In cavity quantum electrodynamics (QED) 1-3 , light-matter interaction is probed at its most fundamental level, where individual atoms are coupled to single photons stored in three-dimensional cavities. This unique possibility to experimentally explore the foundations of quantum physics has greatly evolved with the advent of circuit QED 4-13 , where on-chip superconducting qubits and oscillators play the roles of two-level atoms and cavities, respectively. In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost. This important regime has been reached both in cavity and circuit QED, but the design flexibility and engineering potential of the latter allowed for increasing the ratio between the atom-cavity coupling rate g and the cavity transition frequency ωr above the percent level 8,14,15 . While these experiments are well described by the renowned Jaynes-Cummings model 16 , novel physics is expected when g reaches a considerable fraction of ωr. Promising steps towards this so-called ultrastrong coupling regime 17,18 have recently been taken in semiconductor structures 19,20 . Here, we report on the first experimental realization of a superconducting circuit QED system in the ultrastrong coupling limit and present direct evidence for the breakdown of the Jaynes-Cummings model. We reach remarkable normalized coupling rates g/ωr of up to 12 % by enhancing the inductive coupling of a flux qubit 21 to a transmission line resonator using the nonlinear inductance of a Josephson junction 22 . Our circuit extends the toolbox of quantum optics on a chip towards exciting explorations of the ultrastrong interaction between light and matter.In the strong coupling regime, the atom-cavity coupling rate g exceeds the dissipation rates κ and γ of both, cavity and atom, giving rise to coherent light-matter oscillations and superposition states. This regime was reached in various types of systems operating at different energy scales [1][2][3][23][24][25] . At microwave frequencies, strong coupling is feasible due to the enormous engineerability of superconducting circuit QED systems 4,5 . Here, small cavity mode volumes and large dipole moments of artificial atoms 26 enable coupling rates g of about 15 1 % of the cavity mode frequency ω r . Nevertheless, as in cavity QED, the quantum dynamics of these systems follows the Jaynes-Cummings model, which describes the coherent exchange of a single excitation between the atom and the cavity mode. Although the Hamiltonian of a realistic atom-cavity system contains so-called counterrotating terms allowing the simultaneous creation ior annihilation of an excitation in both atom and cavity mode, these terms can be safely neglected for small normalized coupling rates g/ω r . However, when g becomes a significant fraction of ω r , the counterrotating terms are expected to manifest, giving rise to exciting effects in QED.The ultrastrong coupling regime is difficult to reach in traditional quantum optics, but was recently realized in a solid-stat...

We present a quantum theory for the interaction of a two level emitter with surface plasmon polaritons confined in single-mode waveguide resonators. Based on the Green's function approach, we develop the conditions for the weak and strong coupling regimes by taking into account the sources of dissipation and decoherence: radiative and non-radiative decays, internal loss processes in the emitter, as well as propagation and leakage losses of the plasmons in the resonator. The theory is supported by numerical calculations for several quantum emitters, GaAs and CdSe quantum dots and NV centers together with different types of resonators constructed of hybrid, cylindrical or wedge waveguides. We further study the role of temperature and resonator length. Assuming realistic leakage rates, we find the existence of an optimal length at which strong coupling is possible. Our calculations show that the strong coupling regime in plasmonic resonators is accessible within current technology when working at very low temperatures ( 4K). In the weak coupling regime our theory accounts for recent experimental results. By further optimization we find highly enhanced spontaneous emission with Purcell factors over 1000 at room temperature for NV-centers. We finally discuss more applications for quantum nonlinear optics and plasmon-plasmon interactions.

In this work we study theoretically the coupling of single-molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main result of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (∼ µs), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy 6

Single photon sources are an integral part of various quantum technologies, and solid state quantum emitters at room temperature appear as a promising implementation. We couple the fluorescence of individual silicon vacancy centers in nanodiamonds to a tunable optical microcavity to demonstrate a single photon source with high efficiency, increased emission rate, and improved spectral purity compared to the intrinsic emitter properties. We use a fiber-based microcavity with a mode volume as small as 3.4 λ 3 and a quality factor of 1.9 × 10 4 and observe an effective Purcell factor of up to 9.2. We furthermore study modifications of the internal rate dynamics and propose a rate model that closely agrees with the measurements. We observe lifetime changes of up to 31%, limited by the finite quantum efficiency of the emitters studied here. With improved materials, our achieved parameters predict single photon rates beyond 1 GHz.

