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arXiv:2507.08140 · Physical review. B./Physical review. B

Crystal fields and Zeeman effect for thulium in solid argon

Jason Marfey, Anthony Semenova, Colin Parker

Published Jun 16, 2025• 1 citation
arXivHTMLPDF

Abstract

Optically active defects suspended in an inert solid are an interesting system for sensing and magnetometry at the nanometer scale, in addition to being a potential source of high-density, identical quantum emitters for quantum information. Beyond their response to external fields, the optical absorption and emission spectra also reflect information about the host matrix, which is critical to understand for either application. For the particular system of thulium atoms implanted in solid argon, high resolution laser spectroscopy reveals narrow ensemble linewidths of the 1140 nm f to f ground state spin-orbit transition, which is split due to crystal field effects and hyperfine coupling. Pump-probe spectroscopy is used to identify crystal field levels in at least two stable trapping sites, and the crystal field is determined to be nearly axial in both sites. Strong selection rules indicate that this transition becomes magnetic-electric in the argon host, most likely due to dielectric effects. In the presence of mT magnetic fields, Zeeman shifts are resolvable by laser fluorescence, allowing crystal axis selective polarized spectroscopy. These results show that all-optical detection schemes for DC magnetic fields are already possible with thulium-doped argon, and point towards more informed strategies for monitoring and improving crystal growth and annealing.

