Ultra-high quantum coherent and scalable superconducting circuit optomechanics, from topological lattices to quantum storage

Mechanical oscillators can exhibit modes with ultra-low energy dissipation and compact form factors due to the slow velocity of acoustic waves, and are already used in applications ranging from timing to wireless filters. Over the past decade, novel ways in which mechanical systems can be quantum controlled have been developed, based on either coupling to electromagnetic cavities in quantum optomechanics or superconducting qubits. The former route has utilized the coupling to electromagnetic cavities both in the optical and microwave domains, and enabled to reach a regime where the quantum nature of the optomechanical interaction becomes relevant.This allowed numerous advances such as optomechanical ground state cooling, quantum transduction, or entanglement of macroscopic mechanical resonators.An enduring challenge in constructing such hybrid systems is the dichotomy of engineered coupling to an auxiliary degree of freedom, while being mechanically well isolated from the environment, that is, low quantum decoherence. In this thesis, we show how to overcome this challenge by introducing a superconducting circuit optomechanical platform with an ultra-low quantum decoherence rate. This enabled us to reach 0.07 quanta motional ground state occupation and realize mechanical squeezing of -2.7 dB below zero-point fluctuation. To directly measure the quantum-state lifetime, we observe the free evolution of the phase-sensitive squeezed state for the first time, preserving its non-classical nature over milli-second timescales, substantially longer than conventional superconducting qubits and on par with ion traps.Furthermore, our novel platform enables us to scale up optomechanical systems to arrays and lattices, realizing non-trivial topological modes in such multimode systems. This has been a long-lasting challenge in the field of optomechanics due to the stringent requirements on identical individual optomechanical sites. We introduce a novel technique to exploit optomechanical interaction and directly measure collective mode shapes in a large-scale superconducting lattice and explore the physics of edge states in optomechanical strained-graphene lattices.Such ultra-low quantum decoherence and reproducible platform not only increases the fidelity of quantum control and measurement of macroscopic mechanical systems but may equally benefit interfacing with qubits, exploring emergent nonlinear dynamics in complex optomechanical systems, and placing the system in a parameter regime suitable for tests of quantum gravity. Particularly, the long mechanical quantum-state lifetime has applications in quantum sensing and makes this platform a perfect candidate for quantum storage elements in quantum computing and communication systems.In the last part of this thesis, we report the first proof-of-concept cryogenic electro-optical readout of a superconducting circuit using a lithium niobate modulator to reduce the heat load and address the scaling challenge in future superconducting circuit-based quantum computers. Although the noise level in the electro-optical readout chain is still substantially higher than the conventional electronic methods, we discuss the requirements and envision the parameter regimen that may lead to near-quantum limited optical readout in advanced future platforms.