Erratum: Metrology of high- n Rydberg states of molecular hydrogen with Δν/ν=2×10−10 accuracy [Phys.

Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies ofH2

“…Further excitation from the EF(0,1) state to high-n Rydberg states using the cw UV laser was detected by pulsed-field ionization (PFI), as described in Ref. [37]. The delay between the pulsed VUV radiation and PFI was set to 300 ns, i.e., longer than the lifetime of the EF state (τ (EF) ≈ 200 ns), to ensure that a maximum number of molecules could be excited to Rydberg states.…”

“…To determine the line positions, we fitted the lineshape model described in Ref. [37], which consists, for each Doppler component, of a superposition of three line profiles corresponding to the three hyperfine components of the np1 1 (F = 0 − 2) Rydberg states, with intensities proportional to 2F + 1. For the 54p1 1 and 77p1 1 Rydberg states, we used the hyperfine splittings determined by millimeter-wave spectroscopy [39] and MQDT calculations, respectively.…”

“…Voigt profiles with a full width at half maximum of 9 MHz and a Lorentzian contribution of about 6 MHz were found to best reproduce the measured line profiles. The lineshape depends on the velocity distribution in the volume defined by the intersection of the VUV, UV and gas beams [37,40], with contributions a Estimated by multichannel quantum-defect theory in calculations of the type described in Ref. [39] from transit-time broadening and Doppler-broadening originating from the photon recoil of the B → EF spontaneous emission.…”

“…Table I also lists the other sources of systematic uncertainties considered in our analysis, which were estimated as explained in detail in Ref. [37], and include uncertainties arising from DC and AC Stark shifts, Zeeman shifts, pressure shifts, Doppler shifts, and two contributions of each 100 kHz to account for uncertainties associated with the line-shape model and the unresolved (and unknown) hfs of the EF(0,1) state. The transitions frequencies were corrected by adding 8 kHz for the second-order Doppler shift and subtracting 634 kHz for the photon-recoil shift, which is more than twice as large as the combined statistical and systematic uncertainty of 300 kHz.…”

Dissociation Energy of the Hydrogen Molecule at 10−9 Accuracy

“…The dissociation energies D N =1 0 and D N =0 0 of ortho-and para-H 2 differ by the rota-tional term value of the X(v = 0, N = 1) level, i.e., 118.486 84(10) cm −1 [15].The most accurate previous determination of D 0 (H 2 ), at a relative accuracy of 10 −8 [16], involved two-photon Doppler-free laser excitation to the EF 1 Σ + g (v = 0, N = 1) intermediate state [17], one-photon ultraviolet excitation from the EF 1 Σ + g (0,1) to the 56p1 1 Rydberg state [16], and millimeter wave (MMW) spectroscopy of highlying Rydberg states [18] allowing for an extrapolation to the ionization energy by Multi-Channel Quantum Defect theory (MQDT) [19]. The initial EF-X step in this scheme has recently been improved by two orders of magnitude to an accuracy of 73 kHz [20], but an improvement of D 0 (H 2 ) awaits an improved measurement of the EF-np interval.In the present work, we adopt an alternative excitation scheme to determine D 0 (H 2 ), through the GK 1 Σ + g (1,1) intermediate state, which offers the possibility of using continuous wave (cw) infrared laser excitation to high-n Rydberg states [21]. Experimental results from two laboratories are combined: the measurement of the Dopplerfree two-photon transition GK(1, 1) ← X(0, 1) in Amsterdam, and the determination of the interval between GK(1,1) and the 56p1 1 Rydberg state by near-infrared (NIR) cw-laser spectroscopy in Zürich.In the GK-X experiment, schematically depicted in Fig.…”