DOI
10.1103/x5zx-ykff

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Optically active defects suspended in an inert solid are an interesting system for sensing and magnetometry at the nanometer scale, in addition to being a potential source of high-density, identical quantum emitters for quantum information. Beyond their response to external fields, the optical absorption and emission spectra also reflect information about the host matrix, which is critical to understand for either application. For the particular system of thulium atoms implanted in solid argon, high resolution laser spectroscopy reveals narrow ensemble linewidths of the 1140 nm f to f ground state spin-orbit transition, which is split due to crystal field effects and hyperfine coupling. Pump-probe spectroscopy is used to identify crystal field levels in at least two stable trapping sites, and the crystal field is determined to be nearly axial in both sites. Strong selection rules indicate that this transition becomes magnetic-electric in the argon host, most likely due to dielectric effects. In the presence of mT magnetic fields, Zeeman shifts are resolvable by laser fluorescence, allowing crystal axis selective polarized spectroscopy. These results show that all-optical detection schemes for DC magnetic fields are already possible with thulium-doped argon, and point towards more informed strategies for monitoring and improving crystal growth and annealing.
Optically active defects in solid-state systems have many applications in quantum information and sensing. However, unlike free atoms, which have fixed optical transition frequencies, the inhomogeneous broadening of the transitions in solid-state environments limit their use as identical scatterers for such applications. Here we show that crystals of argon and neon prepared in a closed-cycle cryostat doped with thulium atoms at cryogenic temperatures are an exception. High resolution absorption and emission spectroscopy show that the 1140 nm magnetic dipole transition is split into multiple components. The origin of this splitting is likely a combination of different classes of trapping sites, crystal field effects within each site, and hyperfine interactions. The individual lines have ensemble widths as small as 0.6GHz0.6\phantom{\rule{4.pt}{0ex}}\text{GHz}0.6GHz, which temperature dependence and pump-probe spectroscopy indicate is likely a homogeneous effect, suggesting inhomogeneity is well below the GHz scale.
We investigate the 1140 nm magnetic-dipole transition of thulium atoms trapped in solid argon and neon. These solids can be straightforwardly grown on any substrate at cryogenic temperatures, making them prime targets for surface-sensing applications. Our data are well described by a splitting of the single vacuum transition into three components in both argon and neon, with each component narrower than the 0.8 nm spectrometer resolution. The lifetime of the excited states is 14.6(0.5) ms in argon and 27(3) ms in neon, shorter than in vacuum or in solid helium. We also collected visible laser-induced fluorescence spectroscopy showing broader emission features in the range of 580--600 nm. The narrow infrared features in particular suggest a range of possible applications.
The excitation, emission spectra, and decay curves of the emission intensity of thulium atoms implanted in liquid and solid helium were observed in the presence and absence of an external magnetic field. The observed narrow line (width $\ensuremath{\sim}0.1$ nm) of the excitation spectrum at 590.60 nm is assigned as a zero-phonon transition from the electronic ground state 4f13(2F7/2o)6s2{4f}^{13}{(}^{2}{F}_{7/2}^{o}{)6s}^{2}4f13(2F7/2o​)6s2, which indicates that the transition between the inner shells is weakly perturbed by surrounding helium atoms. The pressure dependence of the emission wavelength suggests that the symmetry of helium atoms distributed around a thulium atom in the solid phase is similar to that in the liquid phase. The emission intensity was stable and large in the solid phase since thulium atoms were trapped at a density of 1010{}^{10}10--1011{}^{11}11 atoms/cm3{}^{3}3. The lifetime of the excited state was measured to be $7.09\ifmmode\pm\else\textpm\fi{}0.04$ $\ensuremath{\mu}$s, which was longer than that of the 4f12(3H6)5d5/26s2{4f}^{12}{(}^{3}{H}_{6}{)5d}_{5/2}{6s}^{2}4f12(3H6​)5d5/2​6s2 (6,5/2)7/2{(6,5/2)}_{7/2}(6,5/2)7/2​ state of free thulium atoms. The excited state is expected to be a mixed state of the 4f125d6s2{4f}^{12}{5d6s}^{2}4f125d6s2 and 4f136s6p{4f}^{13}6s6p4f136s6p configurations. The metastable state 4f13(2F5/2o)6s2{4f}^{13}{(}^{2}{F}_{5/2}^{o}{)6s}^{2}4f13(2F5/2o​)6s2 is populated by a radiative transition from this excited state and relaxes to the ground state through a magnetic dipole transition. The lifetime of the metastable state of a neutral thulium atom was measured to be $75\ifmmode\pm\else\textpm\fi{}3$ ms.
The influence of magnetic interactions in rare-earth-doped crystals under an external magnetic field has been studied in order to obtain an efficient three-level $\ensuremath{\Lambda}$ system with the hyperfine levels of the rare earth. Nuclear Zeeman effect under the action of an external magnetic field removes the nuclear degeneracy. This interaction does not provide an efficient $\ensuremath{\Lambda}$ system because nuclear-spin flipping such as $\ensuremath{\mid}{M}_{I}⟩=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}\ensuremath{\rightarrow}\ensuremath{\mid}{M}_{I}⟩=\ensuremath{\mp}\frac{1}{2}$ (MI{M}_{I}MI​ is the nuclear-spin projection) cannot be induced by an optical transition. However, this selection rule only applies to pure nuclear Zeeman effect. Indeed, it is shown that the coupling of the electronic Zeeman and of the hyperfine interactions releases the nuclear-spin selection rules $\ensuremath{\Delta}{M}_{I}=0$. This can be described in terms of a pseudonuclear Zeeman effect induced by an effective magnetic field. The relative strengths of the two optical transitions involved in the three-level system can be controlled by the orientation of the external magnetic field. The particular case of the Tm3+{\mathrm{Tm}}^{3+}Tm3+ ion in the Y3Al5O12{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ host (YAG) is discussed. Tm3+{\mathrm{Tm}}^{3+}Tm3+ hyperfine structure is determined using a complete Hamiltonian including free-ion, crystal-field, and magnetic interactions. A good three-level $\ensuremath{\Lambda}$ system is obtained in Tm:YAG with a transition strength ratio of 0.24 $(\ensuremath{\sim}1:4)$ between the two optical transitions. An analytical analysis based on a spin-Hamiltonian approach is proposed to explain the results of the complete crystal-field calculations. Finally, an experimental protocol that makes a crystal similar to the atomic samples used in previous quantum information investigations, with the additional benefits of absence of motion and long coherence time, is described.
Rare-earth-doped crystals have been used for optical signal processing and storage applications. In this dissertation, their potential for quantum computing applications is explored. In one quantum computing scheme, information is stored in nuclear spin states and this information is then processed by using optical pulses through the coupling of these nuclear spin states to a common electronic level. To implement this scheme, nuclear spin states and coupling of these nuclear spin states to a common electronic level is required. Preliminary work in rare-earth materials like Pr3+ and Eu3+ has shown promising results regarding their suitability for quantum computing applications. One particular problem with these materials is that their transition wavelengths are only accessible with dye lasers. These lasers are inherently unstable, and currently few available systems exhibit the stability required for quantum computing applications. An alternative choice was to investigate other rare-earth ions like thulium. Thulium has a transition wavelength that can be accessed with diode lasers, which are commercially available, easy to stabilize, and compact. This dissertation is based on our investigations of Tm3+:YAG for quantum computing applications. Investigations involved a detailed characterization of the material. Nuclear spin states, in Tm3+:YAG, were obtained by applying an external magnetic field to the sample. First, interaction of an external magnetic field with the thulium ions at various sites in the crystal was analyzed. This analysis was used to measure the magnetic anisotropy in the material. These results show that it is possible, with the suitable choice of the magnetic orientation and the site in the crystal, to build a working 3-level quantum system. In the demonstration of single qubit operations in Tm3+:YAG, we first theoretically studied the effect of Gaussian spatial beam on the single qubit operations. Later on, we experimentally prepared a single isolated ensemble of ions in the inhomogeneously broadened absorption profile of the medium. This single isolated ensemble of ions was used as a test-bed to implement the single qubit operations. We also isolated two ensembles of ions in the inhomogeneous absorption profile of the medium. The interaction between these two isolated ensembles of ions was also studied.