Sub-second spin and lifetime-limited optical coherences in $^{171}$Yb$^{3+}$:CaWO$_4$

TL;DR

The paper demonstrates that $^{171}$Yb$^{3+}$ ions in CaWO$_4$ provide both lifetime-limited optical coherence and sub-second electron-nuclear spin coherence at zero magnetic field, enabled by clock-like states and a low-nuclear-spin bath. Through high-resolution spectroscopy and all-optical spin control, the authors map the ground and excited state manifolds, determine hyperfine and g-tensors, and reveal a narrow optical inhomogeneous linewidth of $\Gamma_{inh} \approx 185$ MHz alongside an optical $T_2^o$ up to $0.75$ ms. They show spin coherence times $T_2^s$ reaching $0.15$ s under zero-field conditions, with spin-echo and photon-echo measurements illuminating the decoherence channels, notably spin-flip-flop dynamics that can be suppressed by optical pumping. The work highlights CaWO$_4$ as a low-noise host for ensemble memories and spin-photon interfaces, and it points toward scalable strategies (lower dopant concentration, nuclear-spin-free isotopic purification, and nanophotonic integration) to further extend coherence and enable single-ion control and transduction between microwave and optical domains.

Abstract

Optically addressable solid-state spins have been extensively studied for quantum technologies, offering unique advantages for quantum computing, communication, and sensing. Advancing these applications is generally limited by finding materials that simultaneously provide lifetime-limited optical and long spin coherences. Here, we introduce $^{171}$Yb$^{3+}$ ions doped into a CaWO$_4$ crystal. We perform high-resolution spectroscopy of the excited state, and demonstrate all-optical coherent control of the electron-nuclear spin ensemble. We find narrow inhomogeneous broadening of the optical transitions of 185 MHz and radiative-lifetime-limited coherence time up to 0.75~ms. Next to this, we measure a spin-transition ensemble line width of 5 kHz and electron-nuclear spin coherence time reaching 0.15~seconds at zero magnetic field between 50~mK and 1~K temperatures. These results demonstrate the potential of $^{171}$Yb$^{3+}$:CaWO$_4$ as a low-noise platform for building quantum technologies with ensemble-based memories, microwave-to-optical transducers, and optically addressable single-ion spin qubits.

Figures (15)

