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Work Packages of the QuantumPascal Project

Motivation:

Recent advances in optical, microwave, dielectric, and spectroscopic measurement techniques have paved the way for the development of novel and improved means of assessing the number density and pressure of gases. Combined with quantum-based calculations of gas parameters such as the permittivity, and thus the refractivity, novel, powerful, and user-friendly methods can be envisioned which have the potential to become new primary standards of the pascal over the wide pressure range from 1 Pa to 3 MPa and beyond.

Under ideal conditions, when intermolecular forces can be neglected, the refractivity can be linked to the number density of molecules via the dynamic polarisability by use of the Lorentz-Lorenz equation. Moreover, the density can be linked to the pressure by an equation of state which, under ideal conditions (i.e. at low densities/pressures), is given by the ideal gas law. Under more general conditions, both expressions can be expanded to include the intermolecular forces which provide deviations from these ideal relationships by introducing so-called virial coefficients (dielectric or density). If these coefficients have been assessed with sufficient accuracy, or if measurements are taken under conditions where such coefficients play an insignificant role, and if the temperature can be assessed accurately, the pressure of a gas can be assessed with both high precision and high accuracy by measuring the refractivity of the gas. This is the basis for the desired use of the refractivity-based methods as primary pressure standards.

For measurements performed in the optical regime using resonant FP cavities, which is currently the most common means of realising refractometry, the frequencies of the cavity modes will change in proportion to the refractivity of the gas. Hence, since frequency is the entity which can be assessed with the highest accuracy, the refractivity of a gas can be assessed with extraordinarily high precision and accuracy by locking a laser to a given mode of a cavity to monitor the change in the locked laser frequency as the gas is let into the cavity.
Although this is straightforward in theory, there are several issues that, in practice, limit the use of such techniques for accurate assessments of gas density and pressure. Regarding assessment of gas density, any uncontrolled change in the physical length of the cavity will adversely affect the accuracy of the assessment. Such a change in the length of the cavity can have several causes, two of which are cavity deformation due to the pressure of the gas and thermal expansion. When pressure is to be assessed, the accuracy of the assessment of temperature will also affect the accuracy of the pressure assessment. In addition, it is possible that gas can penetrate the cavity spacer material, changing the spacers dimensions and adversely affecting gas exchange processes. Hence, several phenomena prevent such techniques for assessment of gas density and pressure from achieving the highest possible level of precision and accuracy. Similar conditions hold for other types of techniques (e.g. microwave and dielectric methods).

 

WP1 - Pressure measurements by means of Fabry-Perot cavity-based refractometry:

Thus, to develop refractometry to a primary standard, means of circumventing the practical limitations need to be developed. Work package one (WP1) focuses mainly on the causes of the most prominent shortcomings of cavity-based realisations, i.e., cavity deformation, temperature drifts and fluctuations, and gas permeability of the cavity material. After characterising their causes and influences, means of reducing their influence will be worked out. These findings will then serve as the basis for the realisation of FP-based refractometry instrumentation beyond the state of the art.

 

WP2 - Alternative approaches for the realisation of absolute and partial pressure standards:

To explore the potential of quantum-based techniques alternative to FP refractometry, WP2 deals with different means of assessing pressure under a variety of conditions, predominantly using microwave resonators, absorption, and Rayleigh scattering techniques. Overall, the proposed techniques will cover the wide pressure range between 1 Pa to 3 MPa and they not only provide alternative means of assessing gas density/pressure, but can also potentially do so with less influence of the practical limitations which restrict conventional refractometry. In addition, WP2 addresses also a novel experimental validation of theoretical line strength parameter of several absorption lines for the H2O, CO, and CO2 molecules, to realise a partial pressure standard by absorption spectroscopy beyond the state of the art.

 

WP3 - Theoretical values and experimental check:

A prerequisite for developing refractometry for a quantum-based primary pressure standard is accurate knowledge of the polarisability (static or dynamic, depending on the technique used) of the atomic and molecular gas addressed. For the simplest species, this can be obtained from ab-initio calculations. WP3 addresses this issue and deals with calculations of the most prominent virial coefficients, as well as their frequency dependence, since independent realisations utilise different frequency regions. For more complex species, e.g. Ar, the polarisability will obtained by a combination of high accuracy experimental assessments (of the static response) and calculations (of the frequency dependence).

 

WP4 - Comparison with established methods:

To validate the instrumentation developed, WP4 includes a comparison of the novel methods with established ones. It will also encompass a ring comparison of optical transfer standards.