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Liu Qiu

Publications and source records attributed to Liu Qiu.

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Electro-optic conversion of itinerant Fock states

Superconducting qubits are a leading candidate for utility-scale quantum computing due to their fast gate speeds and steadily decreasing error rates. The requirement for millikelvin operating temperatures, however, creates a significant scaling bottleneck. Modular architectures using optical fiber links could bridge separate cryogenic nodes, but superconducting circuits do not have coherent optical transitions and microwave-to-optical conversion has not been shown for any non-classical photon state. In this work, we demonstrate the on-demand generation and tomographic reconstruction of itinerant single microwave photons at 8.9 GHz from a superconducting qubit. We upconvert this non-Gaussian state with a transducer added noise below 0.012 quanta and count the converted telecom photons at 193.4 THz with a signal-to-noise ratio of up to 5.1$\pm$1.1. We characterize the trade-offs between throughput and noise, and establish a viable path toward heralded entanglement distribution and gate teleportation. Looking ahead, these results empower existing superconducting devices to take a key role in distributed quantum technologies and heterogeneous quantum systems.

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All-optical single-shot readout of a superconducting qubit

The rapid development of superconducting quantum hardware is expected to run into significant I/O restrictions due to the need for large-scale error correction in a cryogenic environment. Classical data centers rely on fiber-optic interconnects to remove similar networking bottlenecks and to allow for reconfigurable, software-defined infrastructures. In the same spirit, ultra-cold electro-optic links have been proposed and used to generate qubit control signals, or to replace cryogenic readout electronics. So far, the latter suffered from either low efficiency, low bandwidth and the need for additional microwave drives, or breaking of Cooper pairs and qubit states. In this work we realize electro-optic microwave photonics at millikelvin temperatures to implement a radio-over-fiber qubit readout that does not require any active or passive cryogenic microwave equipment. We demonstrate all-optical single-shot-readout by means of the Jaynes-Cummings nonlinearity in a circulator-free readout scheme. Importantly, we do not observe any direct radiation impact on the qubit state as verified with high-fidelity quantum-non-demolition measurements despite the absence of shielding elements. This compatibility between superconducting circuits and telecom wavelength light is not only a prerequisite to establish modular quantum networks, it is also relevant for multiplexed readout of superconducting photon detectors and classical superconducting logic. Moreover, this experiment showcases the potential of electro-optic radiometry in harsh environments - an electronics-free sensing principle that extends into the THz regime with applications in radio astronomy, planetary missions and earth observation.

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Entangling microwaves with optical light

Entanglement is a genuine quantum mechanical property and the key resource in currently developed quantum technologies. Sharing this fragile property between superconducting microwave circuits and optical or atomic systems would enable new functionalities but has been hindered by the tremendous energy mismatch of $\sim10^5$ and the resulting mutually imposed loss and noise. In this work we create and verify entanglement between microwave and optical fields in a millikelvin environment. Using an optically pulsed superconducting electro-optical device, we deterministically prepare an itinerant microwave-optical state that is squeezed by $0.72^{+0.31}_{-0.25}$\,dB and violates the Duan-Simon separability criterion by $>5$ standard deviations. This establishes the long-sought non-classical correlations between superconducting circuits and telecom wavelength light with wide-ranging implications for hybrid quantum networks in the context of modularization, scaling, sensing and cross-platform verification.

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Coherent optical control of a superconducting microwave cavity via electro-optical dynamical back-action

Recent quantum technologies have established precise quantum control of various microscopic systems using electromagnetic waves. Interfaces based on cryogenic cavity electro-optic systems are particularly promising, due to the direct interaction between microwave and optical fields in the quantum regime. Quantum optical control of superconducting microwave circuits has been precluded so far due to the weak electro-optical coupling as well as quasi-particles induced by the pump laser. Here we report the coherent control of a superconducting microwave cavity using laser pulses in a multimode electro-optical device at millikelvin temperature with near-unity cooperativity. Both the stationary and instantaneous responses of the microwave and optical modes comply with the coherent electro-optical interaction, and reveal only minuscule amount of excess back-action with an unanticipated time delay. Our demonstration enables wide ranges of applications beyond quantum transductions, from squeezing and quantum non-demolition measurements of microwave fields, to entanglement generation and hybrid quantum networks.

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Microwave-optics Entanglement via Cavity Optomagnomechanics

Microwave-optics entanglement is a vital component for building hybrid quantum networks. Here, a new mechanism for preparing stationary entanglement between microwave and optical cavity fields in a cavity optomagnomechanical system is proposed. It consists of a magnon mode in a ferrimagnetic crystal that couples directly to a microwave cavity mode via the magnetic dipole interaction, and indirectly to an optical cavity through the deformation displacement of the crystal. The mechanical displacement is induced by the magnetostrictive force and coupled to the optical cavity via radiation pressure. Both the opto- and magnomechanical couplings are dispersive. Magnon-phonon entanglement is created via magnomechanical parametric down-conversion, which is further distributed to optical and microwave photons via simultaneous optomechanical beamsplitter interaction and electromagnonic state-swap interaction, yielding stationary microwave-optics entanglement. The microwave-optics entanglement is robust against thermal noise, which will find broad potential applications in quantum networks and quantum information processing with hybrid quantum systems.

