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Microwave cavities are commonly used in many experiments, including optomechanics, magnetic field sensing, magnomechanics, and circuit quantum electrodynamics. Noise, such as variations in the magnetic field or mechanical vibrations, can cause fluctuations of the natural frequency of the cavity, creating challenges in operating them in experiments. To overcome these challenges, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne-interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency modulating the microwave generator. The feedback has a bandwidth of 400 Hz, with a reduction of cavity fluctuations by 85% integrating up to a bandwidth of 2 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by 73%. This scheme can be scaled to enable multitone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked multitone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multitone microwave locking technique presented here is expected to be relevant for a wide range of microwave-cavity experiments.
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Microwave cavities are commonly used in many experiments, including optomechanics, magnetic field sensing, magnomechanics, and circuit quantum electrodynamics. Noise, such as variations in the magnetic field or mechanical vibrations, can cause fluctuations of the natural frequency of the cavity, creating challenges in operating them in experiments. To overcome these challenges, we demonstrate a dynamic feedback system implemented by the locking of a microwave drive to the noisy cavity. A homodyne-interferometer scheme monitors the cavity resonance fluctuations due to low-frequency noise, which is mitigated by frequency modulating the microwave generator. The feedback has a bandwidth of 400 Hz, with a reduction of cavity fluctuations by 85% integrating up to a bandwidth of 2 kHz. Moreover, the cavity resonance frequency fluctuations are reduced by 73%. This scheme can be scaled to enable multitone experiments locked to the same feedback signal. As a demonstration, we apply the feedback to an optomechanical experiment and implement a cavity-locked multitone mechanical measurement. As low-frequency cavity frequency noise can be a limiting factor in many experiments, the multitone microwave locking technique presented here is expected to be relevant for a wide range of microwave-cavity experiments.
Silicon nitride (SiN) membrane electromechanics have shown to serve as excellent systems for applied research on sensing and transduction applications. Nevertheless, their relatively large mass in combination with high-Q also makes them suitable formore fundamental research, where gravitational effects can be tested on large mass quantum states, an experiment which has been elusive till so far. However, creating long-lived mechanical quantum states can be challenging for numerous reasons. One difficulty arises when integrating these membranes into a microwave circuit. In particular, the degradation of the mechanical resonator quality factor in an unpredictable manner. Another complication is that we often have to deal with a low coupling between the devices, which makes the control aspect of the mechanical resonator tougher.
In this thesis, we present a robust SiN based electromechanical platform that uses a custom-built flipchip tool. It allows for achieving single photon-phonon coupling on the order of Hz and high-Q factors at cryogenic temperatures consistently. In chapter 1, we introduce the field of optomechanics and the motivations for extending this field to microwave frequencies. In chapter 2, we provide a detailed derivation of the electro mechanical hamiltonian and use the Heisenberg-Langevin equation of motion to derive an analytical expression for the classical cavity field and mechanical amplitudes. After introducing fluctuations operators in the field amplitudes, we are able to obtain an expression for the noise power spectral density using Wiener–Khinchin theorem. In chapter 3, we give an extensive overview of the design and fabrication methods that we followed to make the electromechanical devices used in our experiments. In chapter 4, we optimise the shape of a lumped-element resonator that is to be used in our electro mechanical system. By simulating with electromagnetic software Sonnet EM, we show that a large loop inductor can negatively impact the resonator quality factor in case a copper platform is located at the bottom of the device. The losses improve tremendously when replacing the loop with a meandered design of the inductor. In chapter 5, we combine a square SiN membrane with the optimised lumped-element resonator, using the flipchip tool. We show that the electromechanical system offers large enough sensitivity to quantify the vibrations originating fromthe cryocooler at the mixing chamber stage. This device shows promise to serve as a broadband cryogenic accelerometer. In chapter 6, we demonstrate that placing the square SiN membrane within a silicon phononic shield significantly enhances the mechanical quality factor and therefore the cooperativity. We also discuss the implications of mechanically induced cavity noise on the measurements. In chapter 7, we conclude the thesis and present the prospects of overcoming mechanical induced cavity noise that afflicts our measurements using 2 different methods i.e. a mechanical isolation system and microwave noise locking mechanism.
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Silicon nitride (SiN) membrane electromechanics have shown to serve as excellent systems for applied research on sensing and transduction applications. Nevertheless, their relatively large mass in combination with high-Q also makes them suitable formore fundamental research, where gravitational effects can be tested on large mass quantum states, an experiment which has been elusive till so far. However, creating long-lived mechanical quantum states can be challenging for numerous reasons. One difficulty arises when integrating these membranes into a microwave circuit. In particular, the degradation of the mechanical resonator quality factor in an unpredictable manner. Another complication is that we often have to deal with a low coupling between the devices, which makes the control aspect of the mechanical resonator tougher.
In this thesis, we present a robust SiN based electromechanical platform that uses a custom-built flipchip tool. It allows for achieving single photon-phonon coupling on the order of Hz and high-Q factors at cryogenic temperatures consistently. In chapter 1, we introduce the field of optomechanics and the motivations for extending this field to microwave frequencies. In chapter 2, we provide a detailed derivation of the electro mechanical hamiltonian and use the Heisenberg-Langevin equation of motion to derive an analytical expression for the classical cavity field and mechanical amplitudes. After introducing fluctuations operators in the field amplitudes, we are able to obtain an expression for the noise power spectral density using Wiener–Khinchin theorem. In chapter 3, we give an extensive overview of the design and fabrication methods that we followed to make the electromechanical devices used in our experiments. In chapter 4, we optimise the shape of a lumped-element resonator that is to be used in our electro mechanical system. By simulating with electromagnetic software Sonnet EM, we show that a large loop inductor can negatively impact the resonator quality factor in case a copper platform is located at the bottom of the device. The losses improve tremendously when replacing the loop with a meandered design of the inductor. In chapter 5, we combine a square SiN membrane with the optimised lumped-element resonator, using the flipchip tool. We show that the electromechanical system offers large enough sensitivity to quantify the vibrations originating fromthe cryocooler at the mixing chamber stage. This device shows promise to serve as a broadband cryogenic accelerometer. In chapter 6, we demonstrate that placing the square SiN membrane within a silicon phononic shield significantly enhances the mechanical quality factor and therefore the cooperativity. We also discuss the implications of mechanically induced cavity noise on the measurements. In chapter 7, we conclude the thesis and present the prospects of overcoming mechanical induced cavity noise that afflicts our measurements using 2 different methods i.e. a mechanical isolation system and microwave noise locking mechanism.
While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with 49% concurrence and 73% Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish |01) from |10), unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the |00) and |11) states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.
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While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with 49% concurrence and 73% Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish |01) from |10), unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the |00) and |11) states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.
