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...