Design of an ultra-low mode volume piezo-optomechanical quantum transducer.

Coherent transduction of quantum states from the microwave to the optical domain can play a key role in quantum networking and distributed quantum computing. We present the design of a piezo-optomechanical device formed in a hybrid lithium niobate on silicon platform, that is suitable for microwave-to-optical quantum transduction. Our design is based on acoustic hybridization of an ultra-low mode volume piezoacoustic cavity with an optomechanical crystal cavity. The strong piezoelectric nature of lithium niobate allows us to mediate transduction via an acoustic mode which only minimally interacts with the lithium niobate, and is predominantly silicon-like, with very low electrical and acoustic loss. We estimate that this transducer can realize an intrinsic conversion efficiency of up to 35% with <0.5 added noise quanta when resonantly coupled to a superconducting transmon qubit and operated in pulsed mode at 10 kHz repetition rate. The performance improvement gained in such hybrid lithium niobate-silicon transducers make them suitable for heralded entanglement of qubits between superconducting quantum processors connected by optical fiber links.

A superconducting quantum simulator based on a photonic-bandgap metamaterial.

Synthesizing many-body quantum systems with various ranges of interactions facilitates the study of quantum chaotic dynamics. Such extended interaction range can be enabled by using nonlocal degrees of freedom such as photonic modes in an otherwise locally connected structure. Here, we present a superconducting quantum simulator in which qubits are connected through an extensible photonic-bandgap metamaterial, thus realizing a one-dimensional Bose-Hubbard model with tunable hopping range and on-site interaction. Using individual site control and readout, we characterize the statistics of measurement outcomes from many-body quench dynamics, which enables in situ Hamiltonian learning. Further, the outcome statistics reveal the effect of increased hopping range, showing the predicted crossover from integrability to ergodicity. Our work enables the study of emergent randomness from chaotic many-body evolution and, more broadly, expands the accessible Hamiltonians for quantum simulation using superconducting circuits.

Topological phonon transport in an optomechanical system.

Light is a powerful tool for controlling mechanical motion, as shown by numerous applications in the field of cavity optomechanics. Recently, small scale optomechanical circuits, connecting a few optical and mechanical modes, have been demonstrated in an ongoing push towards multi-mode on-chip optomechanical systems. An ambitious goal driving this trend is to produce topologically protected phonon transport. Once realized, this will unlock the full toolbox of optomechanics for investigations of topological phononics. Here, we report the realization of topological phonon transport in an optomechanical device. Our experiment is based on an innovative multiscale optomechanical crystal design and allows for site-resolved measurements in an array of more than 800 cavities. The sensitivity inherent in our optomechanical read-out allowed us to detect thermal fluctuations traveling along topological edge channels. This represents a major step forward in an ongoing effort to downscale mechanical topological systems.

Stabilizing a Bosonic Qubit Using Colored Dissipation.

Protected qubits such as the 0-π qubit, and bosonic qubits including cat qubits and Gottesman-Kitaev-Preskill (GKP) qubits offer advantages for fault tolerance. Some of these protected qubits (e.g., 0-π qubit and Kerr-cat qubit) are stabilized by Hamiltonians which have (near-)degenerate ground state manifolds with large energy gaps to the excited state manifolds. Without dissipative stabilization mechanisms the performance of such energy-gap-protected qubits can be limited by leakage to excited states. Here, we propose a scheme for dissipatively stabilizing an energy-gap-protected qubit using colored (i.e., frequency-selective) dissipation without inducing errors in the ground state manifold. Concretely we apply our colored dissipation technique to Kerr-cat qubits and propose colored Kerr-cat qubits which are protected by an engineered colored single-photon loss. When applied to the Kerr-cat qubits our scheme significantly suppresses leakage-induced bit-flip errors (which we show are a limiting error mechanism) while only using linear interactions. Beyond the benefits to the Kerr-cat qubit we also show that our frequency-selective loss technique can be applied to a broader class of protected qubits.

Superconducting qubit to optical photon transduction.

