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Superconducting Electromechanical and Nanophotonic Devices for Quantum Measurement and Conversion

Mahmoud Kalaee

Published Oct 29, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.7907/3pmx-2y88

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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.
Summary form only given. The motion of a micromechanical resonator coupled simultaneously to a high-finesse optical cavity and a microwave resonator can be used to transduce the fragile quantum states generated in the realm of microwave superconducting circuits into optical photons that can transport quantum information over large distances in telecom optical fibers at room temperature. We have engineered the optical and mechanical properties of thin membranes patterned in a suspended high-stress Si3N4 film to realize such a hybrid opto-electro-mechanical system. An optical Fabry-Perot cavity with a finesse exceeding 12 000 was realized between a highly reflective photonic crystal patch realized on the suspended membrane and a conventional high-reflectivity mirror. The electromechanical coupling with a nearby planar superconducting circuit is achieved by approaching the membrane at a sub-micron distance from an on-chip interdigitated capacitor. By operating the hybrid opto-electro-mechanical system in a cryogenic environment, the photon-phonon swap rates between microwave, mechanical, and optical degrees of freedom is expected to overcome the mechanical decoherence rate. An artist view of the device envisioned is depicted on Figure 1.
The motion of a micromechanical resonator coupled simultaneously to a high-finesse optical cavity and a microwave resonator can be used to transduce the fragile quantum states generated in the realm of microwave superconducting circuits into optical photons that can transport quantum information over large distances in telecom optical fibers at room temperature. We have engineered the optical and mechanical properties of thin membranes patterned in a suspended high-stress Si3N4 film to realize such a hybrid opto-electro-mechanical system. An optical Fabry-Perot cavity with a finesse exceeding 12 000 was realized between a highly reflective photonic crystal patch realized on the suspended membrane and a conventional high-reflectivity mirror. The electromechanical coupling with a nearby planar superconducting circuit is achieved by approaching the membrane at a sub-micron distance from an on-chip interdigitated capacitor. By operating the hybrid opto-electro-mechanical system in a cryogenic environment, the photon-phonon swap rates between microwave, mechanical, and optical degrees of freedom is expected to overcome the mechanical decoherence rate.
Abstract Electrically actuated optomechanical resonators provide a route to quantum-coherent, bidirectional conversion of microwave and optical photons. Such devices could enable optical interconnection of quantum computers based on qubits operating at microwave frequencies. Here we present a platform for microwave-to-optical conversion comprising a photonic crystal cavity made of single-crystal, piezoelectric gallium phosphide integrated on pre-fabricated niobium circuits on an intrinsic silicon substrate. The devices exploit spatially extended, sideband-resolved mechanical breathing modes at ~3.2 GHz, with vacuum optomechanical coupling rates of up to g0/2π ≈ 300 kHz. The mechanical modes are driven by integrated microwave electrodes via the inverse piezoelectric effect. We estimate that the system could achieve an electromechanical coupling rate to a superconducting transmon qubit of ~200 kHz. Our work represents a decisive step towards integration of piezoelectro-optomechanical interfaces with superconducting quantum processors.
In the late 1960s and early 1970s, the development of mechanical resonators was pushed forward in efforts to record gravitational waves. In order to push down the limit of the smallest detectable force, the radiation circulating in a Fabry-Perot cavity was demonstrated to modify the damping of the cavity end-mirror suspended to act as a mechanical resonator. A few years later, motivated by the study of the internal properties of atoms and ions, the radiation pressure of light was realized as a means to cool atomic motion. In the following years, the ground-state cooling of ion motion was achieved in landmark studies. For mechanical resonators parametrically coupled to Fabry-Perot cavities, it took much longer to reach quantum ground-state cooling, both in the microwave domain, where the original experiments took place, and in the optical domain. Ground-state cooling in both regimes was reached by three groups during the preparation of this thesis and was largely due to advancements in the fabrication methods. \n \nGround-state cooling allows, in principle, the quantum nature of mechanical resonators to be probed and harnessed. Microwave domain devices, which are focused on in this thesis, have the advantage that nonlinear elements (superconducting quantum bits, qubits) are readily available. These elements enable nonclassical state preparation of the qubit and the subsequent transfer to the microwave cavity. The goal is to transfer these quantum states to mechanical resonators. This would allow mechanics to be used as a quantum mechanical memory in quantum information processing thanks to their long lifetimes. \n \nIn this thesis, various aspects of microwave domain circuit optomechanics are studied. The main goal of this thesis is to study how to enhance the coupling between a quantum regime microwave device and a mechanical resonator by using Josephson junction –based qubits. Coherent interaction between a superconducting qubit and a classical driven mechanical field is demonstrated. The analysis presented in this thesis predicts that ground-state cooling and coherent state transfer is possible in the single-phonon regime with transmon-regime qubits. Also, traditional linear optomechanical systems are considered in which the mechanical resonator is coupled to an electrical resonator. Such systems exhibit a rich spectrum of phenomena from which the quantum-limited amplification and multimode effects are considered in this thesis. It is shown that the system operates near quantum-limited amplification, which could be reached if the mechanical resonator was in the ground state.
Continued development of complementary capabilities in two quantum technologies—information processing with microwave-frequency superconducting circuits and networks based on optical-frequency photonic links—have motivated an effort to bridge the frequency gap between them with a transducer capable of preserving quantum signals. At the same time, mechanical resonators have been engineered to interact with electromagnetic waves across the spectrum in a variety of tailorable physical implementations. This thesis describes advances in a transducer using the mechanical mode of a silicon nitride membrane as an intermediary permitting coupling between a superconducting resonant LC circuit and a Fabry-Pérot optical cavity. With this choice of architecture, we have developed transducers of unparalleled efficiency and the unique capability to run continuously without appreciably degrading the performance of the superconductor from scattered optical photons. We have been able to laser-cool the mechanical mode to an occupation of less than one photon, and achieved transducer performance capable of converting a single microwave photon to optical frequencies with a signal-to-noise ratio of 1/3. Furthermore, operating the transducer does not cause appreciable heating of a superconducting transmon qubit linked to its microwave input port. With progress towards a quantum-enabled interface, we have started to develop capabilities towards implementing protocols that optically verify the quantum performance of the transducer.
Abstract Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10 GHz phonons are resonantly coupled with photons in a superconducting cavity and a nanophotonic cavity at the same time. Taking advantage of the large piezo-mechanical cooperativity (Cem ~7) and the enhanced optomechanical coupling boosted by a pulsed optical pump, we demonstrate coherent interactions at cryogenic temperatures via the observation of efficient microwave-optical photon conversion. This hybrid interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in microwave-optical photon entanglement and quantum sensing mediated by gigahertz phonons.