The quantum optics of metamaterials

The interaction of light and matter is a widely studied field in physics: Both quantum mechanical and classical effects have been treated to a large extent in theoretical studies but also in a wide range of experiments. One particularly interesting manifestation of such interactions are macroscopic materials with a linear response to the light field. This can be either a response due to the electric or due to the magnetic field, depending on the internal structure of the medium. However, the magnetic response is typically much weaker than the electric response and magnetic effects have been neglected in the majority of theoretical considerations. The recently emerging field of metamaterials brings new possibilities of tailoring the electromagnetic properties of a medium, which gives rise to a class of materials with both electric and magnetic responses that have not been observed in naturally occurring materials - hence the name metamaterial. For such materials the theories developed for purely dielectric media, materials with no magnetic response, do not hold anymore. The main goal of this thesis is to generalize electromagnetic theory, especially for the interaction of the light field with electric and magnetic dipoles, to arbitrary magneto-dielectric media. In particular, this includes lossy magnetic materials and biaxial anisotropic media, but also a general investigation of the nature of light-matter interactions from the magnetic point of view. Magnetic and electric effects are often treated very differently. It is my aim to show the similarities, and immense symmetry between them, and therefore always treat electric and magnetic effects side by side whenever possible, and wherever a theory is only properly derived for the electric quantities, I shall complement the magnetic analogies to fill these gaps. The second part of this thesis covers another important aspect of light-matter interaction, the transfer of coherence between atoms and the electromagnetic field inside a cavity, which is of particular importance in the context of quantum thermodynamics and the resource theory of coherence. This work is not directly linked to the main body of the thesis, but builds on the same theoretical framework of light-matter interaction in the Jaynes-Cummings model. We examine the catalytic nature of quantum optical coherence, in particular, the degradation of a coherent state in the cavity as coherence is transferred to a sequence of atoms through a Jaynes-Cummings interaction. In comparison with an earlier, rather artificial proposal of the catalytic creation of coherence, we investigate the role of correlations and the robustness of this more natural protocol of coherence transfer

Coherence and catalysis in the Jaynes-Cummings model

There has been substantial interest of late on the issue of coherence as a resource in quantum thermodynamics. To date, however, analyses have focussed on somewhat artificial theoretical models. We seek to bring these ideas closer to experimental investigation by examining the ``catalytic'' nature of quantum optical coherence. Here the interaction of a coherent state cavity field with a sequence of two-level atoms is considered, a state ubiquitous in quantum optics as a model of a stable, classical source of light. The Jaynes-Cummings interaction Hamiltonian is used, so that an exact solution for the dynamics can be formed, and the evolution of the atomic and cavity states with each atom-field interaction analysed. In this way, the degradation of the coherent state is examined as coherence is transferred to the sequence of atoms. The associated degradation of the coherence in the cavity mode is significant in the context of the use of coherence as a thermodynamic resource

Low-depth Circuit Implementation of Parity Constraints for Quantum Optimization

We present a construction for circuits with low gate count and depth, implementing three- and four-body Pauli-Z product operators as they appear in the form of plaquette-shaped constraints in QAOA when using the parity mapping. The circuits can be implemented on any quantum device with nearest-neighbor connectivity on a square-lattice, using only one gate type and one orientation of two-qubit gates at a time. We find an upper bound for the circuit depth which is independent of the system size. The procedure is readily adjustable to hardware-specific restrictions, such as a minimum required spatial distance between simultaneously executed gates, or gates only being simultaneously executable within a subset of all the qubits, for example a single line.Comment: 9 pages, 6 figure

Duality, decay rates, and local-field models in macroscopic QED

Any treatment of magnetic interactions between atoms, molecules, and optical media must start at the form of the interaction energy. This forms the base on which predictions about any number of magnetic atom-light properties stands, spontaneous decay rates and forces included. As is well known, the Heaviside-Larmor duality symmetry of Maxwell's equations, where electric and magnetic quantities are exchanged, is broken by the usual form of the magnetic interaction energy. We argue that this symmetry can be restored by including general local-field effects and that local fields should be treated as a necessity for correctly translating between the microscopic world of the dipole and the macroscopic world of the measured fields. This may additionally aid in resolving a long-standing debate over the form of the force on a dipole in a medium. Finally, we compute the magnetic dipole decay rate in a magnetodielectric with local-field effects taken into account and show that macroscopic quantum electrodynamics can be made to be dual symmetric at an operator level, instead of only for expectation values

Spontaneous emission in anisotropic dielectrics

The emission properties of atoms lie at the foundations of both quantum theory and light-matter interactions. In the context of macroscopic media, exact knowledge thereof is important both in current quantum technologies as well as in fundamental studies. While for isotropic media, this is a very well-studied problem, there are still big gaps in the theory of anisotropic media. In particular, to the best of our knowledge, an explicit expression for the spontaneous emission rate in general anisotropic media has not been presented. In this work, we first derive the quantised electromagnetic field operators to calculate the emission rate in uniaxial media. For the more general case of biaxial media we propose an approximate expression based on interpolation between the limiting cases of uniaxial media. We support our model with numerical simulations which are in strong agreement for typical media configurations, and furthermore show how local field effects can be taken into account in the model

Applications of Universal Parity Quantum Computation

We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the Quantum Fourier Transform and Quantum Addition. Embedding these algorithms in the parity encoding reduces the circuit depth as compared to conventional gate-based implementations while keeping the multi-qubit gate counts comparable. We further propose simple implementations of multi-qubit gates in tailored encodings and an efficient strategy to prepare graph states.Comment: 8 pages, 6 figure

Universal Parity Quantum Computing

We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on the parity encoding. We show that logical CPhase gates and $R_z$ rotations can be implemented in the parity encoding with single-qubit operations. Together with logical $R_x$ rotations, implemented via nearest-neighbor CNOT gates and an $R_x$ rotation, these form a universal gate set. As the CPhase gate requires only single qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms, e.g.\ the Quantum Fourier Transform. We present a method to switch between different encoding variants via partial on-the-fly encoding and decoding.Comment: 6 pages, 3 figure

Modular Parity Quantum Approximate Optimization

The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert-space with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, the implicit approach shows better QAOA performance. Here we combine the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. In particular, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.Comment: 11 pages, 9 figure