Atomic and molecular systems for radiation thermometry

TL;DR

The paper explores a quantum-based approach to radiometric thermometry by linking temperature to blackbody-driven transitions between atomic or molecular states through the rate $\Omega_{ij}$, which scales with the spectral energy density $U_\omega(\omega_{ij}, T)$ and the dipole matrix element $|\langle i|d|j\rangle|^2$. It develops a rate-equation framework to model population dynamics and demonstrates two experimental implementations: the cold atom thermometer (CAT) using Rydberg states at microwave frequencies ($\sim$130 GHz) and the CoBRAS fluorescence-ratio sensor probing infrared frequencies ($\sim$24.5 THz). CAT achieves about 1% relative uncertainty, with prospects to sub-percent levels, while CoBRAS delivers about $u(T)\approx 0.13$ K with rapid averaging and a clear path toward a primary calibration by determining detection-efficiency ratios. The work highlights the potential for primary or semi-primary thermometry based on immutable quantum properties and the well-characterized blackbody spectrum, while noting current limitations from atomic-dipole uncertainties and the need for precise calibration. Overall, the study advances quantum-based radiometric standards and underlines the synergy between accurate BBR knowledge and atomic theory to realize robust temperature sensors.

Abstract

Atoms and simple molecules are excellent candidates for new standards and sensors because they are both all identical and their properties are determined by the immutable laws of quantum physics. Here, we introduce the concept of building a standard and sensor of radiative temperature using atoms and molecules. Such standards are based on precise measurement of the rate at which blackbody radiation (BBR) either excites or stimulates emission for a given atomic transition. We summarize the recent results of two experiments while detailing the rate equation models required for their interpretation. The cold atom thermometer (CAT) uses a gas of laser cooled $^{85}$Rb Rydberg atoms to probe the BBR spectrum near 130~GHz. This primary, {\it i.e.}, not traceable to a measurement of like kind, temperature measurement currently has a total uncertainty of approximately 1~\%, with clear paths toward improvement. The compact blackbody radiation atomic sensor (CoBRAS) uses a vapour of $^{85}$Rb and monitors fluorescence from states that are either populated by BBR or populated by spontaneous emission to measure the blackbody spectrum near 24.5~THz. The CoBRAS has an excellent relative precision of $u(T)\approx 0.13$~K, with a clear path toward implementing a primary

Figures (3)

• Figure 1: Planck's law at $T=300$ K (black curve, left scale) and a stick spectrum showing different atomic dipole strengths (right scale) for different transitions in Rb vs. frequency (bottom axis) and wavelength (top axis). Transitions between $n{\rm S}_{1/2}\rightarrow n{\rm P}_{3/2}$ are show as red, solid sticks; $n{\rm S}_{1/2}\rightarrow (n-1){\rm P}_{3/2}$ are dashed, cyan sticks; $n{\rm P}_{3/2}\rightarrow (n-1){\rm D}_{5/2}$ are dashed-dot purple sticks; and $n{\rm P}_{3/2}\rightarrow (n-2){\rm D}_{5/2}$ are dotted, gray sticks. The highlighted orange and green sticks correspond to the transitions used in the experiments of Secs. \ref{['sec:rydberg_thermometry']} and \ref{['sec:fluorescence_ratio']}, respectively.
• Figure 2: (a) Relevant level diagram of $^{85}$Rb for the cold atom thermometer (CAT) experiment. Atoms in the $5{\rm S}_{1/2}$ ground state are pumped using a 780 nm laser into $5{\rm P}_{3/2}$ intermediate state and further excited using a 480 nm laser into the $32{\rm S}_{1/2}$ state. Blackbody radiation (BBR) then transfers some of the atoms into nearby P states, including 30P, 31P, and 32P. (b) Relative population in various states as a function of BBR interaction time $t$ at $T=296$ K. The theoretical curves are calculated by a rate equation model \ref{['eq:rate_equations']}, using decay rates from ARC sibalic_arc_2017. (c, left panel) Ratio of the 32S+31P peak to the 32P peak $\mathcal{R}$ as a function of blackbody interaction time. Data are shown as points, theoretical prediction with two fit parameters shown as solid curves. (c, right panel) The atomic-determined temperatures (points) together with the contact thermometry determined temperatures (horizontal lines with corresponding uncertainty bars). Figure adapted from Ref. schlossberger_primary_2025.
• Figure 3: (a) Simplified level diagram for the CoBRAS. A laser at 359 nm excites atoms from the ground 5S state to the $7{\rm P}_{3/2}$ state. Atoms can then be further excited by blackbody radiation into states including the 8S or 6D (blue lines) or decay via spontaneous emission to lower energy states including the 7S and 5D states (green lines). Fluorescence from 6D, 7S, and 5D to 5P$_{3/2}$ (red arrows) is monitored by PMTs with the appropriate filter wavelengths indicated. (b, top) The ratio of PMT signals recorded with the 630 nm filter to the 740 nm filter vs. temperature. Blue points indicate the data; solid black curve the thoeretical prediction with one fitted parameter. Gray shaded region indicates the uncertainty in the theory due to atomic physics parameters. (b, bottom) fractional residual of between the data and prediction. Blue band shows the mean and root-mean-squared uncertainty. (c) The ratio of PMT signals recorded with the 762 nm filter to the 740 nm filter (top) and the fractional residuals between the data and prediction (bottom) vs. temperature. Same symbols as is (b). Figure adapted from Ref. mantia_compact_2024.