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Publication# Dissipation as a resource in circuit quantum electromechanics

Abstract

A primary challenge in quantum science and technology is to isolate the fragile quantum states from their environment in order to prevent the irreversible leakage of energy and information which causes decoherence. In the late 1990s, however, a new paradigm emerged, in which the environment itself, as well as the coupling to this environment of the quantum state, are engineered in ways which, counterintuitively, facilitate the creation and stabilization of desired quantum properties. This paradigm, coined reservoir engineering, has been pursued experimentally in various implementations, in which the states of trapped ions, atomic clouds or artificial atoms based on superconducting circuits were driven into a desired target state using a dissipative reservoir. In all these cases, the cold electromagnetic environment served as the engineered reservoir, capitalizing on the tremendous progress in the ability to shape the modes of the electromagnetic field using masers and lasers.

In optomechanics, which is the study of the coupling between light and mechanical motion, a similar scenario has been prevalent. Light is used to read out and control the mechanical motion, and in the past few years, various optomechanical architectures both in the optical and microwave domain have enabled to push mechanical systems into the quantum regime. These results can be interpreted in the context of reservoir engineering: cooling and many other optomechanical phenomena exploit the cold, dissipative nature of light.

This thesis reports on the development of a multimode superconducting circuit with a mechanically compliant element - fitting into the field of circuit cavity electromechanics -, with which we pursue two themes. In the first set of experiments, reversing the roles of dissipation described above, we engineer the mechanical oscillator into a cold, dissipative environment for microwave light. The mechanical element is the fundamental mode of a free-standing top electrode of a capacitor, 100 nm thick and 32 micron in diameter made of aluminum with an effective mass of around 170 pg, vibrating at a resonance frequency of 5.5 MHz. The dissipative mechanical reservoir is prepared using an auxiliary microwave mode with engineered parameters.We utilize it to control the properties - in particular, the susceptibility - of the electromagnetic field and to perform low-noise amplification close to the quantum limit. The noise analysis reveals that the reservoir is close to its quantum ground state with a mean thermal occupation number well below 1, demonstrating its utility as a resource in the quantum regime. We also show that the system can be driven to the parametric instability threshold, above which self-sustained oscillations of the microwave field (masing) is observed. Finally, we demonstrate injection locking of the maser using an external seed pump.

In a second set of experiments, a similar electromechanical circuit is used to implement a microwave isolator based on optomechanical interactions. The overarching theme is that dissipation of the mechanical oscillator, albeit intrinsic and not engineered via an auxiliary mode s a key ingredient for the device to function as a nonreciprocal frequency converter and isolator. In these experiments, an additional mechanical mode is used, such that a 4-mode optomechanical plaquette is realized.

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In quantum mechanics, the Heisenberg uncertainty principle places a fundamental limit in the measurement precision for certain pairs of physical quantities, such as position and momentum, time and energy or amplitude and phase. Due to the Heisenberg uncertainty principle, any attempt to extract certain information from a quantum object would inevitably perturbitinanunpredictableway. This raises one question,"What is the precision limit in such quantum measurements?" The answer, standard quantum limit (SQL), has been obtained by Braginsky to figure out the fundamental quantum limits of displacement measurement in the context of gravitational wave detection. To circumvent the unavoidable quantum back-action from the priori measurement, quantum non-demolition measurement (QND) methods were introduced by Braginsky and Thorne. To surpass the SQL of the displacement measurement in an interferometer, one can measure only one quadrature of the mechanical motion while give up the information about the other canonically conjugated quadrature. Such measurements can be performed by periodic driving the mechanical oscillator, i.e. the back-action evading (BAE) measurement.
Cavity optomechanics provides an ideal table-top platform for the testing of the quantum measurement theory. Mechanical oscillator is coupled to electromagnetic field via radiation pressure, which is enhanced by an optical micro-cavity. Over the last decade, laser cooling has enabled the preparation of mechanical oscillator in the ground state in both optical and microwave systems. BAE measurements of mechanical motion have been allowed in the microwave electromechanical systems, which led to the observations of mechanical squeezing and entanglement. However, despite the theoretical proposal almost 40 years ago, the sub-SQL measurements still remain elusive. This thesis reports our efforts approach the sub-SQL with a highly sideband-resolved silicon optomechanical crystal (OMC) in a 3He buffer gas environment at 2K. The OMC couples an optical mode at telecommunication wavelengths and a colocalized mechanical mode at GHz frequencies. The Helium3 buffer gas environment allows sufficient thermalization of the OMC despite the drastically decreased silicon thermal conductivity. We observe Floquet dynamics in motional sideband asymmetry measurement when employing multiple probe tones. The Floquet dynamics arises due to presence of Kerr-type nonlinearities and gives rise to an artificially modified motional sideband asymmetry, resulting from a synthetic gauge field among the Fourier modes. We demonstrate the first optical continuous two-tone backaction-evading measurement of a localized GHz frequency mechanical mode of silicon OMC close to the ground state by showing the transition from conventional sideband asymmetry to backaction-evading measurement. We discover a fundamental two-tone optomechanical instability and demonstrate its implications on the back-action evading measurement. Such instability imposes a fundamental limitation on other two-tone schemes, such as dissipative quantum mechanical squeezing. We demonstrate state-of-art laser sideband cooling of the mechanical motion to a mean thermal occupancy of 0.09 quantum, which is 7.4dB of the oscillator's zero-point energy and corresponds to 92% ground state probability. This also enables us to observe the dissipative mechanical squeezing below the zero-point motion for the first time with laser light.

Nathan Rafaël Bernier, Tobias Kippenberg, László Dániel Tóth

Isolation of a system from its environment is often desirable, from precision measurements to control of individual quantum systems; however, dissipation can also be a useful resource. Remarkably, engineered dissipation enables the preparation of quantum states of atoms, ions or superconducting qubits as well as their stabilization. This is achieved by a suitably engineered coupling to a dissipative cold reservoir formed by electromagnetic modes. Similarly, in the field of cavity electro- and optomechanics, the control over mechanical oscillators utilizes the inherently cold, dissipative nature of the electromagnetic degree of freedom. Breaking from this paradigm, recent theoretical work has considered the opposite regime in which the dissipation of the mechanical oscillator dominates and provides a cold, dissipative reservoir to an electromagnetic mode. Here we realize this reversed dissipation regime in a microwave cavity optomechanical system and realize a quasi-instantaneous, cold reservoir for microwave light. Coupling to this reservoir enables to manipulate the susceptibility of the microwave cavity, corresponding to dynamical backaction control of the microwave field. Additionally, we observe the onset of parametric instability, i.e. the stimulated emission of microwaves (masing). Equally important, the reservoir can function as a useful quantum resource. We evidence this by employing the engineered cold reservoir to implement a large gain (above 40 dB) phase preserving microwave amplifier that operates 0.87 quanta above the limit of added noise imposed by quantum mechanics. Such a dissipative cold reservoir forms the basis of microwave entanglement schemes, the study of dissipative quantum phase transitions, amplifiers with unlimited gain-bandwidth product and non-reciprocal devices, thereby extending the available toolbox of quantum-limited microwave manipulation techniques.

2017Harmonic 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.