The coupling of electromagnetic fields to nanomechanical systems has ushered in the field of $q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}m$ $o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}s$, in which vibrating objects can be studied and used at the level of their quantum zero-point motion. The authors fabricate a planar technology platform for integrating nanophotonic, nanomechanical, and superconducting microwave circuits. Joining these components could yield a quantum converter between the microwave and optical frequency domains, enabling long-range networks of superconducting qubits for quantum information processing.
The coupling of electromagnetic fields to nanomechanical systems has ushered in the field of q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}mo\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}s, in which vibrating objects can be studied and used at the level of their quantum zero-point motion. The authors fabricate a planar technology platform for integrating nanophotonic, nanomechanical, and superconducting microwave circuits. Joining these components could yield a quantum converter between the microwave and optical frequency domains, enabling long-range networks of superconducting qubits for quantum information processing.
I will present recent work at Caltech on the integration of optomechanical crystals for light and sound with electronic superconducting quantum circuits. Utilizing the silicon-on-insulator (SOI) wafer platform, we have made key advances in the fabrication and integration of extremely low loss microwave phonon structures and low loss microwave superconducting resonators of high impedance. These technical advancements offer several intriguing opportunities for quantum information processing and networking with phonons, photons, and electrons in an integrated, wafer-scale platform. The focus of my talk will be on two examples of our efforts in this direction: (i) nonreciprocal photon transport and amplification arising from synthetic magnetic flux and reservoir engineering in an optomechanical crystal circuit, and (ii) waveguide-QED systems consisting of microwave-bandgap circuits with embedded transmon-like qubits.
Microscale and nanoscale mechanical resonators have been used in advanced technological applications, from high precision time keeping and mass sensing, to processing high frequency signals in mobile communications. In the last few decades, they have been an important part of progress in the field of quantum information and metrology and have been proposed as quantum memories or transducers for measuring or connecting different types of quantum systems. The field of cavity optomechanics and electromechanics is concerned with coupling the electromagnetic field of a resonant optical cavity or electrical circuit to mechanical motion. These systems provide potential means to control and engineer the state of a mechanical object at the quantum level. This thesis contains the description of mechanical systems in megahertz to a few hundred megahertz frequency range formed by nano-fabricating photonic, phononic, and electrical circuits on a chip. These structures are designed to provide a large radiation pressure coupling between mechanical motion and electromagnetic fields to address and manipulate motional degrees of freedom. Qualitatively novel quantum effects are expected when one takes a step beyond linear coupling and exploits higher order interactions. To that end, we integrate electrical, mechanical and photonic structures in a multimode photonic crystal structure to observe "x2-coupling", where the optical cavity frequency is coupled to the square of the mechanical displacement. Moreover, we have developed two integrated on-chip platforms based on Si3N4 and Si nanomembranes capable of interfacing superconducting qubits and optical photons and realizing reversible microwave-to-optical conversion. We employ radiation pressure to cool these mechanical resonators to their quantum ground state. Finally, we demonstrate a form of electromechanical crystal for coupling microwave photons and hypersonic phonons of frequency ωm/2π = 0.425 GHz by capacitively coupling a phononic crystal acoustic cavity to a superconducting microwave resonator. Moving to higher frequency acoustic cavities not only facilitates the integration of electromechanical circuits and nanophotonic systems capable of operation in the resolved sideband limit of optomechanics for noise-free quantum signal conversion, but it opens up the possibility of using phonons as information carriers via phononic circuits. Utilizing a two-photon resonance condition for efficient microwave pumping and phononic bandgap shield to eliminate acoustic radiation, we achieve large cooperative electromechanical coupling (C ≈ 30) and intrinsic decay time of 2.3 ms. Moreover, electrical read-out of the phonon occupancy shows that the acoustic mode thermalizes close to its quantum ground-state of motion (phonon occupancy nm=1.5) at a fridge temperature of Tf = 10 mK. We conclude by considering several designs and fabrication improvements to the hypersonic electromechanical crystals that would enable them to perform quantum conversion between the electrical and acoustic domain.
