Atomic and molecular systems for radiation thermometry

This paper introduces and summarizes recent experimental results for two primary radiation thermometry standards, the cold atom thermometer (CAT) and the compact blackbody radiation atomic sensor (CoBRAS), which utilize laser-cooled and vapor-phase rubidium atoms to measure blackbody radiation rates for precise temperature determination.

The Gist

Imagine you have a room full of identical twins. Because they are identical, they all react to the world in the exact same way. Now, imagine you want to measure the temperature of that room, but you don't want to use a standard thermometer that might be slightly off or need to be calibrated against another thermometer. Instead, you want to use the twins themselves as the thermometer.

This paper describes a new way to do exactly that, but with atoms instead of twins. The authors, scientists from the National Institute of Standards and Technology (NIST), propose using atoms and simple molecules as "primary" thermometers. This means they don't need to be compared to other thermometers; they are based on the unchangeable laws of physics that govern how atoms behave.

Here is the simple breakdown of how it works, using the analogies found in the paper:

The Core Idea: Atoms as Light Absorbers

Think of an atom like a tiny, specific radio receiver. It can only "hear" (absorb) a very specific frequency of sound (light or radiation).

• The Environment: Everything around us emits invisible heat radiation called Blackbody Radiation (BBR). Think of this as a constant, gentle hum of energy coming from the walls, the air, and everything else in the room.
• The Interaction: The hotter the room, the louder and more energetic this "hum" is. When this radiation hits an atom, it can push the atom from a low-energy state (calm) to a high-energy state (excited).
• The Measurement: By counting how many atoms get "excited" by this heat radiation, the scientists can calculate exactly how hot the room is. Because the laws of physics that dictate how atoms react are unchangeable, this measurement is considered a "primary standard"—it's the definition of the measurement, not just a copy of one.

The paper details two different experiments they built to test this idea, each looking at a different "note" in the heat radiation symphony.

Experiment 1: The Cold Atom Thermometer (CAT)

The Analogy: Imagine a quiet library where a few people (atoms) are sitting on a specific chair (a high-energy state called a Rydberg state).

• How it works: The scientists use lasers to cool a cloud of Rubidium atoms down to near absolute zero (making them very still). They then use a laser to boost a few of these atoms up to a very high-energy "Rydberg" state.
• The Heat Effect: The heat radiation in the room (specifically at a frequency of 130 GHz, which is in the microwave range) acts like a gentle breeze. This breeze knocks the excited atoms off their high chair and onto a nearby, slightly lower chair.
• The Measurement: The scientists watch how fast the atoms fall off the high chair. The hotter the room, the stronger the breeze, and the faster the atoms fall. By timing this "fall," they can determine the temperature.
• The Result: They achieved an accuracy of about 1%. The paper notes that with better equipment (like better detectors), they could get this down to 0.1%.

Experiment 2: The Compact Blackbody Radiation Atomic Sensor (CoBRAS)

The Analogy: Imagine a busy dance floor (a warm glass cell filled with Rubidium vapor).

• How it works: Instead of cooling the atoms, this experiment uses a warm cloud of atoms. A laser kicks the atoms onto a high-energy dance floor.
• The Heat Effect: The heat radiation in the room (at a frequency of 24.5 THz, which is in the infrared range) pushes some of these atoms onto a different specific dance move.
• The Measurement: As the atoms dance, they eventually fall back down, flashing a light (fluorescence) when they do. The scientists measure the ratio of two different colors of light. One color comes from atoms that were pushed by the heat radiation; the other comes from atoms that just fell naturally.
• The Result: By comparing the brightness of these two colors, they can tell the temperature. This method is incredibly precise, with a sensitivity of about 0.13 Kelvin (a tiny fraction of a degree) after just 34 seconds of watching.

The Catch: The "Recipe" Problem

The paper points out a major hurdle. To use these atoms as perfect thermometers, the scientists need to know the exact "recipe" of how the atoms behave.

• They know the frequency (the note) the atoms react to very precisely.
• However, they are less certain about the strength of the interaction (how easily the heat radiation pushes the atom). This is like knowing the note a radio plays, but not knowing exactly how sensitive the radio's antenna is.

Currently, the accuracy of these atomic thermometers is limited by how well we understand these atomic "recipes" (theoretical calculations). The paper suggests a twist: because Blackbody Radiation is so well understood, we might actually be able to use these thermometers to improve our knowledge of atomic physics, rather than just measuring temperature.

Summary

The paper claims that atoms are perfect candidates for building new, ultra-precise thermometers because they are all identical and follow unchangeable laws. They demonstrated two working prototypes:

1. CAT: Uses cold, high-energy atoms to measure microwave heat radiation.
2. CoBRAS: Uses warm atoms to measure infrared heat radiation by comparing light colors.

While they are currently limited by our theoretical knowledge of atomic physics, they show a clear path toward creating "primary" thermometers that don't need to be calibrated against anything else, offering a new way to measure the world's temperature from the ground up.