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Dissipative Quantum Feedback in Measurements Using a Parametrically Coupled Microcavity

Micro- and nanoscale optical or microwave cavities are used in a wide range of classical applications and quantum science experiments, ranging from precision measurements, laser technologies to quantum control of mechanical motion. The dissipative photon loss via absorption, present to some extent in any optical cavity, is known to introduce thermo-optical effects and thereby impose fundamental limits on precision measurements. Here, we theoretically and experimentally reveal that such dissipative photon absorption can result in quantum feedback via in-loop field detection of the absorbed optical field, leading to the intracavity field fluctuations to be squashed or antisquashed. Strikingly, this modifies the optical cavity susceptibility in coherent response measurements and causes excess noise and correlations in incoherent interferometric optomechanical measurements using a cavity. We experimentally observe such unanticipated dissipative dynamics in optomechanical spectroscopy of sideband-cooled optomechanical crystal cavitiess at both cryogenic temperature (approximately 8 K) and ambient conditions. The dissipative feedback introduces effective modifications to the optical cavity linewidth and the optomechanical scattering rate and gives rise to excess imprecision noise in the interferometric quantum measurement of mechanical motion. Such dissipative feedback differs fundamentally from a quantum nondemolition feedback, e.g., optical Kerr squeezing. The dissipative feedback itself always results in an antisqueezed out-of-loop optical field, while it can enhance the coexisting Kerr squeezing under certain conditions. Our result has wide-ranging implications for future dissipation engineering, such as dissipation enhanced sideband cooling and Kerr squeezing, quantum frequency conversion, and nonreciprocity in photonic systems.

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Quantum-enabled interface between microwave and telecom light

Photons at telecom wavelength are the ideal choice for high density interconnects while solid state qubits in the microwave domain offer strong interactions for fast quantum logic. Here we present a general purpose, quantum-enabled interface between itinerant microwave and optical light. We use a pulsed electro-optic transducer at millikelvin temperatures to demonstrate nanosecond timescale control of the converted complex mode amplitude with an input added noise of $N^{oe}_\textrm{in} = 0.16^{+0.02}_{-0.01}$ ($N^{eo}_\textrm{in} = 1.11^{+0.15}_{-0.07}$) quanta for the microwave-to-optics (reverse) direction. Operating with up to unity cooperativity, this work enters the regime of strong coupling cavity quantum electro-optics characterized by unity internal efficiency and nonlinear effects such as the observed laser cooling of a superconducting cavity mode. The high quantum cooperativity of $C_q>10$ forms the basis for deterministic entanglement generation between superconducting circuits and light.

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Cryogenic electro-optic interconnect for superconducting devices

Encoding information onto optical fields is the backbone of modern telecommunication networks. Optical fibers offer low loss transport and vast bandwidth compared to electrical cables, and are currently also replacing coaxial cables for short-range communications. Optical fibers also exhibit significantly lower thermal conductivity, making optical interconnects attractive for interfacing with superconducting circuits and devices. Yet little is known about modulation at cryogenic temperatures. Here we demonstrate a proof-of-principle experiment, showing that currently employed Ti-doped LiNbO modulators maintain the Pockels coefficient at 3K---a base temperature for classical microwave amplifier circuitry. We realize electro-optical read-out of a superconducting electromechanical circuit to perform both coherent spectroscopy, measuring optomechanically-induced transparency, and incoherent thermometry, encoding the thermomechanical sidebands in an optical signal. Although the achieved noise figures are high, approaches that match the lower-bandwidth microwave signals, use integrated devices or materials with higher EO coefficient, should achieve added noise similar to current HEMT amplifiers, providing a route to parallel readout for emerging quantum or classical computing platforms.

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Optomechanical generation of a mechanical catlike state by phonon subtraction

We propose a scheme to prepare a macroscopic mechanical oscillator in a catlike state, close to a coherent state superposition. The mechanical oscillator, coupled by radiation-pressure interaction to a field in an optical cavity, is first prepared close to a squeezed vacuum state using a reservoir engineering technique. The system is then probed using a short optical pulse tuned to the lower motional sideband of the cavity resonance, realizing a photon-phonon swap interaction. A photon number measurement of the photons emerging from the cavity then conditions a phonon-subtracted catlike state with a negative Wigner distribution exhibiting separated peaks and multiple interference fringes. We show that this scheme is feasible using state-of-the-art photonic crystal optomechanical system.

