Coupling between CaWO$_4$ phonons and Er$^{3+}$ dopants

TL;DR

This study combines density-functional perturbation theory and inelastic neutron scattering to map the full phonon spectrum of CaWO$_4$, a promising host for Er$^{3+}$-based quantum memories. A symmetry analysis identifies eight phonon modes, predominantly Raman-active $A_g$ and $B_g$, that couple directly to Er$^{3+}$ crystal-field operators, including a low-energy $B_g$ mode at $9.1$ meV that strongly mediates spinlattice relaxation. The work provides a microscopic phonon bath description and outlines phonon-engineering strategies—such as nanostructuring to create gaps and waveguide integration—to suppress deleterious phonons and improve storage times and coherence in Er-doped CaWO$_4$ devices. These insights enable targeted optimization of quantum memories in solid-state crystals by controlling phonon–erbium interactions.

Abstract

We investigate the lattice dynamics of CaWO$_4$, a promising host crystal for erbium-based quantum memories, using inelastic neutron scattering together with density-functional perturbation theory. The measured phonon dispersion along the (100), (001), and (101) reciprocal space direction reveals phonon bands extending up to 130 meV, with a gap between 60 and 80 meV, in good agreement with our calculations. From a symmetry analysis of the phonon eigenmodes, we identify eight Raman-active modes that can couple directly to the Er$^{3+}$ crystal-field operators, including a low-energy $B_g$ mode at 9.1 meV that is expected to play a dominant role in phonon-assisted spin-lattice relaxation. These results provide a microscopic description of the phonon bath in CaWO$_4$ and establish a basis for engineering phononic environments to mitigate the loss of stored quantum states and optimize Er-doped CaWO$_4$ for quantum-memory applications.

Figures (6)

• Figure 1: The interaction between the large Er$^{3+}$ magnetic moment and the lattice vibrations (phonons) of the host crystal causes spin-lattice relaxation.
• Figure 2: a The tetragonal unit cell of CaWO$_4$ is described by the $I4_1/a$ space group. b The corresponding Brillouin zone of CaWO$_4$ with the $(h,0,l)$ scattering plane depicted in red. The labels are the high symmetry points. c Erbium dopants are co-ordinated by eight oxygen ligands in a ErO$_8$ polyhedron.
• Figure 3: The comparison between the experimental (left) and calculated (right) reciprocal space map of CaWO$_4$ in the $(h,0,l)$ scattering plane obtained with single crystal x-ray diffraction. The corresponding first Brillouin zone is depicted by the red rectangle, along with the reciprocal space trajectory of the INS experiments on the EIGER and Taipan triple-axis spectrometers.
• Figure 4: The calculated (red lines) and experimental (blue circles) phonon dispersion of CaWO$_4$ along the Z--$\Gamma$--Z$|$R--$\Gamma$--R$|$X--$\Gamma$--X high-symmetry path.
• Figure 5: Comparison between previously reported infrared Jia2006Goncalves2015cavalcante2012electronic and Raman cavalcante2012electronicnicol1971vibrationalBASIEV2000205Christofilos1996pressureSu2007TunableKAUR202027262KAUR2020154804DESOUSA2021157377 active modes and the $\Gamma$-point phonon modes measured in this work.