperatures is required to understand how the efficiency and added noise are affected by reduced mechanical dissipation, thermal conductivity, and thermal capacity.

Entanglement of propagating optical modes via a mechanical interface

Many applications of quantum information processing (QIP) require distribution of quantum states in networks, both within and between distant nodes. Optical quantum states are uniquely suited for this purpose, as they propagate with ultralow attenuation and are resilient to ubiquitous thermal noise. Mechanical systems are then envisioned as versatile interfaces between photons and a variety of solid-state QIP platforms. Here, we demonstrate a key step towards this vision, and generate entanglement between two propagating optical modes, by coupling them to the same, cryogenic mechanical system. The entanglement persists at room temperature, where we verify the inseparability of the bipartite state and fully characterize its logarithmic negativity by homodyne tomography. We detect, without any corrections, correlations corresponding to a logarithmic negativity of EN = 0.35. Combined with quantum interfaces between mechanical systems and solid-state qubit processors, this paves the way for mechanical systems enabling long-distance quantum information networking over optical fiber networks.

Nonreciprocal interference and coherent photon routing in a three-port optomechanical system

We study the interference between different weak signals in a three-port optomechanical system, which is achieved by coupling three cavity modes to the same mechanical mode. If one cavity serves as a control port and is perturbed continuously by a control signal, nonreciprocal interference can be observed when another signal is injected upon different target ports. In particular, we exhibit frequency-independent perfect blockade induced by the completely destructive interference over the full frequency domain. Moreover, coherent photon routing can be realized by perturbing all ports simultaneously, with which the synthetic signal only outputs from the desired port. We also reveal that the routing scheme can be extended to more-port optomechanical systems. The results in this paper may have potential applications for controlling light transport and quantum information processing.

Radio-frequency optomechanical characterization of a silicon nitride drum

On-chip actuation and readout of mechanical motion is key to characterize mechanical resonators and exploit them for new applications. We capacitively couple a silicon nitride membrane to an off resonant radio-frequency cavity formed by a lumped element circuit. Despite a low cavity quality factor (Q_E ≈ 7.4) and off resonant, room temperature operation, we are able to parametrize several mechanical modes and estimate their optomechanical coupling strengths. This enables real-time measurements of the membrane's driven motion and fast characterization without requiring a superconducting cavity, thereby eliminating the need for cryogenic cooling. Finally, we observe optomechanically induced transparency and absorption, crucial for a number of applications including sensitive metrology, ground state cooling of mechanical motion and slowing of light.

Radiative Cooling of a Superconducting Resonator

Cooling microwave resonators to near the quantum ground state, crucial for their operation in the quantum regime, is typically achieved by direct device refrigeration to a few tens of millikelvin. However, in quantum experiments that require high operation power such as microwave-to-optics quantum transduction, it is desirable to operate at higher temperatures with non-negligible environmental thermal excitations, where larger cooling power is available. In this Letter, we present a radiative cooling protocol to prepare a superconducting microwave mode near its quantum ground state in spite of warm environment temperatures for the resonator. In this proof-of-concept experiment, the mode occupancy of a 10 GHz superconducting resonator thermally anchored at 1.02 K is reduced to 0.44±0.05 from 1.56 by radiatively coupling to a 70 mK cold load. This radiative cooling scheme allows high-operation-power microwave experiments to work in the quantum regime, and opens possibilities for routing microwave quantum states to elevated temperatures.

Proposal for Heralded Generation and Detection of Entangled Microwave-Optical-Photon Pairs

Quantum state transfer between microwave and optical frequencies is essential for connecting superconducting quantum circuits to optical systems and extending microwave quantum networks over long distances. However, establishing such a quantum interface is extremely challenging because the standard direct quantum transduction requires both high coupling efficiency and small added noise. We propose an entanglement-based scheme-generating microwave-optical entanglement and using it to transfer quantum states via quantum teleportation-which can bypass the stringent requirements in direct quantum transduction and is robust against loss errors. In addition, we propose and analyze a counterintuitive design-suppress the added noise by placing the device at a higher temperature environment-which can improve both the device quality factor and power handling capability. We systematically analyze the generation and verification of entangled microwave-optical-photon pairs. The parameter for entanglement verification favors the regime of cooperativity mismatch and can tolerate certain thermal noises. Our scheme is feasible given the latest advances on electro-optomechanics, and can be generalized to various physical systems.

Microwave-to-optical transduction using a mechanical supermode for coupling piezoelectric and optomechanical resonators

The successes of superconducting quantum circuits at local manipulation of quantum information and photonics technology at long-distance transmission of the same have spurred interest in the development of quantum transducers for efficient, low-noise, and bidirectional frequency conversion of photons between the microwave and optical domains. We propose to realize such functionality through the coupling of electrical, piezoelectric, and optomechanical resonators. The coupling of the mechanical subsystems enables formation of a resonant mechanical supermode that provides a mechanically-mediated, efficient single interface to both the microwave and optical domains. The conversion process is analyzed by applying an equivalent circuit model that relates device-level parameters to overall figures of merit for conversion efficiency η and added noise N. These can be further enhanced by proper impedance matching of the transducer to an input microwave transmission line. The performance of potential transducers is assessed through finite-element simulations, with a focus on geometries in GaAs, followed by considerations of the AlN, LiNbO3, and AlN-on-Si platforms. We present strategies for maximizing η and minimizing N, and find that simultaneously achieving η > 50 % and N < 0.5 should be possible with current technology. We find that the use of a mechanical supermode for mediating transduction is a key enabler for high-efficiency operation, particularly when paired with an appropriate microwave impedance matching network. Our comprehensive analysis of the full transduction chain enables us to outline a development path for the realization of high-performance quantum transducers that will constitute a valuable resource for quantum information science.

Microwave-to-optics conversion using a mechanical oscillator in its quantum groundstate

Conversion between signals in the microwave and optical domains is of great interest both for classical telecommunication, as well as for connecting future superconducting quantum computers into a global quantum network. For quantum applications, the conversion has to be both efficient, as well as operate in a regime of minimal added classical noise. While efficient conversion has been demonstrated using mechanical transducers, they have so far all operated with a substantial thermal noise background. Here, we overcome this limitation and demonstrate coherent conversion between GHz microwave signals and the optical telecom band with a thermal background of less than one phonon. We use an integrated, on-chip electro-opto-mechanical device that couples surface acoustic waves driven by a resonant microwave signal to an optomechanical crystal featuring a 2.7 GHz mechanical mode. We initialize the mechanical mode in its quantum groundstate, which allows us to perform the transduction process with minimal added thermal noise, while maintaining an optomechanical cooperativity >1, so that microwave photons mapped into the mechanical resonator are effectively upconverted to the optical domain. We further verify the preservation of the coherence of the microwave signal throughout the transduction process.