Conversion of electrical and optical signals lies at the foundation of the global internet. Such converters are used to extend the reach of long-haul fibre-optic communication systems and within data centres for high-speed optical networking of computers. Likewise, coherent microwave-to-optical conversion of single photons would enable the exchange of quantum states between remotely connected superconducting quantum processors1. Despite the prospects of quantum networking2, maintaining the fragile quantum state in such a conversion process with superconducting qubits has not yet been achieved. Here we demonstrate the conversion of a microwave-frequency excitation of a transmon-a type of superconducting qubit-into an optical photon. We achieve this by using an intermediary nanomechanical resonator that converts the electrical excitation of the qubit into a single phonon by means of a piezoelectric interaction3 and subsequently converts the phonon to an optical photon by means of radiation pressure4. We demonstrate optical photon generation from the qubit by recording quantum Rabi oscillations of the qubit through single-photon detection of the emitted light over an optical fibre. With proposed improvements in the device and external measurement set-up, such quantum transducers might be used to realize new hybrid quantum networks2,5 and, ultimately, distributed quantum computers6,7.

Nano-acoustic resonator with ultralong phonon lifetime.

The energy damping time in a mechanical resonator is critical to many precision metrology applications, such as timekeeping and force measurements. We present measurements of the phonon lifetime of a microwave-frequency, nanoscale silicon acoustic cavity incorporating a phononic bandgap acoustic shield. Using pulsed laser light to excite a colocalized optical mode of the cavity, we measured the internal acoustic modes with single-phonon sensitivity down to millikelvin temperatures, yielding a phonon lifetime of up to [Formula: see text] seconds (quality factor [Formula: see text]) and a coherence time of [Formula: see text] microseconds for bandgap-shielded cavities. These acoustically engineered nanoscale structures provide a window into the material origins of quantum noise and have potential applications ranging from tests of various collapse models of quantum mechanics to miniature quantum memory elements in hybrid superconducting quantum circuits.

Two-dimensional optomechanical crystal cavity with high quantum cooperativity.

Optomechanical systems offer new opportunities in quantum information processing and quantum sensing. Many solid-state quantum devices operate at millikelvin temperatures-however, it has proven challenging to operate nanoscale optomechanical devices at these ultralow temperatures due to their limited thermal conductance and parasitic optical absorption. Here, we present a two-dimensional optomechanical crystal resonator capable of achieving large cooperativity C and small effective bath occupancy nb, resulting in a quantum cooperativity Ceff ≡ C/nb > 1 under continuous-wave optical driving. This is realized using a two-dimensional phononic bandgap structure to host the optomechanical cavity, simultaneously isolating the acoustic mode of interest in the bandgap while allowing heat to be removed by phonon modes outside of the bandgap. This achievement paves the way for a variety of applications requiring quantum-coherent optomechanical interactions, such as transducers capable of bi-directional conversion of quantum states between microwave frequency superconducting quantum circuits and optical photons in a fiber optic network.

Cavity quantum electrodynamics with atom-like mirrors.

It has long been recognized that atomic emission of radiation is not an immutable property of an atom, but is instead dependent on the electromagnetic environment1 and, in the case of ensembles, also on the collective interactions between the atoms2-6. In an open radiative environment, the hallmark of collective interactions is enhanced spontaneous emission-super-radiance2-with non-dissipative dynamics largely obscured by rapid atomic decay7. Here we observe the dynamical exchange of excitations between a single artificial atom and an entangled collective state of an atomic array9 through the precise positioning of artificial atoms realized as superconducting qubits8 along a one-dimensional waveguide. This collective state is dark, trapping radiation and creating a cavity-like system with artificial atoms acting as resonant mirrors in the otherwise open waveguide. The emergent atom-cavity system is shown to have a large interaction-to-dissipation ratio (cooperativity exceeding 100), reaching the regime of strong coupling, in which coherent interactions dominate dissipative and decoherence effects. Achieving strong coupling with interacting qubits in an open waveguide provides a means of synthesizing multi-photon dark states with high efficiency and paves the way for exploiting correlated dissipation and decoherence-free subspaces of quantum emitter arrays at the many-body level10-13.

Quantum electromechanics of a hypersonic crystal.

Recent technical developments in the fields of quantum electromechanics and optomechanics have spawned nanoscale mechanical transducers with the sensitivity to measure mechanical displacements at the femtometre scale and the ability to convert electromagnetic signals at the single photon level. A key challenge in this field is obtaining strong coupling between motion and electromagnetic fields without adding additional decoherence. Here we present an electromechanical transducer that integrates a high-frequency (0.42 GHz) hypersonic phononic crystal with a superconducting microwave circuit. The use of a phononic bandgap crystal enables quantum-level transduction of hypersonic mechanical motion and concurrently eliminates decoherence caused by acoustic radiation. Devices with hypersonic mechanical frequencies provide a natural pathway for integration with Josephson junction quantum circuits, a leading quantum computing technology, and nanophotonic systems capable of optical networking and distributing quantum information.