Optical microcavities are a powerful tool to enhance spontaneous emission of individual quantum emitters. However, the broad emission spectra encountered in the solid state at room temperature limit the influence of a cavity, and call for ultra-small mode volume. We demonstrate Purcellenhanced single photon emission from nitrogen-vacancy (NV) centers in nanodiamonds coupled to a tunable fiber-based microcavity with a mode volume down to 1.0 λ 3 . We record cavity-enhanced fluorescence images and study several single emitters with one cavity. The Purcell effect is evidenced by enhanced fluorescence collection, as well as tunable fluorescence lifetime modification, and we infer an effective Purcell factor of up to 2.0. With numerical simulations, we furthermore show that a novel regime for light confinement can be achieved, where a Fabry-Perot mode is combined with additional mode confinement by the nanocrystal itself. In this regime, effective Purcell factors of up to 11 for NV centers and 63 for silicon vacancy centers are feasible, holding promise for bright single photon sources and efficient spin readout under ambient conditions. II. ULTRA-SMALL MODE VOLUME TUNABLE CAVITYThe microcavity is assembled of a planar mirror onto which the sample is applied, and a concave mirror on the tip of an optical fiber [26], see Fig. 1(a). The tip of the cavity fiber is shaped by advanced CO 2 laser machining [34,35]. In a first step, the extent of the endfacet is tapered to enable sub-micron mirror separations, arXiv:1606.00167v2 [quant-ph]

We report on measurements and modeling of the mode structure of tunable Fabry-Pérot optical microcavities with imperfect mirrors. We find that non-spherical mirror shape and finite mirror size leave the fundamental mode mostly unaffected, but lead to loss, mode deformation, and shifted resonance frequencies at particular mirror separations. For small mirror diameters, the useful cavity length is limited to values significantly below the expected stability range. We explain the observations by resonant coupling between different transverse modes of the cavity and mode-dependent diffraction loss. A model based on resonant state expansion that takes into account the measured mirror profile can reproduce the measurements and identify the parameter regime where detrimental effects of mode mixing are avoided.

We report on the coupling of the emission from a single europium-doped nanocrystal to a fiber-based microcavity under cryogenic conditions. As a first step, we study the properties of nanocrystals that are relevant for cavity experiments and show that embedding them in a dielectric thin film can significantly reduce scattering loss and increase the light-matter coupling strength for dopant ions. The latter is supported by the observation of a fluorescence lifetime reduction, which is explained by an increased local field strength. We then couple an isolated nanocrystal to an optical microcavity, determine its size and ion number, and perform cavity-enhanced spectroscopy by resonantly coupling a cavity mode to a selected transition. We measure the inhomogeneous linewidth of the coherent D F 5 0 7 0 -transition and find a value that agrees with the linewidth in bulk crystals, evidencing a high crystal quality. We detect the fluorescence from an ensemble of few ions in the regime of power broadening and observe an increased fluorescence rate consistent with Purcell enhancement. The results represent an important step towards the efficient readout of single rare earth ions with excellent optical and spin coherence properties, which is promising for applications in quantum communication and distributed quantum computation.

Raman spectroscopy reveals chemically specific information and provides label-free insight into the molecular world. However, the signals are intrinsically weak and call for enhancement techniques. Here, we demonstrate Purcell enhancement of Raman scattering in a tunable high-finesse microcavity, and utilize it for molecular diagnostics by combined Raman and absorption imaging. Studying individual single-wall carbon nanotubes, we identify crucial structural parameters such as nanotube radius, electronic structure and extinction cross-section. We observe a 320-times enhanced Raman scattering spectral density and an effective Purcell factor of 6.2, together with a collection efficiency of 60%. Potential for significantly higher enhancement, quantitative signals, inherent spectral filtering and absence of intrinsic background in cavity-vacuum stimulated Raman scattering render the technique a promising tool for molecular imaging. Furthermore, cavity-enhanced Raman transitions involving localized excitons could potentially be used for gaining quantum control over nanomechanical motion and open a route for molecular cavity optomechanics.