Laser Laboratory for Trace Analysis and Precision Measurements

The Bolztmann constant k_B is one of the fundamental constant in physics. Its current CODATA value is 1.380 648 8(13)×10^-23 J/K, with a relative uncertainty of 0.91 ppm. The international organization CIPM plans to define k_B with a constant value of no errors, and use this constant to redefine the temperature unit Kelvin, thus replacing the present definition based on the triple point of water. In order to avoid unaccounted systematic errors of a singular method, CIPM requires that the planned new definition of k_B must be based on by two independent methods of determination. However, the current level of uncertainty is overwhelmingly due to the acoustic method AGT. Meanwhile, spectroscopic methods based on Doppler broadening of atomic or molecular absorption lines are being developed. Under thermal equilibrium, the absorption lines of low-pressure gas molecules have a Doppler-broadened width (FWHM):

Conventional laser spectroscopy detects an absorption line based on Beer’s absorption law: I = I₀exp[-α(ν) L] , and the line width is determined by fitting the line shape α(ν). As for ro-vibrational transitions of molecules, in order to achieve the required absorption sensitivity, the gas pressure needs to be considerably high (~10² Pa), resulting in relatively complex line shape due to collisions. So far, no models of collision-induced lineshape have achieved the ppm-level of accuracy. Electronic transitions are strong and could be detected at very low pressures. However due to the interference from stray electronic and/or magnetic fields, hyperfine splitting, and power broadening effects, there are tremendous challenges in determining the accurate Doppler width.

Cavity Ring-Down Spectroscopy (CRDS) uses the ring-down time to measure light absorption:

Here $\tau$ and $\tau_{0}$ are ring-down times with and without samples, respectively. They are of the order of micro seconds, and can be determined accurately. This method allows the use of near infrared laser sources. Even on weak infrared transitions of low-pressure gas molecules, sufficient detection sensitivity and dynamic range (Fig.1 vertical axis) can be achieved. We proposes to use a frequency locked CRDS technique, LL-CRDS, which allows controlled scan of laser frequency over 1 GHz (Fig.1 horizontal axis). We believe that LL-CRDS can be advantageous in determining k_B.

Fig.1 CRDS and the Doppler width of an absorption line

We are developing a high precision setup of CRDS, and have already realized a detection sensitivity of 10^-11/cm (equivalent to direct optical absorption path-length of several thousand kilometers) and frequency precision of 1 kHz. The temperature control is at the level of 1 mK. Preliminary results indicate a statistical uncertainty of k_B at 10 ppm. At present, we are building a CRDS setup using a narrow-line diode laser and a cavity temperature at the triple point of water (273.16 K). The transition of CO molecules at 1.6 um is probed. This high-precision method can also find applications in studying molecular collisions, detecting forbidden transitions, and trace analysis for environmental applications.