The transition wave number from the EF 1 ⌺ g + ͑v =0,N =1͒ energy level of ortho-H 2 to the 54p1 1 ͑0͒ Rydberg state below the X + 2 ⌺ g + ͑v + =0,N + =1͒ ground state of ortho-H 2 + has been measured to be 25 209.997 56Ϯ ͑0.000 22͒ statistical Ϯ ͑0.000 07͒ systematic cm −1 . Combining this result with previous experimental and theoretical results for other energy level intervals, the ionization and dissociation energies of the hydrogen molecule have been determined to be 124 417.491 13͑37͒ and 36 118.069 62͑37͒ cm −1 , respectively, which represents a precision improvement over previous experimental and theoretical results by more than one order of magnitude. The new value of the ionization energy can be regarded as the most precise and accurate experimental result of this quantity, whereas the dissociation energy is a hybrid experimental-theoretical determination.

Precision spectroscopy of simple atomic systems has refined our understanding of the fundamental laws of quantum physics. In particular, helium spectroscopy has played a crucial role in describing two-electron interactions, determining the fine-structure constant and extracting the size of the helium nucleus. Here we present a measurement of the doubly-forbidden 1557-nanometer transition connecting the two metastable states of helium (the lowest energy triplet state 2 3 S 1 and first excited singlet state 2 1 S 0 ), for which quantum electrodynamic and nuclear size effects are very strong. This transition is fourteen orders of magnitude weaker than the most predominantly measured transition in helium. Ultracold, sub-microkelvin, fermionic 3 He and bosonic 4 He atoms are used to obtain a precision of 8×10 −12 , providing a stringent test of two-electron quantum electrodynamic theory and of nuclear few-body theory.

With a phase-modulated extreme ultraviolet pulsed laser source the frequency of the 1 1 S-2 1 P transition of helium at 58 nm has been measured. The phase modulation scheme enabled measurement and reduction of frequency chirp, usually limiting pulsed precision spectroscopy. From the measured transition frequency of 5 130 495 083͑45͒ MHz, a fourfold improved value of the ground state Lamb shift of 41 224͑45͒ MHz is deduced, in good agreement with a theoretical value of 41 233͑35͒ MHz based on QED calculations up to order ␣ 5 Z 6 . From these measurements, the well-known binding energy of the 2 1 P state and the previously determined 4 He-3 He isotope shift, accurate values for the ionization energies of the helium atom follow: 198 310.6672 (15) cm Ϫ1 for 4 He and 198 301.8808(15) cm Ϫ1 for 3 He. ͓S1050-2947͑97͒05403-6͔ PACS number͑s͒: 32.30.Jc, 12.20.Fv, 42.65.Ky

Highly accurate results from frequency measurements on neutral hydrogen molecules H2, HD and D2 as well as the HD + ion can be interpreted in terms of constraints on possible fifth-force interactions. Where the hydrogen atom is a probe for yet unknown lepton-hadron interactions, and the helium atom is sensitive for lepton-lepton interactions, molecules open the domain to search for additional long-range hadron-hadron forces. First principles calculations in the framework of quantum electrodynamics have now advanced to the level that hydrogen molecules and hydrogen molecular ions have become calculable systems, making them a search-ground for fifth forces. Following a phenomenological treatment of unknown hadron-hadron interactions written in terms of a Yukawa potential of the form V5(r) = β exp(−r/λ)/r current precision measurements on hydrogenic molecules yield a constraint β < 1 × 10 −7 eV·Å for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e. λ ≈ 1Å and beyond.