Quantum computing is one of the great scientific challenges of the 21st century. Small-scale systems today promise to surpass classical computers in the coming years and to enable the solution of classically intractable computational tasks in the fields of quantum chemistry, optimization, cryptography and more. In contrast to classical computers, quantum computers based on superconducting quantum bits (qubits) can to date not be linked over long distance in a network to improve their computing capacity, since devices, which preserve the quantumstate when it is transferred from one machine to another, are not available. Several approaches are being pursued to realize such a component, one of themost promising to date makes use of an intermediary, micromechanical element that enables quantum coherent conversion between the information present in the quantum computer and an optical fiber, without compromising the quantum nature of the information, via optomechanical interaction. This approach could allow fiber-optic quantum networks between separate quantum computers based on superconducting qubits in the future. In this work a platformfor such a microwave-to-optic link was developed based on the piezoelectric material gallium phosphide. This III-V semiconductor offers not only a piezoelectric coupling between the electric field of a microwave circuit and a mechanicalmode, but also a wide optical bandgap E_g = 2.26eV which reduces nonlinear optical absorption in the device and a large refractive index n(1550nm) = 3.01 which allows strong optical confinement at near-infrared wavelengths. Importantly and in contrast to other approaches with gallium phosphide, an epitaxially grown, single crystal thin film of the material is integrated directly on a silicon wafer with pre-structured niobium electrodes by direct wafer-bonding. This opens up the possibility of integrating the device design presented here directly with superconducting qubits fabricated with this material system. A microwave-to-optical transducer design was simulated and fabricated in the galliumphosphideon- silicon platform. The device was found to exhibit large vacuum optomechanical coupling rates g0/2 pi ~ 290kHz and a high intrinsic optical quality factor Q >10^5 while at the same time permitting electromechanical coupling to a microwave electrode. Coherent microwave-tooptical transductionwas shown at room temperature for this device and the electromechanical coupling rate could be extracted from a model derived by input-output theory. The electromechanical coupling between the electro-optomechanical device and a superconducting qubit was estimated to be g/2 pi = O(200kHz) which indicates that strong coupling between the here presented device and a superconducting transmon qubit is achievable. In addition, superconducting microwave cavities with high quality factor at single photon energy Q ~ 5x10^5 were fabricated and measured to verify that fabrication process of the microwave-to-optical transducer is compatible with high-quality superconducting microwave circuits.
Superconducting circuits are important technological tools that have found various applications, notably hypothetical future superconducting quantum computers. Scaling such systems further is, however, proving challenging because of thermal heat load and space constraints in cryostats. One way of improving the scalability of such systems would be to resort to optical fibers for controlling the circuits in cryostats, as well as mediating long-distance interaction between them while preserving quantum coherence. Such a strategy relies on building a coherent interface between GHz frequencies and optical frequencies. This interface, referred to as "microwave-optical transducer", would need to exhibit high photon conversion efficiencies and very low added noise, ideally less than a quantum, in a cryogenic environment. Since the prospects of weaving networks of optically connected superconducting quantum processors have now attracted the attention of the scientific community for more than a decade, very efficient transducers have already been proposed and realized. However, despite their impressive performances against selected metrics, often equivalent to optimizing the on-chip conversion efficiency alone, none of the approaches pursued so far really solved the qubit interconnection problems in ways that could be applied to large-scale systems in the near future. The aim of this thesis was to develop transduction approaches that would ultimately enable optical driving of superconducting circuits and quantum state transfer between microwave and optical frequencies, while at the same time ensuring good scalability, both in terms of wafer manufacturability and integration in cryogenic environments. Integrated photonic circuits based on silicon nitride appeared as a promising platform, as silicon nitride is a CMOS-certified material, has a transparency window compatible with optical fibers and lacks two photon absorption. Realizing the coupling between microwave and optical frequencies in a way similar to what is done in optomechanics is desirable, because the field of optomechanics has seen the establishement of techniques that enable control of the low frequency degree of freedom at the quantum mechanical level, including ground state cooling, control of the susceptibility by dynamical backaction, quantum state transfer and entanglement. The heterogeneous integration of nonlinear crystalline thin films, such as lithium niobate and lithium tantalate, onto silicon nitride photonic circuitry endows it with an electro-optic activity that emulates the optomechanical interaction, while offering an inherent access to the microwave degree of freedom. However, material nonlinearities, including photorefraction, charge screening, and hysteresis, introduce complications that motivate exploring alternative approaches. Here, alongside an electro-optic implementation, a transducer that leverages the interaction of bulk acoustic resonances excited by micro-electromechanical systems with whispering-gallery-like modes of microresonators is presented. Coherent transduction between microwave and optical fields is demonstrated, and optomechanical dynamical backaction is observed. The transducers fast bandwidth, compatibility with multiplexing and ability to down-convert microwaves suggest interesting prospects, particularly upon further improvements of the optomechanical coupling.
