Absolute Primary Nanothermometry Using Individual Stark Sublevels of Rare-Earth-doped Crystals

Abstract

We present two independent optical methods for absolute primary thermometry using rare-earth-doped nanoparticles. Both approaches rely exclusively on the internal energy levels and population dynamics of the dopant ions, eliminating the need for external temperature references. We experimentally demonstrate the concepts by using Y$_2$O$_3$: Yb$^{3+}$/Er$^{3+}$ nanoparticles, exploiting Boltzmann distribution between individual Stark sublevels of the Er$^{3+}$ ions, emitting in the green spectral region ($\sim$550 nm) and in the near-infrared spectral region ($\sim$1600 nm). Our strategy establishes rare-earth-based luminescence thermometers as genuine absolute primary probes, conceptually comparable to Johnson noise and acoustic gas thermometers, but with the fundamental advantage of possibly being employed at the nanoscale, potentially down to the single-ion limit, with optical readout and over wide temperature ranges.

Figures (4)

• Figure 1: a: Simplified energy-level diagram of Er$^{3+}$ ions in Y$_2$O$_3$ matrix. The arrow and shaded regions represent spontaneous radiative decay from all Stark sublevels of $^4$I$_{13/2}$ to those of $^4$I$_{15/2}$. b: Resulting luminescence spectra of the electronic transitions as a function of the heat transfer rate, $P$. Y-axis was limited to improve reading. c: $P$ sweep of the two particular Stark-Stark lines (Y$_1$$\rightarrow$ Z$_6$ and Y$_2$$\rightarrow$ Z$_6$) chosen as thermometric probes. The energy centers of the lines were measured at an arbitrary $P$ point according to the methods described in section S3. d: Measured $R_\text{Stark}$ as a function of $P$, for the full working range of the cooling/heating device (cryostat). Inset shows a spectrum at an arbitrary $P$ point with the Voigt fittings of the Stark lines used to calculate $R_\text{Stark}$. e: Derivative of the experimental curve $P \cdot \ln R_\text{Stark}$, demonstrating linearity in the limit of high temperatures. Shaded region shows the limits used to calculate the average of the points (red dashed line).
• Figure 2: a: Comparison between temperature measurements of the proposed optical thermometer (measured T) and the internal cryostat high-resolution reference (nominal T). The solid straight line represents the function $y=x$. The right-hand y-axis shows the difference between these two quantities. b: Characterization of the optical nanothermometer showing the relative sensitivity ($S_r$) and thermal uncertainty ($\sigma_T$).
• Figure 3: Sweep of the resulting luminescence spectra of the transition $^4$S$_{3/2}$$\rightarrow$$^4$I$_{15/2}$ as a function of the heat transfer rate, $P$. Counts are normalized to the maximum peak at 564 nm for visualization. The count rate of the maximum peak is 80 counts/s at room temperature. The shaded spectral areas highlight the lines used for absolute temperature measurements.
• Figure 4: Self-referencing via the inflection point method. Left panel by using E$_1$ and E$_2$ Stark sublevels of $^4$S$_{3/2}$ and right panel by using Y$_1$ and Y$_2$ Stark sublevels of $^4$I$_{13/2}$. a and e: $R_\text{Stark}$ curves as a function of the external control parameter. Insets show the spectra at $P_\text{infl}$ with the Voigt fittings of the Stark lines used. b and f: show the first and second derivatives of the respective experimental curves obtained with a Savitzky-Golay algorithm. The horizontal dashed lines on the second derivative plots mark where it is zero. c and g: Comparison between temperature measurements through the luminescence spectra (measured T) with the internal cryostat references (nominal T). The solid straight lines represent the function $y=x$. The right-hand y-axes show the difference between these two quantities. d and h: Characterization of the optical nanothermometers showing the relative sensitivities and thermal uncertainties.