• Figure 1: (color online) Energy level diagram and magnetic field dependence of $^{171}$Yb$^{3+}$:CaWO$_4$. (a) CaWO$_4$ crystal structure, with a $^{171}$Yb$^{3+}$ dopant replacing a Ca$^{2+}$ ion at a site of $S_4$ point symmetry. (b) High-resolution absorption spectra of $^{171}$Yb$^{3+}$:CaWO$_4$ at 4 K for light electric field polarized along the $c$ axis ($E \parallel c$) or perpendicular ($E \perp c$) to the $c$ axis. The labeling of the absorption peaks corresponds to the energy level diagram (c). Absorption peak C corresponds to Yb$^{3+}$ isotopes with zero nuclear spin. Absorption peak D only appears for $E \perp c$. (c) Low-field energy level diagram for the $^2$F$_{7/2}(0) \rightarrow ^2$F$_{5/2}(0)$ transition of $^{171}$Yb$^{3+}$:CaWO$_4$ at 973.1 nm. Energy splittings in the ground and excited state are determined using the ground state and extracted excited-state hyperfine tensors. The transitions corresponding to the observed absorption spectrum in (b) are shown with solid lines. (d) Absorption spectra of $^{171}$Yb$^{3+}$:CaWO$_4$ for varying magnetic field strengths applied perpendicular to the crystalline $c$-axis. The polarization of the incident light is $E \perp c$. Dashed lines show the results of the fit to the model given by Eq. (\ref{['eq:Heff']}). Purple lines denote energy levels of the $^{171}$Yb$^{3+}$ ions and blue lines denote energy levels of the $I=0$ isotopes. The color scale is linear.
• Figure 2: (color online) All-optical coherent spin control. (a) Experimental pulse sequence used for all-optical detection of spin coherence. First, we polarise the spin ensemble of $^{171}$Yb$^{3+}$ ions into the $\ket{1}_g$ state by optical pumping around the $\omega_A$ and $\omega_B$ frequencies. We then use optical pulses with frequency $\omega_A$ and $\omega_E$ to induce a Raman transition between the $\ket{1}_g$ and $\ket{4}_g$ spin states. The spin echo sequence with $\tau_{12}$ delay between the first two spin rotations ends with a pulse at the $\omega_A$ frequency used for detecting the spin echo signal. (b) Measurement of the $\ket{1}_g$ - $\ket{4}_g$ transition illustrating the inhomogeneous broadening at zero magnetic field with $\Delta_{14}/2\pi$ detuning around $\omega_A-\omega_E = 3083.85$ MHz. A Gaussian fit gives a FWHM of $\Gamma^s_{\text{inh}}/2\pi$= 5(1) kHz. The shoulder on the main peak is presumed to arise from fast spin flip-flop dynamics depending on the detuning, which modifies the measured lineshape; further measurements at different doping concentrations are needed to confirm this effect. (c) Spin echo intensity as a function of the delay $\tau_{12}$ between the two spin rotations, at zero magnetic field. The solid line is the fit giving $T^s_2 = 0.15(1)$ s. (d) Spin coherence time as a function of the temperature, explained by the model based on flip-flops. The dashed line represents the measured $2T_1$ limit given by the spin-lattice interaction SM. The spin echo decays were fitted with a pure exponential function; no stretch factor was needed, suggesting that the dominant dephasing mechanism remains spin flip-flop dynamics.
• Figure 3: (color online) Optical coherence of $^{171}$Yb$^{3+}$:CaWO$_4$. (a) Left: flip-flops between the addressed ions and the neighboring spins directly contributes to a reduction in spin coherence. Middle: indirect contribution to decoherence due to flips of neighboring spin pairs (light red) producing magnetic noise for the probed ions (dark red). Right: spin dynamics rates for different transitions are highly transition dependent. Flip-flop rates with states involving $\ket{2,3}_g$ are two orders of magnitude larger than for $\ket{1}_g$ - $\ket{4}_g$ transition. (b) Experimental pulse sequence used for photon echo (PE) measurements. It consists of spin polarisation by optical pumping using $\omega_E$ and $\omega_F$ frequencies (see \ref{['fig:1']}(a)). Optical pulses resonant with the D transition are then used for the photon echo (PE) sequence with a $\tau_{12}$ delay between the two pulses. (c) Measurement of the PE intensity at the lowest temperature (50 mK) as a function of the delay $\tau_{12}$ after polarising the spin ensemble of $^{171}$Yb$^{3+}$ ions into $\ket{4}_g$ state (red) or reshuffling population between all the spin states (blue). Solid lines are exponential fits, giving optical coherence times $T^o_2 = 0.75$ ms and $T^o_2 = 0.54$ ms, respectively. (d) Absorption profile after polarising the spin ensemble into $\ket{4}_g$ state (solid line) or reshuffling population between all the spin states (dashed line). (e) Optical coherence time as a function of temperature while reshuffling the spin populations (blue diamond). The optical coherence time when polarising spins into the $\ket{4}_g$ state is enhanced (red circles) and approaches the $2T_1$ limit (dashed line). The solid and dash-dot lines show predictions from the model SM.
• Figure S1: (color online) Crystal field (CF) levels and emission spectra of $^{171}$Yb$^{3+}$:CaWO$_4$. (a) CF splittings of Yb$^{3+}$ reproduced from Pappalardo1963_S. Emission spectra of $^{171}$Yb$^{3+}$:CaWO$_4$ at 10 K excited on the 0 - 1 transition at 963 nm (b) and the 0 - 2 transition at 954 nm (c). Transitions between CF levels are indicated with dashed lines. The line at 981.7 nm is attributed to another Yb$^{3+}$ site.
• Figure S2: (color online) Excited-state $^2$F$_{5/2}$(0) lifetime measurement via fluorescence decay. An exponential fit (solid line) gives 0.385 ms.