Fundamental Vibration of Molecular Hydrogen

Abstract

The fundamental ground tone vibration of H2, HD, and D2 is determined to an accuracy of 2 × 10 −4 cm −1 from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the X 1 Σ + g , v = 0 and v = 1 levels to a common EF 1 Σ + g , v = 0 level. Agreement within 1σ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically-bound system.Quantum electrodynamics (QED), the fully quantized and relativistic version of electromagnetism, solves the problem of infinities associated with charged point-like particles and includes the effects of spontaneous particleantiparticle generation from the vacuum. QED is tested to extreme precision by comparing values for the electromagnetic coupling constant α obtained from measurements of the g-factor of the electron [1] and from interferometric atomic recoil measurements [2]. These experiments and the Lamb shift measurements in atomic hydrogen [3,4] have made QED the most accurately tested theory in physics. Concerning molecules, significant progress has been made recently in theoretical [5] and experimental [6,7] investigations of QED phenomena in the HD + molecular ion, where multiple angular momenta (rotational, electronic and nuclear spins) play a role. Neutral hydrogen has also recently been targeted for QED-tests, via a measurement of the dissociation energy of the H 2 [8], HD [9], and D 2 [10] molecules, and the experimental determination of rotationally excited quantum levels inThe rotationless fundamental ground tone (i.e. the vibrational energy splitting between the v ′′ = 0, J ′′ = 0 and v ′ = 1, J ′ = 0 quantum states) of the neutral hydrogen molecule is an ideal test system for several reasons. The total electronic angular momentum is zero for the X 1 Σ + g ground state and the total nuclear spin for the rotationless J = 0 state of para-H 2 is also zero resulting in a simple spectrum without hyperfine splitting. The hyperfine splitting is extremely small in HD (down to the Hz level [12]) and D 2 in the absence of an I · J interaction for the J = 0 ground state. The recent progress in theory allows for calculations involving relativistic and QED-effects up to order α 4 [13,14]. Energy contributions in the calculation cancel to a large degree for the fundamental ground tone, leading to a significant reduction in the uncertainty, thereby allowing for accurate QED tests.The present study focuses on a precise laser spectroscopic measurement of the rotationless fundamental quantum of vibration in H 2 , HD and D 2 . In the absence of rotation a one-photon transition between the FIG. 1. (Color online)A schematic layout of the experimental setup. The oscillator cavity is seeded by a cw Ti:Sa laser, the pulsed output of which makes multiple passes in an amplifier stage. The amplified output is frequency up-converted in two frequency doubling (SHG) stages leadin...

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

“…An investigation of ac-Stark effects on two-photon transitions in CO was performed by Girard et al [39]. For molecular hydrogen, various studies have been performed on the two-photon excitation in the EF-X system over the years [19,[40][41][42][43]. In the following, we present our evaluation of the ac-Stark effect in F-X (0, 11) transitions where we first discuss line shape effects.…”

“…Investigations on the E-X (0, 1) band in Ref. [19], and more extensively in Ref. [46], also resulted in positive ac-Stark coefficients for Q(J = 0-3) transitions that are about an order of magnitude lower than for the E-X (0, 0) band.…”

“…From both experimental and theoretical perspectives, this multiplicity allows for consistency checks and assessment of systematic effects. In recent years, we have tested the most accurate H 2 quantum chemical calculations using various transitions, for example, the dissociation limit D 0 or binding energy of the ground electronic state [17]; the rotational sequence in the vibrational ground state [18]; and the determination of the ground tone frequency (v = 0 → 1) [19]. The comparisons exhibit excellent agreement thus far and have in turn been interpreted to provide constraints of new physics, such as fifth forces [20] or extra dimensions [21].…”

Observation of electric-dipole-forbidden infrared transitions in cold molecular ions

“…By contrast, to the best of our knowledge no dipole-forbidden vibrational-that is, IR-spectra of molecular ions have been reported so far. Studies of vibrational transitions in molecules, however, are attractive as they probe different spectral domains and dynamic regimes from those in studies of atomic systems 5,8,12 .Dipole-forbidden vibrational transitions in molecules 13 are several orders of magnitude weaker than dipole-forbidden optical transitions typically used in atoms 2,3 , rendering their observation challenging. Thus far, they were observed only in a handful of neutral diatomics, such as H 2 , N 2 and O 2 , using high-pressure samples and/or very long absorption path lengths [14][15][16] .…”

“…By contrast, to the best of our knowledge no dipole-forbidden vibrational-that is, IR-spectra of molecular ions have been reported so far. Studies of vibrational transitions in molecules, however, are attractive as they probe different spectral domains and dynamic regimes from those in studies of atomic systems 5,8,12 .…”