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Laser cooling of a nanomechanical oscillator to the zero-point energy

Optomechanical cavities in the well-resolved-sideband regime are ideally suited for the study of a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and generation of non-classical states. For these experiments, the mechanical oscillator should be prepared in its ground state; residual motion beyond the zero-point motion must be negligible. The requisite cooling of the mechanical motion can be achieved using the radiation pressure of light in the cavity by selectively driving the anti-Stokes optomechanical transition. To date, however, laser-absorption heating of optical systems far into the resolved-sideband regime has prohibited strong driving. For deep ground-state cooling, previous studies have therefore resorted to passive cooling in dilution refrigerators. Here, we employ a highly sideband-resolved silicon optomechanical crystal in a $^3$He buffer gas environment at $\sim 2\text{K}$ to demonstrate laser sideband cooling to a mean thermal occupancy of $0.09_{-0.01}^{+0.02}$ quantum (self-calibrated using motional sideband asymmetry), which is $-7.4\text{dB}$ of the oscillator's zero-point energy and corresponds to 92% ground state probability. Achieving such low occupancy by laser cooling opens the door to a wide range of quantum-optomechanical experiments in the optical domain.

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Two-Tone Optomechanical Instability and Its Fundamental Implications for Backaction-Evading Measurements

While quantum mechanics imposes a fundamental limit on the precision of interferometric measurements of mechanical motion due to measurement backaction, the nonlinear nature of the coupling also leads to parametric instabilities that place practical limits on the sensitivity by limiting the power in the interferometer. Such instabilities have been extensively studied in the context of gravitational wave detectors, and their presence has recently been reported in Advanced LIGO. Here, we observe experimentally and describe theoretically a new type of optomechanical instability that arises in two-tone backaction-evading (BAE) measurements, designed to overcome the standard quantum limit, and demonstrate the effect in the optical domain with a photonic crystal nanobeam, and in the microwave domain with a micromechanical oscillator coupled to a microwave resonator. In contrast to the well-known oscillatory parametric instability that occurs in single-tone, blue-detuned pumping, which is characterized by a vanishing effective mechanical damping, the parametric instability in balanced two-tone optomechanics is exponential, and is a result of small detuning errors in the two pump frequencies. Its origin can be understood in a rotating frame as the vanishing of the effective mechanical frequency due to an optical spring effect. Counterintuitively, the instability occurs even in the presence of perfectly balanced intracavity fields, and can occur for both signs of detuning. We find excellent quantitative agreement with our theoretical predictions. Since the constraints on tuning accuracy become stricter with increasing probe power, it imposes a fundamental limitation on BAE measurements, as well as other two-tone schemes. In addition to introducing a new limitation in two-tone BAE measurements, the results also introduce a new type of nonlinear dynamics in cavity optomechanics.

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Floquet dynamics in quantum measurement of mechanical motion

The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: from sideband cooling and backaction-evading measurements to pondermotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case, Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiqitious in optomechanical systems. Specifically, employing multiple probe tones, we perform sideband asymmetry measurements, a macroscopic quantum effect, on a silicon optomechanical crystal sideband-cooled to 40% ground-state occupation. We show that the Floquet dynamics, resulting from the presence of multiple pump tones, gives rise to an artificially modified motional sideband asymmetry by redistributing thermal and quantum fluctuations among the initially independently scattered thermomechanical sidebands. For pump tones exhibiting large frequency separation, the dynamics is suppressed and accurate quantum noise thermometry demonstrated. We develop a theoretical model based on Floquet theory that accurately describes our observations. The resulting dynamics can be understood as resulting from a synthetic gauge field among the Fourier modes, which is created by the phase lag of the Kerr-type response. This novel phenomenon has wide-ranging implications for schemes utilizing several pumping tones, as commonly employed in backaction-evading measurements, dissipative optical squeezing, dissipative mechanical squeezing and quantum noise thermometry. Our observation may equally well be used for optomechanical Floquet engineering, e.g. generation of topological phases of sound by periodic time-modulation.

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Optical Backaction-Evading Measurement of a Mechanical Oscillator

Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, as a result of quantum backaction arising from quantum fluctuations in the measurement field. A variety of techniques to surpass this standard quantum limit have been proposed, such as variational measurements, stroboscopic quantum non-demolition and two tone backaction-evading (BAE) measurements. The latter proceed by monitoring only one of the two non-commuting quadratures of the motion. This technique, originally proposed in the context of gravitational wave detection, has not been implemented using optical interferometers to date. Here we demonstrate continuous two-tone backaction-evading measurement in the optical domain of a localized GHz frequency mechanical mode of a photonic crystal nanobeam cryogenically and optomechanically cooled in a $^3$He buffer gas cryostat close to the ground state. Employing quantum-limited optical heterodyne detection, we explicitly show the transition from conventional to backaction-evading measurement. We observe up to 0.67 dB (14%) reduction of total measurement noise, thereby demonstrating the viability of BAE measurements for optical ultrasensitive measurements of motion and force in nanomechanical resonators.

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