Noise, Temperature, and the New SI

NIST has recently made substantial improvements to its Johnson-noise thermometry system, which is playing a vital role in the worldwide effort to determine the value of a key physical constant in time for the impending redefinition of the International System of Units (SI) in 2018. The system is now capable of yielding statistical uncertainties 10 times smaller than its predecessor.

“It’s a new era of electronics and systems for noise thermometry,” says Weston Tew, who heads the Johnson Noise Thermometry (JNT) project at NIST’s Gaithersburg, MD, campus. “We’ve had other systems in the past, but this is now the third generation of technology.”

The upgrades will help Tew and colleagues in their pursuit of the most accurate values possible for the Boltzmann constant (k), which relates the total internal energy of a system to its temperature and will be used to redefine the kelvin, the SI unit of thermodynamic temperature. The measurement determines the ratio of k to another fundamental invariant of nature: the Planck constant (h), which relates energy to frequency.

The best authoritative measurements of the Boltzmann constant to date have been made with acoustic thermometers that relate the speed of sound in a gas to thermodynamic temperature. But it is highly desirable to compare values obtained to a similar uncertainty by different physics and different technology. That’s where JNT comes in the SI redefinition.

Johnson noise is the tiny fluctuation in voltage caused by random thermal motion of charge-carriers (chiefly electrons) in a resistor, which is directly proportional to temperature. The greater the amplitude of the voltage fluctuation, the higher the temperature.

JNT measurements are challenging. The thermal voltage noise signal is exceedingly faint compared to other sources of noise in the system -- on the scale of nanovolts (10^-9 V) per square root of the frequency for a 100 ohm resistor at room temperature. Yet NIST’s system can be utilized to measure k to a statistical uncertainty of only about 12 parts per million over one day of averaging.

The key enabling technology is an innovation developed at NIST’s Boulder, CO, laboratories: the Quantized Voltage Noise Source (QVNS). The QVNS generates a precisely controllable amount of voltage fluctuation which is basically equivalent to thermal voltage noise. But the QVNS signal is the opposite of random. It uses arrays of Josephson junctions, superconducting circuits that operate with quantum accuracy. It can be set to any desired value to match the thermal voltage noise of any resistor at any temperature, with output in perfectly quantized integer units of h/2e, where e is the charge of the electron. Thus is serves as a calculable noise source reference.

NIST’s JNT instruments can operate in either of two modes. In the absolute measurement mode, the noise power of the QVNS is programmed to balance that of a thermally generated Johnson noise source, resulting in a thermodynamic temperature independent of any fixed-point reference. In the relative measurement mode, the process is repeated at another temperature and another synthesized noise power, resulting in a thermodynamic temperature ratio. Both methodologies represent a significant advance over conventional JNT methods, which have less flexibility and functionality. 

“We’re generating noise, or rather, pseudo-noise,” Tew says. “You can program these Josephson junctions with a digital code generator that puts out very fast pulses. It looks like noise for all practical purposes, but is deterministic in the sense that it simply repeats a known pattern over and over again. But in the time domain it looks stochastic, noisy.”

That noise signal can be adjusted until it perfectly matches the amplitude of the thermal Johnson noise that exists in any conductor at a finite temperature.

NIST’s JNT research is conducted at three different locations on NIST’s Maryland and Colorado campuses. It is the only experiment in the world that is measuring the ratio of k to h. Doing so makes the measurement of k more accurate because of the much lower uncertainty in the value of h.

In the experiment, the QVNS output is matched to Johnson noise from a resistor kept at the triple point of water. The thermal noise amplitude is proportional to the Boltzmann constant times the temperature, which is known exactly.* The QVNS noise amplitude is determined by multiples of the Planck constant, which is known to an uncertainty of 12 parts per billion. Thus both k and h are incorporated as a ratio from these measurements.

The JNT process entails amplifying both those signals about 50,000-fold using identical apparatus and then matching the two. NIST’s improved electronics suite helps minimize errors in that process. “The beauty of it is that when you amplify the signal and you amplify the pseudo noise in exactly the same way, with the same instrumentation, a lot of systematic errors cancel out,” Tew says. “You can average away all the extraneous noise and what’s left is the noise you really want to measure.”

This capability can be used to measure absolute temperatures at fixed points on the international temperature scale.**

“We are excitedly anticipating the results of this study,” says Gerald Fraser, Chief of NIST’s Sensor Science Division. “If everything goes as planned, the NIST JNT measurements will provide a robust and independent test of the acoustic thermometry measurements that are presently the primary input for the value of the Boltzmann constant when it becomes fixed under the redefinition of the SI.”

* At present, the kelvin is defined in terms of the triple point of water, which is currently regarded as an exactly fixed value of 273.16 K. In the impending redefinition of the kelvin, the value of the Boltzmann constant will be exactly fixed, and the triple-point temperature will be determined experimentally.

** The International Temperature Scale of 1990 and companion documents specify numerous fixed reference points from less than a millikelvin to more than 1350 K. One important function of the JNT is to provide absolute primary thermometer measurements for several of the fixed points in the international temperature scale -- notably those between about 500 K and 1000 K. This is higher than that range typically measured by acoustic thermometry, and overlaps with the range measured with radiometers.