Superconducting qubits, realized by incorporating Josephson junctions into superconducting circuits, behave as artificial atoms with anharmonic energy spectra and can be precisely controlled and measured using microwave cavities within the framework of circuit quantum electrodynamics (cQED). Since its emergence in the early 2000s, cQED has established superconducting qubits as leading candidates for scalable quantum devices and has enabled the exploration of hybrid quantum systems that integrate disparate physical platformsThis review surveys superconducting hybrid quantum electromechanical systems in which mechanical resonators are coupled to superconducting qubits, with a focus on two widely used qubit platforms: the transmon and the fluxonium. We provide an overview of the underlying coupling mechanisms arising from interactions through the phase and charge degrees of freedom of the qubit, and discuss how these mechanisms give rise to both longitudinal and transverse qubit-mechanical interactions. We further review extensions of electromechanical platforms to electro-optomechanical architectures, in which optical cavities are integrated to enable coherent interfacing between superconducting circuits and optical photons. This review aims to present a unified framework and perspective on qubit-mechanical and qubit-mechanical-optical hybrid systems in superconducting quantum technologies and applications related to sensors.
Due to its high coherence in transmission over a large distance in the ambient environment, the quantum optical system has been a prevailing platform for long-distance quantum communication, which was recently realized over a continental distance with a low earth orbit satellite and ground stations [102, 70]. However, the pure quantum optical system has so far shown weak interactions between photon and matter, which makes it inefficient in carrying out deterministic quantum gates for quantum repeater based scalable quantum network and quantum computing. On the other hand, superconducting quantum systems operating in the microwave domain with Josephson junction transmon qubits have proven to be capable of efficient deterministic quantum operations on quantum states [86, 87, 66]. Nevertheless, such architecture is prone to errors and decoherence due to cross-talk between microwave elements in a large-scale superconducting quantum circuit. Furthermore, superconducting systems, in general, also have large footprint (100s um) elements (resonators and superconducting quantum bits) [92, 60] that limit the ability to scale up a superconducting quantum system. Moreover, microwave quantum circuits require cooling to around 10 mK, making it unsuitable for communicating quantum information outside a dilution refrigerator (DF). Micro- and nano- acoustic elements have been extensively used in conventional integrated information processing systems due to their compactness and high coherence [97]. Acoustic systems in quantum engineering also have the advantage of being a platform for universal couplings between various quantum systems including spins, optical photons, and superconducting circuits. As it will be discussed in this thesis, elements critical to scalable optical quantum network and superconducting quantum circuit can be constructed relying on the cavity optomechanics and piezoelectric interactions. Optomechanical interaction is concerned with the light pressure coupling of cavity mechanical deformation to a strong optical field. This interaction has allowed the close to mechanical ground state cooling of mechanical resonators using laser and the ultra-sensitive displacement measurement that led to the detection of gravitational waves in the LIGO collaboration [125, 25]. Optomechanical crystals (OMCs) are lithographically patterned devices which contain a periodic structure that host bandgaps for both optical band electromagnetic waves and microwave band acoustic waves. A properly engineered defect in the crystal can confine and localize acoustic and electromagnetic modes of similar wavelengths into a small mode volume [17, 20, 21]. A strong optomechanical coupling, which can be achieved between such strongly confined co-localized optical and acoustic modes, can be used in engineering the quantum state of mechanical motion to realize useful quantum devices such as a high-coherence quantum memory [74] and an optomechanical high efficiency optical isolator for unidirectionally connecting distant optical cavities via an acoustic bus [37]. To strongly couple the mechanical degree of freedom with a superconducting quantum circuit, various methods can be used, ranging from electromechanic coupling (electric coupling to a mechanically compliant capacitor), magnetomechanical coupling (magnetic coupling to a vibrating SQUID loop), and piezoelectric coupling. The recent advent of quantum acoustics [23, 8, 9] was realized with the strong piezoelectric coupling between a superconducting transmon qubit and a high-coherence mechanical resonator. The engineered strong piezoacoustic coupling provides the possibility to carry out deterministic ultra-high fidelity two-qubit quantum gates on non-classical mechanical quantum states [52]. This ability together with the recent demonstration of ultra-long phonon lifetime mechanical resonators show the possibility of integrating the ultra-high quality mechanical resonator as a compact quantum memory element and even a new ultra-compact (10s um) quantum bit architecture for scalable superconducting quantum circuits. Furthermore, the strong piezoelectric coupling that can transduce quantum state in a superconducting circuit into mechanical wave also makes it possible to efficiently transduce a quantum state between a superconducting quantum circuit and a telecommunication band optical channel via a mechanical waveguide connected to an optomechanical crystal cavity.