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.

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.

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.

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.

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.

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.

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.

Laser cooling of a nanomechanical oscillator into its quantum ground state.

The simple mechanical oscillator, canonically consisting of a coupled mass-spring system, is used in a wide variety of sensitive measurements, including the detection of weak forces and small masses. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion. On the macroscopic scale of our everyday experience, owing to interactions with its highly fluctuating thermal environment a mechanical oscillator is filled with many energy quanta and its quantum nature is all but hidden. Recently, in experiments performed at temperatures of a few hundredths of a kelvin, engineered nanomechanical resonators coupled to electrical circuits have been measured to be oscillating in their quantum ground state. These experiments, in addition to providing a glimpse into the underlying quantum behaviour of mesoscopic systems consisting of billions of atoms, represent the initial steps towards the use of mechanical devices as tools for quantum metrology or as a means of coupling hybrid quantum systems. Here we report the development of a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip, in which radiation pressure from a laser is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of 0.85 ± 0.08). This cooling is realized at an environmental temperature of 20 K, roughly one thousand times larger than in previous experiments and paves the way for optical control of mesoscale mechanical oscillators in the quantum regime.

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.

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.

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.

Optomechanical crystals.

Periodicity in materials yields interesting and useful phenomena. Applied to the propagation of light, periodicity gives rise to photonic crystals, which can be precisely engineered for such applications as guiding and dispersing optical beams, tightly confining and trapping light resonantly, and enhancing nonlinear optical interactions. Photonic crystals can also be formed into planar lightwave circuits for the integration of optical and electrical microsystems. In a photonic crystal, the periodicity of the host medium is used to manipulate the properties of light, whereas a phononic crystal uses periodicity to manipulate mechanical vibrations. As has been demonstrated in studies of Raman-like scattering in epitaxially grown vertical cavity structures and photonic crystal fibres, the simultaneous confinement of mechanical and optical modes in periodic structures can lead to greatly enhanced light-matter interactions. A logical next step is thus to create planar circuits that act as both photonic and phononic crystals: optomechanical crystals. Here we describe the design, fabrication and characterization of a planar, silicon-chip-based optomechanical crystal capable of co-localizing and strongly coupling 200-terahertz photons and 2-gigahertz phonons. These planar optomechanical crystals bring the powerful techniques of optics and photonic crystals to bear on phononic crystals, providing exquisitely sensitive (near quantum-limited), optical measurements of mechanical vibrations, while simultaneously providing strong nonlinear interactions for optics in a large and technologically relevant range of frequencies.

A picogram- and nanometre-scale photonic-crystal optomechanical cavity.

The dynamic back-action caused by electromagnetic forces (radiation pressure) in optical and microwave cavities is of growing interest. Back-action cooling, for example, is being pursued as a means of achieving the quantum ground state of macroscopic mechanical oscillators. Work in the optical domain has revolved around millimetre- or micrometre-scale structures using the radiation pressure force. By comparison, in microwave devices, low-loss superconducting structures have been used for gradient-force-mediated coupling to a nanomechanical oscillator of picogram mass. Here we describe measurements of an optical system consisting of a pair of specially patterned nanoscale beams in which optical and mechanical energies are simultaneously localized to a cubic-micron-scale volume, and for which large per-photon optical gradient forces are realized. The resulting scale of the per-photon force and the mass of the structure enable the exploration of cavity optomechanical regimes in which, for example, the mechanical rigidity of the structure is dominantly provided by the internal light field itself. In addition to precision measurement and sensitive force detection, nano-optomechanics may find application in reconfigurable and tunable photonic systems, light-based radio-frequency communication and the generation of giant optical nonlinearities for wavelength conversion and optical buffering.

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.

Phonon engineering of atomic-scale defects in superconducting quantum circuits.

Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longest T1 time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.

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.

Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system.

Cavity quantum electrodynamics, the study of coherent quantum interactions between the electromagnetic field and matter inside a resonator, has received attention as both a test bed for ideas in quantum mechanics and a building block for applications in the field of quantum information processing. The canonical experimental system studied in the optical domain is a single alkali atom coupled to a high-finesse Fabry-Perot cavity. Progress made in this system has recently been complemented by research involving trapped ions, chip-based microtoroid cavities, integrated microcavity-atom-chips, nanocrystalline quantum dots coupled to microsphere cavities, and semiconductor quantum dots embedded in micropillars, photonic crystals and microdisks. The last system has been of particular interest owing to its relative simplicity and scalability. Here we use a fibre taper waveguide to perform direct optical spectroscopy of a system consisting of a quantum dot embedded in a microdisk. In contrast to earlier work with semiconductor systems, which has focused on photoluminescence measurements, we excite the system through the photonic (light) channel rather than the excitonic (matter) channel. Strong coupling, the regime of coherent quantum interactions, is demonstrated through observation of vacuum Rabi splitting in the transmitted and reflected signals from the cavity. The fibre coupling method also allows us to examine the system's steady-state nonlinear properties, where we see a saturation of the cavity-quantum dot response for less than one intracavity photon. The excitation of the cavity-quantum dot system through a fibre optic waveguide is central to applications such as high-efficiency single photon sources, and to more fundamental studies of the quantum character of the system.

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.

Slot-mode-coupled optomechanical crystals.

We present a design methodology and analysis of a cavity optomechanical system in which a localized GHz frequency mechanical mode of a nanobeam resonator is evanescently coupled to a high quality factor (Q > 10(6)) optical mode of a separate nanobeam optical cavity. Using separate nanobeams provides flexibility, enabling the independent design and optimization of the optics and mechanics of the system. In addition, the small gap (≈ 25 nm) between the two resonators gives rise to a slot mode effect that enables a large zero-point optomechanical coupling strength to be achieved, with g/2 π > 300 kHz in a Si(3)N(4) system at 980 nm and g/2 π ≈ 900 kHz in a Si system at 1550 nm. The fact that large coupling strengths to GHz mechanical oscillators can be achieved in Si(3)N(4) is important, as this material has a broad optical transparency window, which allows operation throughout the visible and near-infrared. As an application of this platform, we consider wide-band optical frequency conversion between 1300 nm and 980 nm, using two optical nanobeam cavities coupled on either side to the breathing mode of a mechanical nanobeam resonator.