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Coherent coupling of magnon excitations and microwave photons in a cavity may disclose new paths to unconventional phenomena and for novel applications. Here, we show that large couplings and cooperativities can be achieved with YIG (Yttrium Iron Garnet) films in contact with coplanar resonators made of superconducting YBCO. Transmission spectra, which are analysed by a modified Hopfield model, show that the coupling of the dominant magnetic mode with photons exceeds 0.2 times the cavity frequency, thus demonstrating the achievement of the ultra strong coupling regime with this architecture.

We introduce a gauge-invariant model of planar, square molecules coupled to a quantized spatially-varying cavity electromagnetic vector potential A(r). Specifically, we choose a temporally chiral cavity hosting a uniform magnetic field B, as this is the simplest instance in which a transverse spatially-varying A(r) is at play. We show that when the molecules are in the Van Vleck paramagnetic regime, an equilibrium quantum phase transition to a photon condensate state occurs., Comment: 14 pages, 3 figures

The quantum Rabi model is a widespread description for the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results in any interaction regime was introduced [Nature Physics 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the dipole approximation., Comment: 10 pages, 2 figures

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Here we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light-matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics., Comment: 22 pages, 4 figures

The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling have been explored in several settings. These regimes, where the interaction strength is comparable (ultrastrong) or even higher (deep-strong) than the transition frequencies in the system, can give rise to new physical effects and applications. At the same time, they challenge our understanding of cavity QED. When the interaction strength is so high, fundamental issues like the proper definition of subsystems and of their quantum measurements, the structure of light-matter ground states, or the analysis of time-dependent interactions are subject to ambiguities leading to even qualitatively distinct predictions. The resolution of these ambiguities is also important for understanding and designing next-generation quantum devices that will exploit the ultrastrong coupling regime. Here we discuss and provide solutions to these issues., Comment: 52 pages and 10 figures

We consider two separate atoms interacting with a single-mode optical resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between \textit{one} photon and \textit{two} atoms, via intermediate virtual states connected by counter-rotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission processes can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems., Comment: 16 pages, 5 figures

In quantum field theory, bare particles are dressed by a cloud of virtual particles to form physical particles. The virtual particles affect properties such as the mass and charge of the physical particles, and it is only these modified properties that can be measured in experiments, not the properties of the bare particles. The influence of virtual particles is prominent in the ultrastrong-coupling regime of cavity quantum electrodynamics (QED), which has recently been realized in several condensed-matter systems. In some of these systems, the effective interaction between atom-like transitions and the cavity photons can be switched on or off by external control pulses. This offers unprecedented possibilities for exploring quantum vacuum fluctuations and the relation between physical and bare particles. Here we show that, by applying external electromagnetic pulses of suitable amplitude and frequency, each virtual photon dressing a physical excitation in cavity-QED systems can be converted into a physical observable photon, and back again. In this way, the hidden relationship between the bare and the physical excitations becomes experimentally testable. The conversion between virtual and physical photons can be clearly pictured using Feynman diagrams with cut loops., Comment: 32 pages including supplementary material