Technical Summary

Technical Summary: Atomic and Molecular Systems for Radiation Thermometry

Problem Statement
The scientific community has long recognized that atoms and simple molecules possess identical properties dictated by immutable quantum laws, making them ideal candidates for primary measurement standards. While atoms are established standards for time, magnetic fields, and electric fields, their application as primary standards for radiative temperature remains an emerging frontier. Traditional thermometry often relies on traceability to other thermometers. This paper addresses the challenge of developing primary radiation thermometers based on the fundamental interaction between blackbody radiation (BBR) and quantum states. The core problem is measuring the rate at which BBR induces transitions (absorption or stimulated emission) between atomic states, a rate governed by fundamental constants and atomic properties, thereby allowing temperature determination without reference to a "like-kind" thermometer.

Methodology
The authors propose a framework where temperature is derived from the transition rate $\Omega_{ij}$ between two quantum states $i$ and $j$. This rate is a function of the BBR photon energy density $U_\omega(\omega, T)$ and the atomic dipole matrix element $|\langle i|d|j\rangle|^2$. To interpret experimental data, the authors utilize a system of coupled rate equations (Eq. 3) that model the population dynamics of multi-level atomic systems under the influence of BBR.

Two distinct experimental implementations using Rubidium-85 ($^{85}$Rb) are detailed, probing different regions of the BBR spectrum:

1. Cold Atom Thermometer (CAT):

   • System: A gas of laser-cooled $^{85}$Rb atoms prepared in the Rydberg state $32S_{1/2}$.
   • Mechanism: The atoms are excited via a two-photon process (780 nm and 480 nm lasers). BBR at approximately 130 GHz drives transitions from the $32S$ state to nearby $P$ states (specifically $32P$).
   • Detection: Population transfer is measured using selective field ionization. The timing of ionization peaks relative to the electric field ramp distinguishes between states (e.g., $32S$ vs. $32P$).
   • Analysis: The ratio of populations in the initial state ($32S$ + unresolved $31P$) to the BBR-populated state ($32P$) is tracked over time. The slope of this ratio's evolution is directly proportional to temperature.

2. Compact Blackbody Radiation Atomic Sensor (CoBRAS):

   • System: A warm vapor cell containing $^{85}$Rb atoms.
   • Mechanism: Atoms are optically pumped from the ground state ($5S$) to the $7P_{3/2}$ state using a 359 nm laser. BBR at 12.2 $\mu$m (24.5 THz) drives transitions from $7P$ to the $6D$ state.
   • Detection: The system monitors fluorescence ratios from spontaneous decays. Specifically, it compares the intensity of photons emitted from the BBR-populated $6D$ state (630 nm) against those from the spontaneous-emission populated $7S$ state (741 nm).
   • Analysis: The ratio of these fluorescence signals is independent of laser intensity and atom number, depending primarily on the BBR-induced transition rate. The detection efficiency ratio is determined via calibration against a known temperature.

Key Contributions and Results

• Theoretical Framework: The paper establishes the rate equation models necessary to interpret complex multi-level atomic dynamics driven by BBR, moving beyond idealized two-level systems to account for cascading decays and competing transitions.
• CAT Performance: The CAT experiment successfully demonstrated a primary temperature measurement with a total uncertainty of approximately 1%. The data showed excellent agreement between atomic-determined temperatures and contact thermometry. The authors identify that systematic uncertainties (e.g., detector non-linearity, ion time-of-flight overlap) currently limit precision, but propose that switching to Faraday cup detectors and optimizing optical pumping could reduce uncertainty below 0.1%.
• CoBRAS Performance: The CoBRAS experiment achieved a high relative precision of $u(T) \approx 0.13$ K with only 34 seconds of averaging. While the current implementation relies on calibration to determine detection efficiency ratios, the authors demonstrate that the theoretical shape of the response is governed by Planck's law ($U_\omega$) rather than uncertain atomic parameters, suggesting a clear path toward a primary measurement.
• Spectral Flexibility: The work demonstrates that by selecting different atomic transitions, thermometry can be performed across a vast range of the electromagnetic spectrum, from microwaves (130 GHz) to the mid-infrared (24.5 THz).

Significance and Claims
The authors claim that these systems represent a step toward "primary" radiation thermometry, defined as a measurement not traceable to another thermometer of the same kind. By relying on fundamental constants and immutable atomic properties, these sensors offer the potential for calibration-free operation.

However, the paper maintains a modest stance regarding current limitations. The authors acknowledge that the accuracy of both systems is currently constrained by the precision of atomic theory calculations, specifically the dipole matrix elements $|\langle i|d|j\rangle|^2$, which have uncertainties of roughly 1% in the near-IR and microwave regimes. Consequently, the authors suggest a reciprocal relationship: while BBR thermometry aims to measure temperature, the high accuracy of known BBR sources (uncertainty $< 10^{-4}$) may now be better utilized to refine atomic physics parameters.

The paper concludes that while fully primary thermometers may require further refinement of atomic data, these systems can function as "semi-primary" standards. Such devices would offer the critical advantage of immutability and stability, providing a constant reference that is immune to the drift common in remote sensing radiometers and other conventional thermal sensors.