Experimental setup. a Energy level diagram for the optical 2 F 7/2 (0) ↔ 2 F 5/2 (0) transition of site II in 171 Yb 3+ :Y 2 SiO 5 , with relevant optical and MW transition used in the experiments. b Picture of the loop-gap resonator and the crystal illustrating the common volume excited by the laser E and microwave B MW fields, aligned along the D 2 and b crystal axes, respectively. c MW transmission spectra recorded through the resonator at 5 K and 300 K. d Rabi oscillation time sequence, see text for details, with an example of laser power transmission showing the Rabi oscillations. e MW Hahn echo time sequence, see text for details. The inset shows an example of the optical RHS echo signal, detected through balanced heterodyne detection at a beat frequency of 3 MHz.

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... this work, we study 171 39 . The two electronic states have four nondegenerate hyperfine states at zero magnetic field, see Fig. 1a, due to the highly anistropic hyperfine interaction in Y 2 SiO 5 40 . Previous zero-field spin coherence measurements focused on the low-frequency transitions at 528 and 655 MHz 31,35 , which can be rather efficiently excited by a solenoid coiled around the crystal 21,31 . It is interesting, however, to be able to address any MW ...

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... drive the high-frequency MW transition, we designed a loopgap resonator based on the work by Angerer et al. 42 , which enables efficient and homogeneous driving of the spins over the entire 1-cm length of the Y 2 SiO 5 crystal. In short, the resonator consists of bow-tie type elements, see Fig. 1b, resulting in a lumped element LC-type electrical circuit where the resonance frequency can be tuned by adjusting the distance between the bow ties and the lid. The design of Ref. 42 was modified by adding optical access through two small holes, allowing optical and MW excitation of a common mode, as shown in Fig. 1b. The crystal was ...

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... of bow-tie type elements, see Fig. 1b, resulting in a lumped element LC-type electrical circuit where the resonance frequency can be tuned by adjusting the distance between the bow ties and the lid. The design of Ref. 42 was modified by adding optical access through two small holes, allowing optical and MW excitation of a common mode, as shown in Fig. 1b. The crystal was placed in between the bow ties, with the crystal b-axis along the optical beam, resulting in a good overlap of the MW and optical modes over the length of the crystal. This feature allowed us to generate strong spectroscopic signals in this work, and it will be key for future quantum memory experiments. Note that the ...

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... Fig. 1c, we show transmission spectra acquired with a vector network analyzer (VNA), at a temperature of 300 K and 5 K. Cooling down the resonator typically increased the frequency by ≈10 MHz, which was consistent enough between cool downs such that tuning at room temperature was possible. The transmission linewidth is 4.5 MHz, corresponding ...

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... 2 g states. The transmitted power of the probe laser is recorded on a photodiode, effectively measuring the population in 4 g . The strong ω 41 transition allows a high contrast measurement of the population. An amplified MW pulse at 2496.55 MHz was sent to the resonantor, reaching a power of 43 dBm at the MW input of the cryostat. As shown in Fig. 1d, the MW field induces clear Rabi oscillations between the 2 g and the 4 g states, reaching a frequency of 2π × 560 kHz. The Rabi frequency is comparable to the inhomogeneous spin broadening, which is about 680 kHz. In this spectroscopic study, we employ simple square pulses for the spin echo sequences. Quantum memory experiments will ...

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... spin coherence time can be measured using a Hahn echo sequence on the MW transition, which can be optically detected using Raman heterodyne scattering (RHS) 17,31,45 , see Fig. 1e. A pulsed probe laser tuned to the ω 21 transition first polarizes spins into the 4 g state. Then, the MW Hahn echo sequence is applied, consisting of a 0.42-μs long π/2-pulse and a 0.84-μs long π-pulse, separated by a time τ. The MW echo is detected by applying another probe pulse at the moment of the echo, which produces an RHS ...

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... by a time τ. The MW echo is detected by applying another probe pulse at the moment of the echo, which produces an RHS signal on the strong ω 41 transition. For an increased sensitivity, the RHS signal field amplitude is detected through a balanced heterodyne detection with a local oscillator (LO) detuned by 3 MHz from the RHS signal, see Fig. 1e. The spin echo results will be discussed in the following ...

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... coupled through the hyperfine tensor A g,e . The magnetic dipole moment is μ g,e = μ B g g,e ⋅ S, where g g,e is the Zeeman tensor and μ B the Bohr magneton. In a C 1 point symmetry, A x ≠ A y ≠ A z , which completely lifts degeneracy at B = 0 and results in four hyperfine eigenstates k i j i (k = 1 to 4) in each electronic level (i = g, e), see Fig. 1 a. At B = 0, the hyperfine states are completely hybridized in their electronic and nuclear components, such that 〈S〉 = 〈I〉 = 0. As a consequence, the expectation value of the dipole moment is zero 〈μ g,e 〉 = 0 for all states, and to first order there is no linear Zeeman effect. The zero first-order Zeeman effect (ZEFOZ) at B = 0 leads ...