1. 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

2. 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= (12) cm−1 [2] D0(H2)exp= (10) cm−1 [3]
Theoretical: E i(H2)cal = cm− [4] D0(H2)cal = cm− [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 >~ cm-1.
[2] A. de Lange, E. Reinhold, and W. Ubachs, Phys. Rev. A 65, (2002).
[3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, and E. E. Eyler, Phys. Rev. Lett. 92, (2004).
[4] L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995).

3. 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)

4. 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

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

6. Relative frequency calibration
He-Ne stabilized etalon
Coherent 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

7. 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)

8. 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

9. Sample spectrum with calibration

10. Measurement of Doppler shift
Beam 1
Beam 2

11. Statistics
(10) cm−1

12. Corrections and error budget

13. 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, (2006).
[6] A. Osterwalder, A. W¨uest, F. Merkt, and Ch. Jungen, J. Chem. Phys. 121, (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, (2006).
[10] V. I. Korobov, Physical Review A 74, (2006).
[11] V. I. Korobov, Physical Review A 77, (2008).
[25] J.-P. Karr, F. Bielsa, A. Douillet, J. P. Gutierrez, V. I. Korobov, and L. Hilico, Phys. Rev. A 77, (2008).

14. 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,
[33] G. Herzberg, Phys. Rev. Lett. 23, 1081 (1969).

15. 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,
[33] G. Herzberg, Phys. Rev. Lett. 23, 1081 (1969).

16. Dissociation energy of H2

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

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

19. 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!

20. DC Stark shift

21. Ar seeding

22. 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)

23. 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 ( 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).

24. Result: pump power-dependence

25. Simulation of frequency excursion

26. Simulation of frequency excursion