These notes discuss electromechanical devices in the quantum regime, a topic closely related to cavity optomechanics. Both cavity optomechanics and quantum electromechanics have their roots in gravitational-wave detection. As such, most of their applications are associated with ultrasensitive sensing. In contrast, these notes deal with an emerging application of quantum electromechanics: signal processing. Such applications are a natural consequence of shrinking the mechanical elements from the metre-scale resonators used in gravitational wave detectors to the micron scale, where quantum effects are more evident. Indeed, MEMS are a crucial technology for classical information processing and modern wireless communication. The advent of quantum information processing, particularly with superconducting circuits, means that there is now a need for analogue signal processing functions operating at microwave frequencies and in the quantum regime. Electromechanical devices have now entered this regime as they can store, amplify, squeeze, entangle, temporally shape, and frequency convert microwave signals.
These notes discuss electromechanical devices in the quantum regime, a topic closely related to cavity optomechanics. Both cavity optomechanics and quantum electromechanics have their roots in gravitational-wave detection. As such, most of their applications are associated with ultrasensitive sensing. In contrast, these notes deal with an emerging application of quantum electromechanics: signal processing. Such applications are a natural consequence of shrinking the mechanical elements from the metre-scale resonators used in gravitational wave detectors to the micron scale, where quantum effects are more evident. Indeed, MEMS are a crucial technology for classical information processing and modern wireless communication. The advent of quantum information processing, particularly with superconducting circuits, means that there is now a need for analogue signal processing functions operating at microwave frequencies and in the quantum regime. Electromechanical devices have now entered this regime as they can store, amplify, squeeze, entangle, temporally shape, and frequency convert microwave signals.
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.
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.
Harmonic oscillators might be one of the most fundamental entities described by physics. Yet they stay relevant in recent research. The topological properties associated with exceptional points that can occur when two modes interact have generated much interest in recent years. Harmonic oscillators are also at the heart of new quantum technological applications: the long lifetime of high-Q resonators make them advantageous as quantum memories, and they are employed for narrowband processing of quantum signals, as in Josephson parametric amplifiers. The goal of this thesis is to explore different fundamental regimes of two coupled harmonic oscillators using cavity optomechanics as the experimen- tal platform. With consistent progress in attaining ever increasing Q factors, mechanical and electromagnetic resonators realize near-ideal harmonic oscillators. By parametrically modulating the nonlinear optomechanical interaction between them, an effective linear coupling is achieved, which is tunable in strength and in the relative frequencies of the two modes. Thus cavity optomechanics provides a framework with excellent control over system parameters for the study of two coupled harmonic modes. The specific optomechanical implementation employed are superconducting circuits with the vibrating top plate of a capacitor as the mechanical element. Multimode optomechanical circuits are realized, with two microwave modes interacting with one or two mechanical oscillators. The supplementary modes serve either as intermediaries in the relation of the two modes of interest, or as auxiliaries used to control a parameter of the system. Three main experimental results are achieved. First, an auxiliary microwave mode allows the engineering of the effective dissipation rate of a mechanical oscillator. The latter then acts as a reservoir for the main microwave mode with which it interacts. The microwave mode susceptibility can be tuned, resulting in an instability akin to that of a maser and in resonant amplification of incoming microwave signals with an added noise close to the quantum minimum. Second, we study the conditions for a nonreciprocal interaction between two microwave modes, when the information flows in one direction but not in the other. The two modes interact through two mechanical oscillators, leading to frequency conversion between the two cavities. Dissipation in the mechanical modes is essential to the scheme in two ways: it provides a reciprocal phase necessary for the interference and eliminates the unwanted signals. Third, level attraction between a microwave and a mechanical mode is demonstrated, where the eigenfrequencies of the system are drawn closer as the result of interaction, rather distancing themselves as in the more usual case of level repulsion. The phenomenon is theoretically connected to exceptional points, and a general classification of the possible regimes of interaction between two harmonic modes is exposed, including level repulsion and attraction as special cases.
The ability to control the motion of mechanical systems through interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the focus has now turned towards creating and exploiting interesting non-classical states of motion and entanglement in optomechanical systems. Quantumness has also shifted from being the very reason why experiments are constructed to becoming a resource for the investigation of fundamental physics and the creation of quantum technologies. Here, by focusing on opto- and electromechanical platforms we review recent progress in quantum state preparation and entanglement of mechanical systems, together with applications to signal processing and transduction, quantum sensing and topological physics, as well as small-scale thermodynamics.
Cavity optomechanics originated from the research of interferometric detection of gravitational waves, and later became a fast-growing area of techniques and approaches ranging from the fields of atomic, molecular, and optical physics to nano-science and condensed matter physics as well. Recently, it focused on the exploration of operating mechanical oscillators deep in the quantum regime, with an interest ranging from quantum-classical interface tests to high-precision quantum metrology. In this paper, recent theoretical work of our group in the field of quantum measurement with cavity optomechanical systems is reviewed. We explore the quantum measurement theory and its applications with several unconventional cavity optomechanical schemes working in the quantum regime. This review covers the basics of quantum noises in the cavity optomechanical setups and the resulting standard quantum limit of precision displacement and force measurement. Three novel quantum measurement proposals based on the hybrid optomechanical system are introduced. First, we describe a quantum back-action insulated weak force sensor. It is realized by forming a quantum-mechanics-free subsystem with two optomechanical oscillators of reversed effective mass. Then we introduce a role-reversed atomic optomechanical system which enables the preparation and the quantum tomography of a variety of non-classical states of atoms. In this system, the cavity field acts as a mechanical oscillator driven by the radiation pressure force from an ultracold atomic field. In the end, we recommend a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain. These proposals demonstrate the possible applications of optomechanical devices in understanding of quantum-classical crossover and in achieving quantum measurement limit.
In the past several years, the field of optomechanics has progressed from proof-of-principle experiments to the realization of mechanical oscillators and measurements in the quantum regime. Mechanical oscillators are of great interest because they can have small dissipation rates, can couple to many different systems of interest, and are the fundamental elements of ultrasensitive force detectors. Coupling these mechanical oscillators to microwave or optical fields provides a twofold advantage. Firstly, information about mechanical position can be encoded in the interrogating field, enabling sensitive readout of the mechanical oscillator. Secondly, the radiation pressure force of that field can be used to control the state of the mechanical oscillator. Including a high-quality microwave or optical cavity enhances both of these effects, as the field strength is resonantly increased.\nThe major questions in the field of optomechanics in the last several years have dealt with using mechanical oscillators for ultrasensitive measurements and as tools for quantum information. Both of these goals have the prerequisite that we be able to read out the motion of the mechanical oscillator in a quantum efficient manner. To that end, we developed a nearly shot-noise limited microwave interferometer capable of measuring mechanical motion with an imprecision below that at the standard quantum limit. This achievement is not only a critical improvement for the electromechanical experiments we do, but is also an important tool for any experiment that encodes the information of interest in microwave fields. In order to use mechanical oscillators as tools for quantum information, the mechanical oscillator must also be cooled into the quantum regime and fully controllable by the interrogating fields. To this end, we used the radiation pressure of microwave fields to cool our macroscopic mechanical oscillator to less than one phonon. We also demonstrated coherent transfer between itinerant microwave states and the mechanical oscillator, even for incident fields with less than one photon of energy.\nThese accomplishments have set the foundation for further experiments to extend the quantum information abilities of optomechanical systems, couple diverse quantum systems via a mechanical intermediary, and potentially explore the foundations of quantum mechanics at macroscopic scales.