Investigation into flux-coupled electromechanical devices

Abstract

Cavity optomechanical systems involve modulation of the resonance frequency of an optical cavity by the motion of a mechanical resonator. These systems are used to control and manipulate mechanical motion down to the quantum regime. Such control over the quantum states of the mechanical object is essential for various technological applications and for testing the limits of quantum mechanics in macroscopic objects. By harnessing the interaction of confined radiation fields with a mechanical resonator, optomechanical devices have achieved several milestones regarding the control of motion of mechanical objects. These include cooling to the quantum ground state, precise displacement detection with sensitivity below standard quantum limit, preparing nonclassical states of motion, and entanglement between two mechanical objects.

Traditionally, in the microwave domain, electromechanical coupling is achieved via a capacitive coupling scheme, where the mechanical resonator’s motion modulates the microwave cavity’s capacitance and resonance frequency. However, this approach typically results in weak intrinsic electromechanical coupling, which is usually mitigated by a strong microwave drive. The strong drive linearizes the otherwise nonlinear optomechanical interaction, limiting the mechanical state preparation fidelity.

In the thesis presented here, we demonstrate a cavity optomechanical system based on a fundamentally different magnetic-flux coupling scheme. In this system, a mechanical resonator is coupled to a frequency-tunable transmon qubit using Josephson inductance. The transmon qubit is additionally coupled to a readout cavity. The mechanical resonator is realized by suspending one of the arms of the SQUID loop and its vibration parametrically modulates the loop’s inductance in the presence of a magnetic field, thereby modulating the transmon frequency. The electromechanical coupling stems from the quantum interference of the superconducting phase across the tunnel junction. By making the transmon resonant with the readout cavity, we demonstrate achieving large electromechanical coupling, leading to interesting results.

In the first generation of the devices studied in this thesis, we use a single-ended 3-dimensional (3D) transmon qubit, which is coupled to an aluminum-coated silicon nitride (SiN) nanobeam serving as the mechanical resonator. A 3D rectangular waveguide cavity is utilized as the readout cavity. In the resonant regime of the transmon-cavity system, we demonstrate electromechanical coupling up to 4 kHz between the in-plane vibrational mode of the mechanical resonator and the transmon-cavity hybridized electromagnetic (EM) mode. Furthermore, by driving the EM mode with less than 0.1 photons, we observe the thermal motion of the mechanical resonator in the power spectral density (PSD) of the output signal. Additionally, in the dispersive regime of the transmon-cavity coupled system, we observe LZS interference patterns in the transmon qubit spectrum by actuating the mechanical mode.

In the second generation of devices studied in this thesis, we employ a λ/4 coaxial cavity as the readout cavity and demonstrate enhancement of the electromechanical coupling using various strategies. First, we use a thinner aluminum film (without SiN underneath) to fabricate the mechanical resonator, resulting in a low resonator mass and a larger zero-point motion. Second, leveraging the idea of a higher in-plane critical magnetic field of the aluminum film, we use the out-of-plane vibrational mode of the mechanical resonator and apply a higher magnetic field. These modifications result in enhancement of the electromechanical coupling rate up to 160 kHz, which is nearly 4% of the mechanical mode frequency. As a consequence of large coupling, we observe strong backaction on the mechanical mode and demonstrate an unstable response with less than one mean photon occupation in the electromagnetic (EM) mode. Moreover, by adjusting the transmon-cavity detuning, we control the EM mode’s Kerr nonlinearity and explore the mechanical instability phase diagram in both weak and strong nonlinear regimes of the EM mode. We observe that the mechanical instabilities are governed by the nonlinearity of the electromechanical interaction and the Kerr nonlinearity of the EM mode, which originates from the Josephson junctions. Additionally, akin to optomechanically induced transparency (OMIT), we observe cavity-enabled-qubit-absorption (CEQA) features in the EM mode’s transmission spectrum in both weak and strong nonlinear regimes.

We further develop theoretical models to explain the results in addition to the experimental observations. The models include deriving analytical expressions for the CEQA features in both strong and weak nonlinear regimes. Further, based on semi classical analysis, we utilize a theoretical framework for the backaction on the mechanical resonator. We observe that while the semi-classical theory can explain the results in a weakly nonlinear regime, it falls short in explaining the observed mechanical instabilities in a strongly nonlinear regime of the EM mode. In that direction, we develop a model based on polariton transitions, which can explain the instabilities at low drive power. However, it cannot explain the instabilities arising at higher drive power, concluding the need for further theoretical study.