Strong coupling of an ${\mathrm{Er}}^{3+}$-doped ${\mathrm{YAlO}}_3$ crystal to a superconducting resonator

Quantum memories are integral parts of both quantum computers and quantum communication networks. Naturally, such a memory is embedded into a hybrid quantum architecture, which has to meet the requirements of fast gates, long coherence times, and long distance communication. Erbium-doped crystals are well suited as a microwave quantum memory for superconducting circuits with additional access to the optical telecom $C$ band around 1.55 $\mu \mathrm{m}$. Here, we report on circuit QED experiments with an ${\mathrm{Er}}^{3+}$:${\mathrm{YAlO}}_3$ crystal and demonstrate strong coupling to a superconducting lumped element resonator. The low magnetic anisotropy of the host crystal allows for attaining the strong coupling regime at relatively low magnetic fields, which are compatible with superconducting circuits. In addition, ${\mathrm{Ce}}^{3+}$ impurities were detected in the crystal, which showed strong coupling as well.

Figure 1

Simulated ESR spectrum of the Er:YAP crystal. The color bar represents the amplitude of the HF transitions of ${}^{167}\mathrm{Er}$ (23% abundance). The dashed line shows the electronic spin transition of the even isotopes. The horizontal blue line indicated by #1 denotes the resonance frequency of the superconducting LE resonator used in our experiment. The HF spin transitions are labeled accordingly by their nuclear spin projection number $m_I$.

Figure 2

(a) Picture of the hybrid system. The Er:YAP crystal of dimension $2\times 3\times 4$ ${\mathrm{mm}}^3$ is placed on the niobium chip with three LE resonators. The magnetic field is applied parallel to the chip's surface coinciding with the (001) plane of the crystal. The crystal occupies the mode volumes of resonators #1 and #2. (b) The orientation of the crystal's axis is displayed by using $P_{nma}$ notation. The dimensions of the crystal are given in millimeters.

Figure 3

Experimental setup. The hybrid system (see Fig. 2) is placed into a solenoid coil and its complex microwave transmission at 25 mK is measured by a vector network analyzer. The typical probing power at the entrance of the chip is between $-120$ and $-140$ dBm. Attenuators are installed at several temperature stages of the cryostat. A circulator followed by a bandpass filter and cryogenic amplifiers ensure a good signal-to-noise ratio at low powers down to the single photon limit.

Figure 4

ESR sprectrum of the Er:YAP crystal coupled to the LE chip. Two resonators fall into the frequency region of our interest, denoted by #1 and #2. Eight HF transitions of ${}^{167}\mathrm{Er}$ between the states with nuclear spin number $m_I=7/2,5/2,...,-7/2$ are clearly resolved and identified.

Figure 5

(a) Transmission spectrum of resonator #1 strongly coupled to Er:YAP showing an avoided level crossing. (b) The amplitude of transmission spectrum $|S_{21}\left(\omega \right)|$ of an unperturbed and coupled resonator. Arrows indicate the position of the normal mode splitting. (c) Corrected power spectrum $|S_{21}{\left(\omega \right)|}^2$ of normal mode splitting (light gray) at 35 mT. The solid line shows the fit to the theory for zero detuning between the spins and cavity.

Figure 6

Temperature dependence of the coupling strength $v/2\pi$ from 25 to 600 mK. The light gray circles denote the data points and the solid line displays the fit to the theory.

Figure 7

(a) Normalized ESR spectrum $|{\tilde{S}}_{21}{\left(\omega \right)|}^2$ of the Er:YAP crystal coupled to the 50 $\Omega$ transmission line. The absorption line is clearly visible on the spectrum and allows for the determination of the relaxation time $T_1$. The inset shows the typical microwave absorption profile of the Er:YAP crystal taken at 52 mT (gray line) and its fit to a Lorentzian. (b) Spin linewidth versus magnetic field. (c) Dependence of SLR time $T_1$ versus the spin resonance frequency (light gray dots). The solid line shows the fit to the theory. The error bars display statistical error from the fit.

Figure 8

(a) Transmission spectrum of the ${\mathrm{Ce}}^{3+}$:YAP spin ensemble magnetically coupled to LE resonators #1 and #2. Due to the misalignment of the field with respect to the crystal axis, two magnetically inequivalent transitions are observed. (b) Extracted mode splitting (light gray) of the power spectrum $|S_{21}{\left(\omega \right)|}^2$ at 252 mT, where the cerium spins and the LE cavity are in resonance. The solid line displays the fit to the theory.