Superconducting metamaterials for waveguide quantum electrodynamics.

Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter-emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of ng = 450, we observe an anomalous Lamb shift of -28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states.

Pseudomagnetic fields for sound at the nanoscale.

There is a growing effort in creating chiral transport of sound waves. However, most approaches so far have been confined to the macroscopic scale. Here, we propose an approach suitable to the nanoscale that is based on pseudomagnetic fields. These pseudomagnetic fields for sound waves are the analogue of what electrons experience in strained graphene. In our proposal, they are created by simple geometrical modifications of an existing and experimentally proven phononic crystal design, the snowflake crystal. This platform is robust, scalable, and well-suited for a variety of excitation and readout mechanisms, among them optomechanical approaches.

Design of tunable GHz-frequency optomechanical crystal resonators.

We present a silicon optomechanical nanobeam design with a dynamically tunable acoustic mode at 10.2 GHz. The resonance frequency can be shifted by 90 kHz/V2 with an on-chip capacitor that was optimized to exert forces up to 1 µN at 10 V operation voltage. Optical resonance frequencies around 190 THz with Q-factors up to 2.2 × 106 place the structure in the well-resolved sideband regime with vacuum optomechanical coupling rates up to g0/2π = 353 kHz. Tuning can be used, for instance, to overcome variation in the device-to-device acoustic resonance frequency due to fabrication errors, paving the way for optomechanical circuits consisting of arrays of optomechanical cavities.

Nonlinear Radiation Pressure Dynamics in an Optomechanical Crystal.

Utilizing a silicon nanobeam optomechanical crystal, we investigate the attractor diagram arising from the radiation pressure interaction between a localized optical cavity at λ_{c}=1542 nm and a mechanical resonance at ω_{m}/2π=3.72 GHz. At a temperature of T_{b}≈10 K, highly nonlinear driving of mechanical motion is observed via continuous wave optical pumping. Introduction of a time-dependent (modulated) optical pump is used to steer the system towards an otherwise inaccessible dynamically stable attractor in which mechanical self-oscillation occurs for an optical pump red detuned from the cavity resonance. An analytical model incorporating thermo-optic effects due to optical absorption heating is developed and found to accurately predict the measured device behavior.

Silicon-chip source of bright photon pairs.

Integrated quantum photonics relies critically on the purity, scalability, integrability, and flexibility of a photon source to support diverse quantum functionalities on a single chip. Here we report a chip-scale photon-pair source on the silicon-on-insulator platform that utilizes dramatic cavity-enhanced four-wave mixing in a high-Q silicon microdisk resonator. The device is able to produce high-quality photon pairs at different wavelengths with a high spectral brightness of 6.24×10(7) pairs/s/mW(2)/GHz and photon-pair correlation with a coincidence-to-accidental ratio of 1386 ± 278 while pumped with a continuous-wave laser. The superior performance, together with the structural compactness and CMOS compatibility, opens up a great avenue towards quantum silicon photonics with capability of multi-channel parallel information processing for both integrated quantum computing and long-haul quantum communication.

Strong opto-electro-mechanical coupling in a silicon photonic crystal cavity.

We fabricate and characterize a microscale silicon opto-electromechanical system whose mechanical motion is coupled capacitively to an electrical circuit and optically via radiation pressure to a photonic crystal cavity. To achieve large electromechanical interaction strength, we implement an inverse shadow mask fabrication scheme which obtains capacitor gaps as small as 30 nm while maintaining a silicon surface quality necessary for minimizing optical loss. Using the sensitive optical read-out of the photonic crystal cavity, we characterize the linear and nonlinear capacitive coupling to the fundamental ω(m)/2π = 63 MHz in-plane flexural motion of the structure, showing that the large electromechanical coupling in such devices may be suitable for realizing efficient microwave-to-optical signal conversion.

Phonon counting and intensity interferometry of a nanomechanical resonator.

