#
Quantum Optics and Waveguide Quantum Electrodynamics in Superconducting Circuits
Doctoral thesis, 2021

In this thesis, we first introduce circuit quantisation, giving the basis for the next part, where we investigate a transmon, a charge-insensitive artificial atom, coupled to a semi-infinite transmission line. An atom coupled to a semi-infinite waveguide is referred to as an

*atom in front of a mirror*and is the subject of all appended papers. We proceed by summarising Paper I and III's main results: in Paper I, we investigate the spontaneous emission of a transmon coupled to a semi-infinite transmission line, where we take time-delay effects into account. We find that the system dynamics strongly depend on the coupling strength to the transmission line and the atom's position with respect to the electromagnetic field, leading to the Purcell effect or the convergence to a dark state with finite excitation probability. In the high-impedance regime, which we investigate in Paper III, the properties of the transmon coupled to the high-impedance transmission line change drastically. It becomes highly reflective and creates its own cavity with the mirror, resulting in the emergence of cavity modes and vacuum Rabi oscillations in the spontaneous emission dynamics.

In the next chapter of the thesis, we demonstrate how to quantise an electromagnetic field and derive a light-matter interaction Hamiltonian within dipole approximation. We then give an introduction to open quantum systems and derive the quantum-optical master equation in Lindblad form. Furthermore, we introduce the dressed state picture, where the interaction of light and matter is so strong that the individual energy levels of light and matter are no longer separable. Both the quantum optical master equation and the dressed state picture are relevant in Paper II and IV. In Paper II, an experimental collaboration, we perform several experiments to characterise and discriminate different decay rates of a superconducting qubit coupled to the end of a transmission line. One experiment measured the atomic fluorescence spectral density, which shows an asymmetry for off-resonant driving, resulting from pure dephasing: an effect that we explain in more detail in this thesis and Paper II. In Paper IV, we theoretically investigate amplification mechanisms realised by different set-ups of an atom coupled to a semi-infinite waveguide. In the considered systems, the amplification of a probe field happens either due to population inversion between the pure states or dressed states or multi-photon processes. We find that compared to an open waveguide, we can achieve a higher gain in the amplification with a semi-infinite waveguide.

Artificial Atoms

Circuit Quantum Electrodynamics

Waveguide Quantum Electrodynamics

Quantum Optics

Superconducting Qubits

## Author

### Emely Wiegand

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

### Semiclassical analysis of dark-state transient dynamics in waveguide circuit QED

PHYSICAL REVIEW A,; Vol. 101(2020)

**Journal article**

### Characterizing decoherence rates of a superconducting qubit by direct microwave scattering

npj Quantum Information,; Vol. 7(2021)

**Journal article**

### "Wiegand, E., Rousseaux, B., Johansson, G. Transmon in a semi-infinite high-impedance transmission line: Appearance of cavity modes and Rabi oscillations"

### "Wiegand, E., Wen, PY., Delsing, P., Hoi, IC., Kockum, AF. Ultimate quantum limit for amplification: a single atom in front of a mirror"

In recent years, there has been tremendous progress in developing quantum bits, so-called qubits, that replace bits in a classical computer to build a so-called quantum computer. A quantum computer is believed to solve specific problems exponentially faster than any supercomputer, potentially leading to novel discoveries in a diverse range of fields, e.g., chemistry and medicine. These recent developments have led to a second quantum revolution. With the quantum computer also comes the idea of the quantum internet or a quantum network, which could, for instance, be built with superconducting circuits. These circuits consist of superconducting qubits coupled to waveguides. It is crucial to investigate both the qubits' properties to be able to control them and the electromagnetic field responsible for the transmission of information from one part to another. The quantum networks have to be huge to realise a quantum internet, leading to unwanted time-delay effects caused by the long propagation distance of the electromagnetic field in the waveguides. Using specially designed transmission lines with low microwave velocity, coupled to superconducting qubits, it is possible to investigate quantum time-delay effects in much smaller systems, on the order of centimetres or meters. This is the topic of this thesis.

Apart from studying the properties of superconducting qubits and waveguides themselves, this thesis studies quantum optical phenomena realised in superconducting circuits. Some examples are spontaneous emission, Rabi oscillations, photon scattering, and on-chip amplification.

### Kvantplasmonik – en teknologi för foton-fotonväxelverkan på kvantnivå vid rumstemperatur

Swedish Research Council (VR), 2017-01-01 -- 2022-12-31.

### Areas of Advance

Nanoscience and Nanotechnology (SO 2010-2017, EI 2018-)

### Subject Categories

Atom and Molecular Physics and Optics

Other Physics Topics

Nano Technology

Condensed Matter Physics

### ISBN

978-91-7905-477-9

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4944

### Publisher

Chalmers University of Technology

Online via Zoom

Opponent: Prof. Luis Martin-Moreno, Instituto de Nanociencia y Materiales de Aragon (INMA), CSIC-Universidad de Zaragoza, Spain