Quantum state preparation and tomography of entangled mechanical resonators

Ultracoherent Gigahertz Diamond Spin-Mechanical Lamb Wave Resonators

We report the development of an all-optical approach that excites the fundamental compression mode in a diamond Lamb wave resonator with an optical gradient force and detects the induced vibrations via strain coupling to a silicon vacancy center, specifically, via phonon sidebands in the optical excitation spectrum of the silicon vacancy. Sideband optical interferometry has also been used for the detection of in-plane mechanical vibrations, for which conventional optical interferometry is not effective. These experiments demonstrate a gigahertz fundamental compression mode with a Q factor of >107 at temperatures near 7 K, providing a promising platform for reaching the quantum regime of spin mechanics, especially phononic cavity quantum electrodynamics of electron spins.

Single-photon induced instabilities in a cavity electromechanical device

Cavity-electromechanical systems are extensively used for sensing and controlling the vibrations of mechanical resonators down to their quantum limit. The nonlinear radiation-pressure interaction in these systems could result in an unstable response of the mechanical resonator showing features such as frequency-combs, period-doubling bifurcations and chaos. However, due to weak light-matter interaction, typically these effects appear at very high driving strengths. By using polariton modes formed by a strongly coupled flux-tunable transmon and a microwave cavity, here we demonstrate an electromechanical device and achieve a single-photon coupling rateg 0 / 2 π of 160 kHz, which is nearly 4% of the mechanical frequency ωm. Due to large g0/ωm ratio, the device shows an unstable mechanical response resulting in frequency combs in sub-single photon limit. We systematically investigate the boundary of the unstable response and identify two important regimes governed by the optomechanical backaction and the nonlinearity of the electromagnetic mode. Such an improvement in the single-photon coupling rate and the observations of microwave frequency combs at single-photon levels may have applications in the quantum control of the motional states and critical parametric sensing. Our experiments strongly suggest the requirement of newer approaches to understand instabilities.

Digital Homodyne and Heterodyne Detection for Stationary Bosonic Modes

Homo- and heterodyne detection are fundamental techniques for measuring propagating electromagnetic fields. However, applying these techniques to stationary fields confined in cavities poses a challenge. As a way to overcome this challenge, we propose to use repeated indirect measurements of a two-level system interacting with the cavity. We demonstrate numerically that the proposed measurement scheme faithfully reproduces measurement statistics of homo- or heterodyne detection. The scheme can be implemented in various physical architectures, including circuit quantum electrodynamics. Our results pave the way for implementation of quantum algorithms requiring linear detection of stationary modes, including quantum verification protocols.

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (n ¯ ≃ 1 - 10 phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

Autonomous Stabilization of Fock States in an Oscillator against Multiphoton Losses

Fock states with a well-defined number of photons in an oscillator have shown a wide range of applications in quantum information science. Nonetheless, their usefulness has been marred by single and multiphoton losses due to unavoidable environment-induced dissipation. Though several dissipation engineering methods have been developed to counteract the leading single-photon-loss error, averting multiple-photon losses remains elusive. Here, we experimentally demonstrate a dissipation engineering method that autonomously stabilizes multiphoton Fock states against losses of multiple photons using a cascaded selective photon-addition operation in a superconducting quantum circuit. Through measuring the photon-number populations and Wigner tomography of the oscillator states, we observe a prolonged preservation of nonclassical Wigner negativities for the stabilized Fock states |N⟩ with N=1, 2, 3 for a duration of about 10 ms. Furthermore, the dissipation engineering method demonstrated here also facilitates the implementation of a nonunitary operation for resetting a binomially encoded logical qubit. These results highlight potential applications in error-correctable quantum information processing against multiple-photon-loss errors.

Monolithic Strong Coupling of Topological Surface Acoustic Wave Resonators on Lithium Niobate

Coherent phonon transfer via high-quality factor (Q) mechanical resonator strong coupling has garnered significant interest. Yet, the practical applications of these strongly coupled resonator devices are largely constrained by their vulnerability to fabrication defects. In this study, topological strong coupling of gigahertz frequency surface acoustic wave (SAW) resonators with lithium niobate is achieved. The nanoscale grooves are etched onto the lithium niobate surface to establish robust SAW topological interface states (TISs). By constructing phononic crystal (PnC) heterostructures, a strong coupling of two SAW TISs, achieving a maximum Rabi splitting of 22 MHz and frequency quality factor product fQm of ≈1.2 × 1013 Hz, is realized. This coupling can be tuned by adjusting geometric parameters and a distinct spectral anticrossing is experimentally observed. Furthermore, a dense wavelength division multiplexing device based on the coupling of multiple TISs is demonstrated. These findings open new avenues for the development of practical topological acoustic devices for on-chip sensing, filtering, phonon entanglement, and beyond.

