Microwave Cavity Lattices for Quantum Simulation with Photons

Abstract

Historically our understanding of the microscopic world has been impeded by limitations

in systems that behave classically. Even today, understanding simple problems

in quantum mechanics remains a dicult task both computationally and experimentally.

As a means of overcoming these classical limitations, the idea of using a

controllable quantum system to simulate a less controllable quantum system has been

proposed. This concept is known as quantum simulation and is the origin of the ideas

behind quantum computing.

In this thesis, experiments have been conducted that address the feasibility of using

devices with a circuit quantum electrodynamics (cQED) architecture as a quantum

simulator. In a cQED device, a superconducting qubit is capacitively coupled to a

superconducting resonator resulting in coherent quantum behavior of the qubit when

it interacts with photons inside the resonator. It has been shown theoretically that

by forming a lattice of cQED elements, dierent quantum phases of photons will

exist for dierent system parameters. In order to realize such a quantum simulator,

the necessary experimental foundation must rst be developed. Here experimental

eorts were focused on addressing two primary issues: 1) designing and fabricating low

disorder lattices that are readily available to incorporate superconducting qubits, and

2) developing new measurement tools and techniques that can be used to characterize

large lattices, and probe the predicted quantum phases within the lattice.

Three experiments addressing these issues were performed. In the rst experiment

a Kagome lattice of transmission line resonators was designed and fabricated, and a

comprehensive study on the eects of random disorder in the lattice demonstrated

that disorder was dependent on the resonator geometry. Subsequently a cryogenic

3-axis scanning stage was developed and the operation of the scanning stage was

demonstrated in the nal two experiments. The rst scanning experiment was conducted

on a 49 site Kagome lattice, where a sapphire defect was used to locally perturb

each lattice site. This perturbative scanning probe microscopy provided a means to

measure the distribution of photon modes throughout the entire lattice. The second

scanning experiment was performed on a single transmission line resonator where a

transmon qubit was fabricated on a separate substrate, mounted to the tip of the

scanning stage and coupled to the resonator. Here the coupling strength of the qubit

to the resonator was mapped out demonstrating strong coupling over a wide scanning

range, thus indicating the potential for a scanning qubit to be used as a local quantum

probe.