Long spin coherence times in the ground state and in an optically excited state of ${}^{167}\mathrm{Er}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ at zero magnetic field

Spins in solids are an ideal candidate to act as a memory and interface with superconducting qubits due to their long coherence times. We spectroscopically investigate erbium-167-doped yttrium orthosilicate as a possible microwave-addressed memory employing its microwave frequency transitions that occur without applying an external magnetic field. We obtain coherence times of 380 $\mu \mathrm{s}$ in a ground state spin transition and 1.48 ms in an excited state spin transition. This is 28 times longer compared to previous zero field measurements, as well as 200 times longer than a previous microwave memory demonstration in the same material. These long coherence times show that erbium-167-doped yttrium orthosilicate has potential as a microwave-addressed quantum memory.

Figure 1

(a) Energy levels of the ${}^4{\mathrm{I}}_{15/2}{Z}_1$ ground [37] and optically excited ${}^4{\mathrm{I}}_{13/2}{Y}_1$ [38] states of ${}^{167}\mathrm{Er}^{3+}$ as a function of magnetic field applied along the $D_1$ axis. Adjacent levels are plotted with different colors for distinguishability. (b) More detail of the behavior in the ground state near zero magnetic field. The transitions for which we investigate coherence properties are indicated.

Figure 2

(a) Level scheme for Raman heterodyne measurements. (b) Cross section of resonator (green) with the sample (blue) inside. The orientation of the $D_1$, $D_2$, and $b$ axes are indicated on the side. (c) Setup diagram for pulsed Raman heterodyne measurements (see main text for acronym definitions). For CW measurements, most of the setup is bypassed and a network analyzer is placed between points 2 and 1, where it sends a probing signal at point 1 and receives it at point 2.

Figure 3

Raman heterodyne signal as a function of laser and microwave frequencies. Laser frequency is given by the detuning from 195116.5 GHz. Color scales logarithmically with signal intensity (in dB). The dots indicate transitions investigated with applied magnetic fields including transition E which is discussed further in the text. White dots indicated transitions from which spin echoes were measured (A, B, C, and D). The inset shows an enlarged view of the particularly narrow transitions A and B.

Figure 4

Comparison of Raman heterodyne spectra [(a) to (d)] and corresponding predictions from (e), (f), and (h) the ground-state spin Hamiltonian parameters from [37] and (g) excited-state parameters [38]. Color scales linearly with signal intensity for (a) to (d), normalized to the minimum and maximum intensities given by the color bar. For (a), (c), and (d), $B\left|\right|D_2$, and for (b), $B\left|\right|b$, and likewise for the corresponding theory plots. In (e) to (f), bold red lines indicate the predicted transition that corresponds to the measured transition, while black lines indicate other predicted transitions in the same field and frequency range. Note the $y$-axis values differ between the Raman heterodyne data and corresponding theory plot, but are on the same scale.

Figure 5

Dependence of echo intensity on dark time ${\tau }_d$ for transitions A and B at 3.2 K. A linear fitting to the echo height is plotted for transitions B, but only a guiding line between the points is shown for transition A. Inset shows the laser and microwave (MW) pulse sequence used.

Figure 6

Comparison of coherence times measured using two pulse spin echoes. (a) Raman heterodyne spectra as a function of magnetic field from the four transitions, with $B\parallel D_2$, except for B where $B\parallel b$. Color scales linearly with signal intensity. White dotted guiding lines indicate the location of the particular transition and do not come from theory or fitting. (b) Intensities of the echoes measured, with corresponding linear fits, normalized using said linear fits. The resonator temperature was 3.2 K for A and B and 3.14 K for C and D.

Figure 7

(a) Pulse sequences used, where the laser sequence is the same for both MW pulse sequences: on until just before the initial $\pi /2$-pulse, then gated on again where the echo is expected to be. MW1 corresponds to a two-pulse spin echo sequence and MW2 to a dynamic decoupling pulse sequence. (b) Example of an echo from a dynamic decoupling measurement. The yellow trace indicates the timing of the final $\pi$ pulse (ii), the green dashed trace indicates the timing of the laser pulse, and the blue trace indicates the detected Raman heterodyne signal, with the main echo shown darker (i); (iii) indicates an extra echo resulting solely from the $\pi$ pulses and (iv) is leftover free induction decay picked up by the laser gating on. Echo intensity as a function of the total time $T$ since the $\pi /2$ pulse for (c) transitions A and (d) transitions B; for the two-pulse measurements, $T=2\tau$, and for the dynamic decoupling measurements, $T=2N\tau$ where $N$ is the number of $\pi$ pulses. ‘Warm’ and ‘Cold’ correspond to two-pulse spin echo measurements (MW1) made at 4.5 K and 3.2 K, respectively; DD1 and DD2 correspond to the two different frequency components of the echo from dynamic decoupling (MW2, see main text).