Using a submillimeter-sized YIG (yttrium-iron-garnet) sphere mounted in a magnetic-field-focusing cavity, we demonstrate an ultrahigh cooperativity of 10 5 between magnon and photon modes at millikelvin temperatures and microwave frequencies. The cavity is designed to act as a magnetic dipole by using a novel multiple-post approach, effectively focusing the cavity magnetic field within the YIG crystal with a filling factor of 3%. Coupling strength (normal-mode splitting) of 2 GHz (equivalent to 76 cavity linewidths or 0.3 Hz per spin) is achieved for a bright cavity mode that constitutes about 10% of the photon energy and shows that ultrastrong coupling is possible in spin systems at microwave frequencies. With straightforward optimizations we demonstrate that this system has the potential to reach cooperativities of 10 7 , corresponding to a normal-mode splitting of 5.2 GHz and a coupling per spin approaching 1 Hz. We also observe a three-mode strong-coupling regime between a dark cavity mode and a magnon-mode doublet pair, where the photon-magnon and magnon-magnon couplings (normal-mode splittings) are 143 and 12.5 MHz, respectively, with a HWHM bandwidth of about 0.5 MHz.

Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realisation of such devices by doping solid state cavities with paramagnetic ions imposes a trade-off between ion concentration and cavity coherence time.Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultra-pure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid Whispering Gallery/Electron Spin Resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8-19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of a high purity sapphire cooled close to 100 mK reveal the presence of Fe 3+ , Cr 3+ , and V 2+ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition (∆ms = 2) for Fe 3+ , as well as hyperfine transitions of V 2+ .

Employing a sapphire whispering gallery mode resonator, we demonstrate features of the spinphoton interaction in cavities with broken time-reflection symmetry. The broken symmetry leads to a lifting of the degeneracy between left-handed and right-handed polarised cavity photons, which results in an observable gyrotropic effect. In the high-Q cavity limit, such a situation requires a modification of the Tavis-Cummings Hamiltonian to take into account conservation of spin angular momentum and the corresponding selection rules. As a result, the system is represented by a system of two linearly coupled bosonic modes, with each one coupled to its own sub-ensemble of two-level systems with different energy splittings. In the experimental example, these sub-ensembles originate from Fe 3+ impurity ions effectively seen as a two level systems at the interaction frequency. The temperature dependence of the population of each sub-ensemble (in terms of effective susceptibility of the medium) is determined experimentally in accordance with the theoretical predictions revealing various paramagnetic impurity types in the solid. The regimes of backscatterer and spin ensemble domination are discussed and compared.