DETERMINATION OF THE IONIZATION AND DISSOCIATION ENERGIES OF THE HYDROGEN MOLECULE Jinjun Liu,1 Edcel J. Salumbides,2 Urs Hollenstein,1 Jeroen C. J. Koelemeij,2 Kjeld S. E. Eikema,2 Wim Ubachs,2 and Frédéric Merkt1 “A new precision measurement and…” 1 Laboratorium für Physikalische Chemie, ETH-Zürich, 8093 Zürich, Switzerland 2 Department of Physics and Astronomy, Laser Centre, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

Motivation The hydrogen molecule is an important system for testing molecular quantum mechanics. The ionization energy (E i) and dissociation energy (D0) of H2 are benchmark quantities for ab initio calculations. The precision of both the experimental and theoretical values for E i(H2) and D0(H2) has been improved by more than an order of magnitude over the past three decades and the latest ones are: Experimental: E i(H2)exp=124417.476(12) cm−1 [2] D0(H2)exp=36 118.062(10) cm−1 [3] Theoretical: E i(H2)cal =124417.491 cm−1 [4] D0(H2)cal =36 118.069 cm−1 [4] New experimental determination of E i(H2) and/or D0(H2) with improved precision would represent a more stringent test for future theoretical calculations. Uncertainty of Ei(H2)cal is believed to be >~ 0.001 cm-1. [2] A. de Lange, E. Reinhold, and W. Ubachs, Phys. Rev. A 65, 064501 (2002). [3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, and E. E. Eyler, Phys. Rev. Lett. 92, 203003 (2004). [4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).

Energy level diagram binding energy 397 nm 202 nm (6) (7) (5) (4) (3) 1 Explain: Why EF (Ed Eyler, Wim Ubachs) Why 54p Binding energy Not to scale 397 nm 202 nm (2) 2 1 (1)

Experimental setup 202 nm 397 nm Beam 1 Beam 2 Make sure it’s not 2-photon consecutive Beam 1 Beam 2 202 nm 397 nm

Absolute frequency calibration Frequency comb at VU NIR Doppler-free saturation absorption spectroscopy of I2 at VU & ETH

Relative frequency calibration He-Ne stabilized etalon Coherent 899-29 Ti:Sa Ring Laser Lock-in / Piezo Driver/ Oscillator / RF Rriver Polarization Stabilized He-Ne PD1 AOM PD2 PZT Confocal Fabry-Perot Cavity Piezoelectric Transducer

Photoionization spectra of H2 The wave numbers are given relative to the X ^1 \Sigma ^+ _g (v = 0,N = 0) ground state. Assignment based on MQDT (Multichannel Quantum Defect Theory)

Photoionization spectra of H2 397 nm laser ~ 700 µJ The wave numbers are given relative to the X ^1 \Sigma ^+ _g (v = 0,N = 0) ground state. Assignment based on MQDT . 397 nm laser ~ 40 µJ

Sample spectrum with calibration

Measurement of Doppler shift Beam 1 Beam 2

Statistics 12604.99879(10) cm−1

Corrections and error budget

Determination of E i(H2) IR quadrupole laboratory spectrum using a FTIR, plus observational data of the Orion emission lines. [5] S. Hannemann, E. J. Salumbides, S. Witte, R. T. Zinkstok, E. J. van Duijn, K. S. E. Eikema, and W. Ubachs, Phys. Rev. A 74, 062514 (2006). [6] A. Osterwalder, A. W¨uest, F. Merkt, and Ch. Jungen, J. Chem. Phys. 121, 11810 (2004). [8] D. E. Jennings, S. L. Bragg, and J.W. Brault, Astrophys. J. 282, L85 (1984). [9] V. I. Korobov, Physical Review A 73, 024502 (2006). [10] V. I. Korobov, Physical Review A 74, 052506 (2006). [11] V. I. Korobov, Physical Review A 77, 022509 (2008). [25] J.-P. Karr, F. Bielsa, A. Douillet, J. P. Gutierrez, V. I. Korobov, and L. Hilico, Phys. Rev. A 77, 063410 (2008).

History of determination of E i(H2) In late 80s, because of the application of high-resolution laser amplifiers… Ed Eyler. Explain a little bit theory. Order of magnitude of corrections. “…which included adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born–Oppenheimer energies, and are believed to be accurate to within 0.01 cm−1” [4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995). [24] G. Herzberg and Ch. Jungen, J. Mol. Spectrosc. 41, 425 1972. [33] G. Herzberg, Phys. Rev. Lett. 23, 1081 (1969).

History of determination of E i(H2) In late 80s, because of the application of high-resolution laser amplifiers… Ed Eyler. Explain a little bit theory. Order of magnitude of corrections. “…which included adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born–Oppenheimer energies, and are believed to be accurate to within 0.01 cm−1” [4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995). [24] G. Herzberg and Ch. Jungen, J. Mol. Spectrosc. 41, 425 1972. [33] G. Herzberg, Phys. Rev. Lett. 23, 1081 (1969).

Dissociation energy of H2

Dissociation energy of H2 The latest experimental and theoretical values for D0(H2) are: Experimental: D0(H2)exp=36118.062(10) cm−1 [3] Theoretical: D0(H2)cal =36118.069 cm−1 [4] New determination of D0(H2) E i(H2)exp =124417.49111(43) cm-1 E i(H2+)cal=131058.1219761(10) cm-1 [9-11] E i(H)cal =109678.7717414(18) cm-1 D0(H2) =E i(H2)+E i(H2+)-2E i(H) = 36118.06962(37) cm-1 [3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, and E. E. Eyler, Phys. Rev. Lett. 92, 203003 (2004). [4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995). [9] V.I. Korobov, Phys. Rev. A 73, 024502 (2006). [10] V.I. Korobov, Phys. Rev. A 74, 052506 (2006). [11] V.I. Korobov, Phys. Rev. A 77, 022509 (2008).

Conclusions and future work Published in: J. Chem. Phys. 130(17), 174306 (2009) Why HD? D2 and HD

Acknowledgments Thank you! Merkt Group Ubachs Group Dr. H. Knöckel (ETH Zurich) Ubachs Group (VU Amsterdam) Dr. H. Knöckel (Hannover) Edcel J. Salumbides council Merkt Group $ Swiss National Science Foundation $ $ ERC Single Investigator Award $ Thank you!

DC Stark shift

Ar seeding

Frequency chirp measurement Heterodyne (beat-note signal)[18] [18] "Optical heterodyne measurement of pulsed lasers: Toward high-precision pulsed spectroscopy", M. S. Fee, K. Danzmann, and S. Chu, Phys. Rev. A 45, 4911 (1992)

Chirp analysis (a) A low-frequency-pass Fourier filter (<0.1 GHz) was applied to the photodiode signal to retrieve the pulse-amplified NIR power signal (red traces). (b) A Fourier bandpass (0.9-1.1 GHz) was used to obtain the pure beat-note signal. (c) Every 30 points in the pure beat-note signal was fit to a sin function (a “running” fit): , where is the AOM frequency (1 GHz) and the instantaneous phase shift, shown in (Figs. 1-5c). (d) The numerical derivative of was determined to obtain the instantaneous frequency excursion (e) The overall frequency change was obtained by averaging weighted by the NIR power (red trace).

Result: pump power-dependence

Simulation of frequency excursion

Simulation of frequency excursion