The remarkable precision of frequency-comb (FC) lasers is transferred to the extreme ultraviolet (XUV, wavelengths shorter than 100 nm), a frequency region previously not accessible to these devices. A frequency comb at XUV wavelengths near 51 nm is generated by amplification and coherent upconversion of a pair of pulses originating from a near-infrared femtosecond FC laser. The phase coherence of the source in the XUV is demonstrated using helium atoms as a ruler and phase detector. Signals in the form of stable Ramsey-like fringes with high contrast are observed when the FC laser is scanned over P states of helium, from which the absolute transition frequency in the XUV can be extracted. This procedure yields a 4 He ionization energy at h  5 945 204 212ð6Þ MHz, improved by nearly an order of magnitude in accuracy, thus challenging QED calculations of this two-electron system. Mode-locked frequency-comb (FC) lasers [1,2] have revolutionized the field of precision laser spectroscopy. Optical atomic clocks using frequency combs are about to redefine the fundamental standard of frequency and time [3]. FC lasers have also vastly contributed to attosecond science by providing a way to synthesize electric fields at optical frequencies [4], made long distance absolute length measurements possible [5], and have recently been employed to produce ultracold molecules [6]. FC based precision spectroscopy on simple atomic systems has provided one of the most stringent tests of bound state quantum electrodynamics (QED) as well as upper bounds on the drift of fundamental constants [7]. Extending these methods into the extreme ultraviolet (XUV, wavelengths below 100 nm) spectral region is highly desirable since this would, for example, allow novel precision QED tests [8].Currently the wavelength range below 120 nm is essentially inaccessible to precision frequency metrology applications due to a lack of power of single frequency lasers and media for frequency up-conversion. Spectroscopic studies on neutral helium using amplified nanosecond laser pulses [9,10] are notoriously plagued by frequency chirping during amplification and harmonic conversion which limits the accuracy. These kind of transient effects can be avoided if a continuous train of high power laser pulses (produced by a FC) can be coherently up-converted. This would transfer the FC modes, at frequencies f n ¼ f CEO þ nf rep , where f CEO is the carrier-envelope offset frequency, f rep is the repetition frequency of the pulses, and n an integer mode number, to the XUV. Similar to what was shown in the visible [11,12], the up-converted pulse train could be used to directly excite a transition, with each of the up-converted modes acting like a single frequency laser.By amplification of a few pulses from the train, and producing low harmonics in crystals and gasses, sufficient coherence has been demonstrated down to 125 nm to perform spectroscopic experiments [13,14]. To reach wavelengths below 120 nm in the extreme ultraviolet or even x rays, high harmonic generati...

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...

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.

Recently the finding of an indication for a decrease of the proton-to-electron mass ratio l = m p /m e by 0.002% in the past 12 billion years was reported in the form of a Letter [E. Reinhold, R. Buning, U. Hollenstein, P. Petitjean, A. Ivanchik, W. Ubachs, Phys. Rev. Lett. 96 (2006) 151101]. Here we will further detail the methods that led to that result and put it in perspective. Laser spectroscopy on molecular hydrogen, using a narrow-band and tunable extreme ultraviolet laser system at the Laser Centre Vrije Universiteit Amsterdam, results in transition wavelengths of spectral lines in theWerner band systems at an accuracy of (4-11) · 10 À8, depending on the wavelength region. This corresponds to an absolute accuracy of 0.000004-0.000010 nm. A database of 233 accurately calibrated H 2 lines is presented here for future reference and comparison with astronomical observations. Recent observations of the same spectroscopic features in cold hydrogen clouds at redshifts z = 2.5947325 and z = 3.0248970 in the line of sight of two quasar light sources (Q 0405À443 and Q 0347À383) resulted in 76 reliably determined transition wavelengths of H 2 lines at accuracies in the range 2 · 10 À7 to 1 · 10 À6 . Those observations were performed with the Ultraviolet and Visible Echelle Spectrograph at the Very Large Telescope of the European Southern Observatory at Paranal, Chile. A third ingredient in the analysis is the calculation of an improved set of sensitivity coefficients K i , a parameter associated with each spectral line, representing the dependence of the transition wavelength on a possible variation of the proton-to-electron mass ratio l. The new model for calculation of the K i sensitivity coefficients is based on a Dunham representation of ground state and excited state level energies, derived from the most accurate data available in literature for the X 1 R þ g ground electronic state and the presently determined level energies in the B 1 R þ u and C 1 P u states. Moreover, the model includes adiabatic corrections to electronic energies as well as local perturbation effects between B and C levels. The full analysis and a tabulation of the resulting K i coefficients is given in this paper. A statistical analysis of the data yields an indication for a variation of the proton-to-electron mass ratio of Dl/l = (2.45 ± 0.59) · 10 À5 for a weighted fit and Dl/l = (1.99 ± 0.58) · 10 À5 for an unweighted fit. This result, indicating the decrease of l, has a statistical significance of 3.5r. Mass-variations as discussed relate to inertial or kinematic masses, rather than gravitational masses. Separate treatment of the data gives a similar positive result for each of the quasars Q 0405À443 and Q 0347À383. The statistical analysis is further documented and possible systematic shifts underlying the data, with the possibility of mimicking a non-zero Dl/l value, are discussed. The observed decrease in l corresponds to a rate of change of d lnl/dt = À2 · 10 À15 per year, if a linear variation with time is assumed. Expe...