Low-temperature microwave properties of biaxial ${\mathrm{YAlO}}_3$

Low-loss crystals with defects due to paramagnetic or rare earth impurity ions are a major area of investigation for quantum hybrid systems at both optical and microwave frequencies. In this work we examine the single-crystal yttrium aluminium perovskite ${\mathrm{YAlO}}_3$ using the whispering gallery mode technique. Multiple resonant microwave modes were measured from room temperature to 20 mK allowing precise characterization of the permittivity tensor at microwave frequencies. We show that it is biaxial and characterize the tensor as a function of temperature with estimated uncertainties below 0.26%. Electron spin resonance spectroscopy was also performed at 20 mK, with transitions identified with zero-field splittings of 16.72 and 9.92 GHz. Spin-photon couplings of order 4.2 and 8.4 MHz were observed for residual levels of concentration, which are stronger than the photon cavity linewidths of 116 kHz but of the same order as the linewidths of the discovered spin transitions.

Figure 1

Room temperature measurement of the mode frequency versus azimuthal mode number ($m$).

Figure 2

Measurement of the YAP real permittivity tensor components as a function of temperature.

Figure 3

Measured temperature dependence of the electrical $Q$ factor of the modes ${\mathrm{WGE}}_{311}$ and ${\mathrm{WGH}}_{511}$ and their respective doublet pairs (marked with an asterisk).

Figure 4

TCP data of the biaxial YAP, YSO [19], and uniaxial sapphire (SAP) [18] crystal permittivity elements.

Figure 5

Energy level splitting of two ionic impurity transitions with applied magnetic field. Each dot corresponds to an avoided level crossing (ALC), the horizontal shaded line represents the WGM at 15.18 GHz, and the angled solid and broken lines show the Zeeman effect of the $f_{ZF1}$ and $f_{ZF2}$ zero-field splittings, respectively. The effective $g$ factors of the transitions are also included.

Figure 6

Magnetic field dependence of the cavity transmission from 0 to 0.25 T. Three interactions under study between the 15.18 GHz photonic mode and the crystal spin ensembles are labeled by the letters A, B, and C. More weakly coupled spin transitions are present below 0.03 T; however these were not investigated further due to poor signal-to-noise ratio, which was not good enough to be seen in the other WGMs at the spread of frequencies shown in Fig. 5.

Figure 7

Frequency shift as a function of the magnetic field: (a) A, (b) B, and (c) C normal mode splittings due the interactions between the spins ensembles and the 15.18 GHz WGM. $\mathrm{\Delta }{f}_{+}$ and $\mathrm{\Delta }{f}_{-}$ correspond to the two coupled modes; (d), (e), and (f) show $Q$ factors of the coupled modes as a function of the magnetic field and correspond to the interactions A, B, and C, respectively. The magnetic field zero detunings are 0.516 T in (a) and (d), 0.88 T in (b) and (e), and 0.169 T in (c) and (f).