Anisotropic Rare-Earth Spin Ensemble Strongly Coupled to a Superconducting Resonator

Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins, magnetically coupled to a superconducting resonator. We report on an on-chip cavity QED experiment with magnetically anisotropic ${\mathrm{Er}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystals and demonstrate collective strong coupling of rare-earth spins to a lumped element resonator. Moreover, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without the aid of a cavity.

Figure 1

(a) Picture of the experiment: two $\mathrm{Er}:\mathrm{YSO}$ crystals are placed on the SC chip with nine LE resonators. The dc magnetic field is applied along the chip’s surface. (b) The simulated ac magnetic field in the plane perpendicular to the dc field in the vicinity of the LE inductor (meander structure). (Inset) Footprint of a LE resonator with a size of $0.6\times 0.6\mathrm{mm}$. (c) Orientation of the crystal’s axis. (d) Dependence of $g$ and $g_1$ on the rotation angle of the crystal around the $x$ axis of the $g$ tensor. The maximal coupling is reached when the ac field is aligned along the largest component of the $g$ tensor.

Figure 2

ESR spectrum of the $\mathrm{Er}:\mathrm{YSO}$ crystals coupled to the LE chip. The dashed lines correspond to four electronic spin transitions of the $\mathrm{Er}:\mathrm{YSO}1$ crystal and the dotted lines to transitions of the $\mathrm{Er}:\mathrm{YSO}2$ crystal. The resonator labels are given on the right. (Inset a) Positions of the LE resonators beneath the crystals were partially identified by measuring the local photo response of the circuit in a separate laser-scanning-microscope (LSM) setup at 4 K [42, 43]. (Inset b) LSM photo-response map measured at the excitation frequency of resonator #5.

Figure 3

(a) Transmission spectrum of resonator #5 strongly coupled to the electronic spin of the $S{2}_a$ transition of the $\mathrm{Er}:\mathrm{YSO}2$ crystal. (Inset) The internal damping rate of the resonator $k_i/2\pi$ clearly resolves the hyperfine spectrum of ${}^{167}\mathrm{Er}^{3+}$. The “HFs” denote magnetic hyperfine transitions and “Q” marks a quadrupole transition. (b) The dark gray line displays the power spectrum $P_{21}=|S_{21}(\omega ){|}^2$ at the anticrossing at 251.3 mT, which is fit using Eq. (3) (blue line). The gray dashed line is the transmitted power measured away from the avoided level crossing at 204.3 mT. (c) The corrected transmitted power spectra taken at 250.6 mT (dark gray line) and at 251.3 mT (gray line) clearly show a normal mode splitting. The dashed lines show the fit to this splitting.

Figure 4

(a) The gray curve presents the absorption profile of the erbium spins coupled to the transmission line at 273.2 mT. The solid line shows a Lorentzian fit to the data. (b) Reappearance of the absorption signal (gray curve) at 5.331 GHz after irradiation of the chip with an intense microwave pulse. The solid line is a fit of the data to an exponential decay.