Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD(.).

J Biesheuvel,K S E Eikema,J C J Koelemeij,L Hilico,L Hilico,L Hilico,L Hilico,L Hilico,L Hilico,L Hilico,J-Ph Karr,W Ubachs,J-Ph Karr

doi:10.1038/ncomms10385

Abstract

The simplest molecules in nature, molecular hydrogen ions in the form of H2+ and HD+, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD+ by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.

Highlights

The simplest molecules in nature, molecular hydrogen ions in the form of H2þ and HD þ, provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter
The most precise experimental result3, a frequency measurement of the (v,L): (0,0)–(1,1) rovibrational line at 5.1 mm in HD þ with a relative uncertainty of 1.1 p.p.b., was found to disagree by 2.7 p.p.b. with a more accurate theoretical value obtained from state-of-the-art ab initio molecular theory1,2
Our experimental apparatus and procedure for HD þ spectroscopy are described in detail in the Methods section

Summary

Introduction

The simplest molecules in nature, molecular hydrogen ions in the form of H2þ and HD þ , provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. The most precise experimental result, a frequency measurement of the (v,L): (0,0)–(1,1) rovibrational line at 5.1 mm in HD þ with a relative uncertainty of 1.1 p.p.b., was found to disagree by 2.7 p.p.b. with a more accurate theoretical value obtained from state-of-the-art ab initio molecular theory. The most precise experimental result, a frequency measurement of the (v,L): (0,0)–(1,1) rovibrational line at 5.1 mm in HD þ with a relative uncertainty of 1.1 p.p.b., was found to disagree by 2.7 p.p.b. with a more accurate theoretical value obtained from state-of-the-art ab initio molecular theory1,2 This disagreement has far been unresolved, and additional high-precision experimental data are needed to draw conclusions about the validity of the theoretical framework, and to open up the wide range of applications of molecular hydrogen ion spectroscopy mentioned above. We subsequently exploit the agreement between theory and experiment for the first determination of the proton–electron mass ratio from a molecular system, and to put tighter constraints on the strength and range of ‘fifth forces’ at the molecular scale

Methods

Results

Conclusion