Precision frequency measurements

Hertkorn, N., Ruecker, C., Meringer, M., Gugisch, R., Frommberger, M., Perdue, E. M., Witt, M., and Schmitt-Kopplin, P. (2007). High-precision frequency measurements Indispensable tools at the core of molecular-level analysis of complex systems. Anal. Bioanal. Chem. 389,1311-1327. 

The cold collision frequency shift is important in precision frequency measurements and has been observed in hydrogen maser [31] and fountain clock [32,33] experiments. From the point of view of precision measurements, the cold collision shift is an obstacle. However, in BEC experiments, the shift provides a helpful diagnostic for the density. 

Abstract. A review is given of the latest adjustment of the values of the fundamental constants. The new values are recommended by the Committee on Data for Science and Technology (CODATA) for international use. Most of the fundamental constants are obtained by the comparison of the results of critical experiments and the corresponding theoretical expressions based on quantum electrodynamics (QED). An important case is the Rydberg constant which is determined primarily by precise frequency measurements in hydrogen and deuterium. 

Bagayev S N, and Chebotaev V P 1990, High-Stability - He-Ne/CHL Laser for Precision Frequency Measurements , Opt. Spectrosc. JSSR), 69, 406-407. 

We have seen that, for diatomic radicals, such as Cl J and SiBr, there are narrow levels belonging to different electronic states that are separated by < 1 cm , while the natural widths of these levels are on the order of 10 Hz. This comes close to what is needed in order to reach the sensitivity of 8a/a 10 , similar to that achieved in the best atomic laboratory tests. In the high-precision frequency measurements, the accuracy is typically better than the linewidth by a few orders of magnitude. In order to be able to benefit from such narrow lines, the molecules need to be cooled. In this respect, the Cl J ion seems particularly promising. 

For an asymmetric top, all three rotation constants can in principle be determined from pure rotation spectra or from vibration-rotation spectra, but the accuracy of some of the constants might be low even though they are derived from very precise frequencies measured in the microwave spectrum. This arises in part because of the problems of centrifugal distortion, but also because the measured line positions could well depend only weakly on one of the rotation constants, which is then correspondingly uncertain. 

As indicated in Section 4.1 (and as should be apparent from the discussion thus far in this chapter), titrimetric analysis methods heavily utilize solution chemistry, and therefore volumes of solutions are prepared, measured, transferred, and analyzed with some degree of frequency in this type of analysis. It should not be surprising that analytical laboratory workers need to be well versed in the selection and proper use of the glassware and devices used for precise volume measurement. 

In the equation s is the measured dielectric constant and e0 the permittivity of the vacuum, M is the molar mass and p the molecular density, while Aa and A (po2) are the isotope effects on the polarizability and the square of the permanent dipole moment respectively. Unfortunately, because the isotope effects under discussion are small, and high precision in measurements of bulk phase polarization is difficult to achieve, this approach has fallen into disfavor and now is only rarely used. Polarizability isotope effects, Aa, are better determined by measuring the frequency dependence of the refractive index (see below), and isotope effects on permanent dipole moments with spectroscopic experiments. 

Section IV explains a new approach to high resolution spectroscopy based on various kinds of saturation effects. Some of the experiments are performed inside the laser resonator, which implies the presence of coupling phenomena between the absorbing molecules under investigation and the laser oscillation itself. These feedback effects can be used for high-precision frequency stabilization and to measure frequency shifts and line profiles with an accuracy never... 

A spectral absorption or emission line does not occur at one precise frequency rather, the line has a measurable width. A convenient measure of this width is Av, the half-width at half maximum, if the line s peak occurs at frequency v0, then at v0 + Av and at v0 — Av the line s intensity has fallen to half its value at v0. There are several causes of the finite width of lines. 

For the isotopes of water, the subgroup is Cs, consisting in the identity and mirror-plane operations. The deuterium isotopes can also be used in calculating force constants for simple molecules. However, even for such simple molecules as HCN and DCN, the use of isotopes does not lead to a unique solution of the vibrational problem. It was emphasized23 that a certain chemical intuition and a feel for the relative magnitude of force constants is involved. Additional information could be taken from other isotopes (13C, 15N, I70), and this helps in determination of a unique solution. However, such isotopes cause only small frequency shifts, so that frequency measurements must be extremely precise. It appears, then, that the use of isotopic substitution leads to some uncertainties in determination of force constants. 