Surface modification and coherence in lithium niobate SAW resonators

Lithium niobate is a promising material for developing quantum acoustic technologies due to its strong piezoelectric effect and availability in the form of crystalline thin films of high quality. However, at radio frequencies and cryogenic temperatures, these resonators are limited by the presence of decoherence and dephasing due to two-level systems. To mitigate these losses and increase device performance, a more detailed picture of the microscopic nature of these loss channels is needed. In this study, we fabricate several lithium niobate acoustic wave resonators and apply different processing steps that modify their surfaces. These treatments include argon ion sputtering, annealing, and acid cleans. We characterize the effects of these treatments using three surface-sensitive measurements: cryogenic microwave spectroscopy measuring density and coupling of TLS to mechanics, X-ray photoelectron spectroscopy and atomic force microscopy. We learn from these studies that, surprisingly, increases of TLS density may accompany apparent improvements in the surface quality as probed by the latter two approaches. Our work outlines the importance that surfaces and fabrication techniques play in altering acoustic resonator coherence, and suggests gaps in our understanding as well as approaches to address them.

Engineering multimode interactions in circuit quantum acoustodynamics

In recent years, important progress has been made towards encoding and processing quantum information in the large Hilbert space of bosonic modes. Mechanical resonators have several practical advantages for this purpose, because they confine many high-quality-factor modes into a small volume and can be easily integrated with different quantum systems. However, it is challenging to create direct interactions between different mechanical modes that can be used to emulate quantum gates. Here we demonstrate an in situ tunable beamsplitter-type interaction between several mechanical modes of a high-overtone bulk acoustic-wave resonator. The engineered interaction is mediated by a parametrically driven superconducting transmon qubit, and we show that it can be tailored to couple pairs or triplets of phononic modes. Furthermore, we use this interaction to demonstrate the Hong-Ou-Mandel effect between phonons. Our results lay the foundations for using phononic systems as quantum memories and platforms for quantum simulations.

Locating sources of Szegedy's quantum network

Source location in quantum networks is a critical area of research with profound implications for cutting-edge fields such as quantum state tomography, quantum computing, and quantum communication. In this study, we present groundbreaking research on the technique and theory of source location in Szegedy's quantum networks. We develop a linear system evolution model for a Szegedy's quantum network system using matrix vectorization techniques. Subsequently, we propose a highly precise and robust source-location algorithm based on compressed sensing specifically tailored for Szegedy's quantum network. To validate the effectiveness and feasibility of our algorithm, we conduct numerical simulations on various model and real networks, yielding compelling results. These findings underscore the potential of our approach in practical applications.

Realistic prediction and engineering of high-Q modes to implement stable Fano resonances in acoustic devices

Quasi-bound states in the continuum (QBICs) coupling into the propagating spectrum manifest themselves as high-quality factor (Q) modes susceptible to perturbations. This poses a challenge in predicting stable Fano resonances for realistic applications. Besides, where and when the maximum field enhancement occurs in real acoustic devices remains elusive. In this work, we theoretically predict and experimentally demonstrate the existence of a Friedrich-Wintgen BIC in an open acoustic cavity. We provide direct evidence for a QBIC by mapping the pressure field inside the cavity using a Laser Doppler Vibrometer (LDV), which provides the missing field enhancement data. Furthermore, we design a symmetry-reduced BIC and achieve field enhancement by a factor of about three compared to the original cavity. LDV measurements are a promising technique for obtaining high-Q modes' missing field enhancement data. The presented results facilitate the future applications of BICs in acoustics as high-intensity sound sources, filters, and sensors.

