Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics. To this end, the strong nonlinearitiesof superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain. In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task. In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach-Zehnder interferometer composed of two superconducting microwave beam splitters. By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment. At high frequencies, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit. At low frequencies, we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators. Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.

The study of the interaction of light and matter has led to many fundamental discoveries as well as numerous important technologies. Over the last decades, great strides have been madein increasing the strength of this interaction at the single-photon level, leading to a continual exploration of new physics and applications. In recent years, a major achievement has been the demonstration of the so-called strong coupling regime, a key advancement enabling great progress in quantum information science. In this work, we demonstrate light-matter interaction over an order of magnitude stronger than previously reported, reaching a new regime of ultrastrong coupling (USC). We achieve this using a superconducting artificial atom tunably coupled to the electromagnetic continuum of a one-dimensional waveguide. For the largest values of the coupling, the spontaneous emission rate of the atom is comparable to its transition frequency. In this USC regime, the conventional quantum description of the atom and light as distinct entities breaks down, and a new description in terms of hybrid states is required. Our results open the door to a wealth of new physics and applications. Beyond light-matter interaction itself, the tunability of our system makes it promising as a tool to study a number of important physical systems such as the well-known spin-boson and Kondo models.

We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductancebetween the resonators. From the mode distance observed in spectroscopy experiments, we derive a coupling strength ranging between -320MHz and 37 MHz. In the case where the coupling strength is about zero, the microwave power cross transmission between the two resonators can be reduced by almost four orders of magnitude compared to the case where the coupling is switched on. In addition, we observe parametric amplification by applying a suitable additional drive tone.

We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanicallyto the qubit. With a coupling strength as high as 17% of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings model. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.

. We"]explore the full phase diagram of the model using Matrix-Product-State methods. Guided by these numerical results, we describe a modified variational ansatz to improve our analytic description of the groundstate at low boson frequencies. Additionally, we introduce an experimental protocol capable of inferring the low-energy excitations of the system by means of Fano scattering spectroscopy. Finally, we discuss the implementation and characterization of this model with current circuit-QED technology.

We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent currentflux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit drive power and the dynamic range of the resonator input power

We study the time and space resolved dynamics of a qubit with an Ohmic coupling to propagating 1D photons, from weak coupling to the ultrastrong coupling regime. A nonperturbative studybased on Matrix Product States (MPS) shows the following results: (i) The ground state of the combined systems contains excitations of both the qubit and the surrounding bosonic field. (ii) An initially excited qubit equilibrates through spontaneous emission to a state, which under certain conditions, is locally close to that ground state, both in the qubit and the field. (iii) The resonances of the combined qubit-photon system match those of the spontaneous emission process and also the predictions of the adiabatic renormalization [A. J. Leggett et al., Rev. Mod. Phys. 59, 1, (1987)]. Finally, a non-perturbative ab-initio calculations show that this physics can be studied using a flux qubit galvanically coupled to a superconducting transmission line.

The scattering through a Josephson junction interrupting a superconducting line is revisited including power leakage. We discuss also how to make tunable and broadband resonant mirrorsby concatenating junctions. As an application, we show how to construct cavities using these mirrors, thus connecting two research fields: JJ quantum metamaterials and coupled cavity arrays. We finish by discussing the first non-linear corrections to the scattering and their measurable effects.

In this work we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbor pairing term, $sum_{< i,j>} a^dagger_i a^dagger_j + mathrm{H.c.}$Like the original Bose-Hubbard model, the nearest-neighbor term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form pairing cannot be studied with a simple mean-field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.

Coupled superconducting transmission line resonators have applications in
quantum information processing and fundamental quantum mechanics. A particular
example is the realization offast beam splitters, which however is hampered by
two-mode squeezer terms. Here, we experimentally study superconducting
microstrip resonators which are coupled over one third of their length. By
varying the position of this coupling region we can tune the strength of the
two-mode squeezer coupling from 2.4% to 12.9% of the resonance frequency of
5.44GHz. Nevertheless, the beam splitter coupling rate for maximally suppressed
two-mode squeezing is 810MHz, enabling the construction of a fast and pure beam
splitter.