Frequencies assigned to the fundamental vibrations of the triatomic germylenes, stannylenes and plumbylenes are collected in Table 7 together with corresponding data on triatomic silylenes for comparison. The vibrational frequencies are sensitive to the environment of the molecule. Therefore, the most precise frequency values measured under each type of condition used (in the gas phase and in different low-temperature inert matrices) by different spectroscopic methods are shown in the table for each of the CAs. Nonfundamental frequencies of triatomic and observed frequencies of polyatomic germylenes, stannylenes and plumbylenes are listed in the text. 

For maximum sensitivity, the wavelength of the infrared pyrometer should also be selected based on where the spectral radiancy changes most rapidly. For example, in the temperature range depicted in Figure 8.3, a frequency of 1.5 x 10u Hz (2 /im) will permit more precise temperature measurement than a frequency of 0.4 x 1014 Hz (7.5 /im). 

Precision frequency metrology is now compatible for the search of a variation of the constants [38]. A new generation of frequency chains [8] allows to easily do two kind of frequency measurements which were hardly available previously ... 

Two years later, a detection system for Balmer-/ fluorescence was added to the 2S — 45/40 apparatus. Because of the better signal to noise ratio of that signal a remeasurement for both hydrogen and deuterium [23] resulted in improved values. By that time, the relative precision of the 15 Lamb shift already exceeded that of radio frequency measurements of the classic 2S—2P Lamb shift. 

As already mentioned in the second part of this review, we made an average of these different determinations of R00 by performing a least squares adjustment [72] which takes into account all the precise experiments the measurements of the 251/2 Lamb shift, the optical frequency measurements of the 15— 25 and 25 — nD transitions in hydrogen and deuterium, and also the measurements of... 

Another way to obtain the 15 2 Lamb shift is to use the precise optical frequency measurements of the 15 — 25 and 25 — nD5/2 transitions. A first method uses the experimental value of the 25i/2 Lamb shift to extract R00 from the 25i/2 — n-D5/2 splitting (see the first part of table 2). Then the 15i/2 Lamb shift is deduced from the 15 — 25 frequency. The results are given in the second part of table 3. The final result (Lh(1Si/2) = 8 172.840(31) MHz) is more precise than the precedent ones because of the very high accuracy of the optical frequency measurements. The 31 kHz uncertainty is due to the optical frequency measurements (15 kHz) and to the measurement of the 25i/2 Lamb shift (27 kHz). In a second method, we can avoid this limitation by using the 1/n3 scaling law of the Lamb shift. The values obtained this way are slightly... 

In addition to the Rydberg constant a number of different quantities, all based on intrinsically accurate frequency measurements, are needed. Experiments are under way in Stanford in S. Chu s group to measure the photon recoil shift free = fmh/2mcs( of the cesium Di line [48]. Together with the proton-electron mass ratio mp/me, that is known to 2 x 10-9 [49] and even more precise measurements of the cesium to proton mass ratio mcs/mp in Penning traps, that have been reported recently [50], our measurement has already yielded a new value of a [45]. 

In Florence, we have chosen an approach that combines laser spectroscopy with the direct frequency measures of the microwave experiments [4]. We take advantage of the obvious consideration that to obtain the FS separations there s no need to precisely know the optical transitions frequencies but just their differences. Thus, if we have two laser frequencies whose difference can be accurately controlled, we may use one as a fixed reference and tune the second across the atomic resonances, as illustrated by Fig. 1. In fact, our approach reverts to an heterodyne technique, where all the transitions are measured with respect to the same reference frequency, that can take any arbitrary but stable value. In the experimental realisation we obtain the two frequencies by phase-locking two diode lasers (master and slave), i.e. phase-locking their beat note to a microwave oscillator [14]. We show in Fig 2 a full-view of the experimental set-up. 

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