Instabilities near Ultrastrong Coupling in a Microwave Optomechanical Cavity

With artificially engineered systems, it is now possible to realize the coherent interaction rate, which can become comparable to the mode frequencies, a regime known as ultrastrong coupling (USC). We experimentally realize a cavity-electromechanical device using a superconducting waveguide cavity and a mechanical resonator. In the presence of a strong pump, the mechanical-polaritons splitting can nearly reach 81% of the mechanical frequency, overwhelming all the dissipation rates. Approaching the USC limit, the steady-state response becomes unstable. We systematically measure the boundary of the unstable response while varying the pump parameters. The unstable dynamics display rich phases, such as self-induced oscillations, period-doubling bifurcation, and period-tripling oscillations, ultimately leading to the chaotic behavior. The experimental results and their theoretical modeling suggest the importance of residual nonlinear interaction terms in the weak-dissipative regime.

Phononic bath engineering of a superconducting qubit

Phonons, the ubiquitous quanta of vibrational energy, play a vital role in the performance of quantum technologies. Conversely, unintended coupling to phonons degrades qubit performance and can lead to correlated errors in superconducting qubit systems. Regardless of whether phonons play an enabling or deleterious role, they do not typically admit control over their spectral properties, nor the possibility of engineering their dissipation to be used as a resource. Here we show that coupling a superconducting qubit to a bath of piezoelectric surface acoustic wave phonons enables a novel platform for investigating open quantum systems. By shaping the loss spectrum of the qubit via the bath of lossy surface phonons, we demonstrate preparation and dynamical stabilization of superposition states through the combined effects of drive and dissipation. These experiments highlight the versatility of engineered phononic dissipation and advance the understanding of mechanical losses in superconducting qubit systems.

Splitting phonons: Building a platform for linear mechanical quantum computing

Linear optical quantum computing provides a desirable approach to quantum computing, with only a short list of required computational elements. The similarity between photons and phonons points to the interesting potential for linear mechanical quantum computing using phonons in place of photons. Although single-phonon sources and detectors have been demonstrated, a phononic beam splitter element remains an outstanding requirement. Here we demonstrate such an element, using two superconducting qubits to fully characterize a beam splitter with single phonons. We further use the beam splitter to demonstrate two-phonon interference, a requirement for two-qubit gates in linear computing. This advances a new solid-state system for implementing linear quantum computing, further providing straightforward conversion between itinerant phonons and superconducting qubits.

Nonlinear Sideband Cooling to a Cat State of Motion

The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.

Macroscopic Quantum Test with Bulk Acoustic Wave Resonators

Recently, solid-state mechanical resonators have become a platform for demonstrating nonclassical behavior of systems involving a truly macroscopic number of particles. Here, we perform the most macroscopic quantum test in a mechanical resonator to date, which probes the validity of quantum mechanics by ruling out a classical description at the microgram mass scale. This is done by a direct measurement of the Wigner function of a high-overtone bulk acoustic wave resonator mode, monitoring the gradual decay of negativities over tens of microseconds. While the obtained macroscopicity of μ=11.3 is on par with state-of-the-art atom interferometers, future improvements of mode geometry and coherence times could test the quantum superposition principle at unprecedented scales and also place more stringent bounds on spontaneous collapse models.

Single-Spin Readout and Quantum Sensing Using Optomechanically Induced Transparency

Solid-state spin defects are promising quantum sensors for a large variety of sensing targets. Some of these defects couple appreciably to strain in the host material. We propose to use this strain coupling for mechanically mediated dispersive single-shot spin readout by an optomechanically induced transparency measurement. Surprisingly, the estimated measurement times for negatively charged silicon-vacancy defects in diamond are an order of magnitude shorter than those for single-shot optical fluorescence readout. Our scheme can also be used for general parameter-estimation metrology and offers a higher sensitivity than conventional schemes using continuous position detection.

Shaped Microwave Field in a Three-Level Closed Loop Dense Atomic System

In this work, we investigate the atomic properties of a three-level system under the effect of a shaped microwave field. The system is simultaneously driven by a powerful laser pulse and a weak constant probe that drives the ground state to an upper level. Meanwhile, an external microwave field drives the upper state to the middle transition with shaped waveforms. Hence, two situations are considered: one in which the atomic system is controlled by a strong laser pump and a classical constant microwave field, and another in which both the microwave and pump laser fields are shaped. Finally, for sake of comparison, we investigate the tanh-hyperbolic, the Gaussian and the power of the exponential microwave form in the system. Our results reveal that shaping the external microwave field has a significant impact on the absorption and dispersion coefficient dynamics. In comparison with the classical scenario, where usually the strong pump laser is considered to have a major role in controlling the absorption spectrum, we show that shaping the microwave field leads to distinct results.

Determination of Multimode Motional Quantum States in a Trapped Ion System

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.