In optics, the ability to measure individual quanta of light (photons) enables a great many applications, ranging from dynamic imaging within living organisms to secure quantum communication. Pioneering photon counting experiments, such as the intensity interferometry performed by Hanbury Brown and Twiss to measure the angular width of visible stars, have played a critical role in our understanding of the full quantum nature of light. As with matter at the atomic scale, the laws of quantum mechanics also govern the properties of macroscopic mechanical objects, providing fundamental quantum limits to the sensitivity of mechanical sensors and transducers. Current research in cavity optomechanics seeks to use light to explore the quantum properties of mechanical systems ranging in size from kilogram-mass mirrors to nanoscale membranes, as well as to develop technologies for precision sensing and quantum information processing. Here we use an optical probe and single-photon detection to study the acoustic emission and absorption processes in a silicon nanomechanical resonator, and perform a measurement similar to that used by Hanbury Brown and Twiss to measure correlations in the emitted phonons as the resonator undergoes a parametric instability formally equivalent to that of a laser. Owing to the cavity-enhanced coupling of light with mechanical motion, this effective phonon counting technique has a noise equivalent phonon sensitivity of 0.89 ± 0.05. With straightforward improvements to this method, a variety of quantum state engineering tasks using mesoscopic mechanical resonators would be enabled, including the generation and heralding of single-phonon Fock states and the quantum entanglement of remote mechanical elements.

Two-dimensional phononic-photonic band gap optomechanical crystal cavity.

We present the fabrication and characterization of an artificial crystal structure formed from a thin film of silicon that has a full phononic band gap for microwave X-band phonons and a two-dimensional pseudo-band gap for near-infrared photons. An engineered defect in the crystal structure is used to localize optical and mechanical resonances in the band gap of the planar crystal. Two-tone optical spectroscopy is used to characterize the cavity system, showing a large coupling (g0/2π≈220 kHz) between the fundamental optical cavity resonance at ωo/2π=195 THz and colocalized mechanical resonances at frequency ωm/2π≈9.3 GHz.

Squeezed light from a silicon micromechanical resonator.

Monitoring a mechanical object's motion, even with the gentle touch of light, fundamentally alters its dynamics. The experimental manifestation of this basic principle of quantum mechanics, its link to the quantum nature of light and the extension of quantum measurement to the macroscopic realm have all received extensive attention over the past half-century. The use of squeezed light, with quantum fluctuations below that of the vacuum field, was proposed nearly three decades ago as a means of reducing the optical read-out noise in precision force measurements. Conversely, it has also been proposed that a continuous measurement of a mirror's position with light may itself give rise to squeezed light. Such squeezed-light generation has recently been demonstrated in a system of ultracold gas-phase atoms whose centre-of-mass motion is analogous to the motion of a mirror. Here we describe the continuous position measurement of a solid-state, optomechanical system fabricated from a silicon microchip and comprising a micromechanical resonator coupled to a nanophotonic cavity. Laser light sent into the cavity is used to measure the fluctuations in the position of the mechanical resonator at a measurement rate comparable to its resonance frequency and greater than its thermal decoherence rate. Despite the mechanical resonator's highly excited thermal state (10(4) phonons), we observe, through homodyne detection, squeezing of the reflected light's fluctuation spectrum at a level 4.5 ± 0.2 per cent below that of vacuum noise over a bandwidth of a few megahertz around the mechanical resonance frequency of 28 megahertz. With further device improvements, on-chip squeezing at significant levels should be possible, making such integrated microscale devices well suited for precision metrology applications.

Optical coupling to nanoscale optomechanical cavities for near quantum-limited motion transduction.

A significant challenge in the development of chip-scale cavity-optomechanical devices as testbeds for quantum experiments and classical metrology lies in the coupling of light from nanoscale optical mode volumes to conventional optical components such as lenses and fibers. In this work we demonstrate a high-efficiency, single-sided fiber-optic coupling platform for optomechanical cavities. By utilizing an adiabatic waveguide taper to transform a single optical mode between a photonic crystal zipper cavity and a permanently mounted fiber, we achieve a collection efficiency for intracavity photons of 52% at the cavity resonance wavelength of λ ≈ 1538 nm. An optical balanced homodyne measurement of the displacement fluctuations of the fundamental in-plane mechanical resonance at 3.3 MHz reveals that the imprecision noise floor lies a factor of 2.8 above the standard quantum limit (SQL) for continuous position measurement, with a predicted total added noise of 1.4 phonons at the optimal probe power. The combination of extremely low measurement noise and robust fiber alignment presents significant progress towards single-phonon sensitivity for these sorts of integrated micro-optomechanical cavities.

Coherent optical wavelength conversion via cavity optomechanics.

Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4-GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1,460 nm and a second cavity mode at 1,545 nm with a 93% internal (2% external) peak efficiency. The thermal- and quantum-limiting noise involved in the conversion process is also analysed, and in terms of an equivalent photon number signal level are found to correspond to an internal noise level of only 6 and 4 × 10(-3) quanta, respectively.