Boltzmann Thermometry at Cryogenic Temperatures Exploiting Stark Sublevels in Er ³⁺ /Yb ³⁺ -Codoped Yttrium Oxide Nanoparticles

The development of reliable luminescent nanothermometers for cryogenic applications is essential for advancing quantum technologies, superconducting systems, and other fields that require precise, high-spatial-resolution temperature monitoring. Lanthanide-doped systems are vastly employed to this purpose, and typically perform optimally at or above room temperature when manifold-to-manifold transitions are used. In this work we exploit individual Stark sublevels to demonstrate an optical Boltzmann thermometer based on Er³⁺/Yb³⁺ codoped yttria (Y₂O₃) nanoparticles that operates effectively across the temperature range from 25 to 175 K. This is achieved due to the pronounced crystal field environment of the Y₂O₃ host matrix, leading to well-separated Stark lines in the luminescence spectrum of the Er³⁺ ions. By applying the Luminescence Intensity Ratio (LIR) method to transitions originating from two Stark components of the ⁴S_3/2 manifold of the Er³⁺ ions, we achieve thermal sensitivities up to 1.22% K^-1 at 100 K and temperature resolutions reaching 0.6 K. Our results further experimentally confirm recently published theoretical predictions, demonstrating that thermometric performance is not directly dependent on the peak energy separation of the resulting spectral lines of the involved electronic energy levels when using individual Stark transitions to evaluate the LIR. The proposed procedure gives an energy gap calibration that matches the one determined by sample spectroscopy for nonoverlapping lines in the luminescence spectrum. These insights provide a robust foundation for the design of high-performance cryogenic thermometers based on rare-earth-doped materials.