1. (Towards) Extreme Ultraviolet Frequency Comb Spectroscopy of Helium and Helium+ Ions VU University, Netherlands Kjeld Eikema € from ECT* 28 September – 2 november 2012 "Proton size conundrum" Jonas Morgenweg, Itan Barmes, Tjeerd Pinkert Dominik Kandula, Chirstoph Gohle, Anne Lisa Wolf, Stefan Witte

2. Outline  Introduction  To the XUV (at 51-85 nm) with frequency combs: Two-pulse “Ramsey Comb” excitation.  The next generation: “Ramsey-Fourier-Frequency Comb”  First signal with two-pulse two-photon excitation in Rb  Summary en Outlook

3. Frequency comb laser activities @ LaserLaB XUV comb metrology, QED tests: Jonas Morgenweg, Tjeerd Pinkert, Itan Barmes, Dominik Kandula, Christoph Gohle Coherent control: Itan Barmes, Stefan Witte Precision spectroscopy on ions: Anne Lisa Wolf, Jonas Morgenweg, Wim Ubachs, Steven v.d. Berg Dual-comb spectroscopy & mid-IR combs: Axel Ruehl, Alissio Gambetta, Marco Marangoni et al. Precision dissemination over fiber: Tjeerd Pinkert, Jeroen Koelemeij Precision frequency comb calibrations, collaborations with: Wim Ubachs, Jeroen Koelemeij, Rick Bethlem, and others. Wim Vassen: He 2 3 S 1 - 2 1 S 0 transition, Science 333, 196-198 (2011) 15 51 nm = 6 PHz 100µm

4. Introduction QED / Ry issues? Hydrogen 1S 2S 243 nm Muonic-hydrogen 1S 2S 2 keV… 6 m C.G. Parthey et al., PRL 107, 203001 (2011) R. Pohl et al, Nature, vol. 466, pp. 213-216 (2010). 2P 1S-2S: 2 466 061 413 187 035 (10) Hz

5. Comparison normal vs. muonic matter 1S 2S Energy 2x 243 nm 1S 2S 2x 60 nm He + H HH Energy  He + 6 mm 0.6 nm (2 keV) 1S 2S 2P 812 nm 0.15 nm (8.2 keV) 1S 2S 2P

6. The 1S-2S values for H and H Theory Experiment  1S-2S  L 1S-2S  1S-2S B 60 +B 7i  L(  R ∞ ) 1S-2S Rel. acc.  L 1S-2S Finite size (nucl. pol.) Rel.  L(  R ∞ ) Z2Z2 Z ≥3.7 Z4r2Z4r2 Z ≥6 Z2Z2 9.869...×10 12 93 856 127(348)* 62 079(295) -543(185) (40 or 15**) 3.7 ppm**** not measured 65 0.7 ppm 2.466...×10 12 7 127 887(44) 1102(44) -8(3) (2) 6.3 ppm 246606143187.035(10) 16 2.2 ppm H (kHz) He + (kHz)Scaling Test B 60 +B 7i 25% 7% or 4%***  1S-2S Z4Z4 83×10 -3 1.3×10 -3 H 1S-2S from C.G. Parthey et al., PRL 107, 203001 (2011)

7. The experimental challenge Hydrogen 1S 2S 2x 243 nm Helium+ 1S 2S 2x 60 nm Helium 1s 2 1s2s 2x 120 nm 51 nm 1s5p <30 nm

8. Frequency comb lasers  T Frequency Comb laser Mode-locked laser Nobel Prize Physics 2005 J. Hall T.W. Hänsch R.J. Glauber

9. Frequency comb lasers frequency Int. 0 f n = f 0 + n. f rep f rep = 1/T f 0 = f rep x  φ CE / 2  time φ CE =  /2 φ CE = 0 v g ≠ v φ T R. Holzwarth et al. PRL 85, 2264 (2000), D.J. Jones et al. Science 288, 635 (2000)

10. Frequency comb lasers as optical rulers  T Experiment beat note measurement; f = f 0 + n f rep + f beat Single-mode laser freq. f Frequency Comb laser

11. Direct frequency comb excitation  T Experiment beat note measurement; f = f 0 + n f rep + f beat Single-mode laser freq. f Frequency Comb laser

12. Upconversion through high-harmonic generation IR pulses XUV (<100 nm) 10 14 W/cm 2 NIR (800 nm) DUV frequency VUVXUVX-RAY harmonic conversion UV Noble gas jet 3rd5th7th9th 333rd …

13. High-harmonic generation (HHG) Corkum & Krausz, Nature Physics 3, 381 (2007) IR ~10 14 W/cm 2

14. Phase coherence of HHG Other experiments: E.g. excitation Kr continuum @ 88 nm, delays~ 100 fs – ps range Cavalieri et al., PRL 13, 133002 (2002) A. Pirri et al. PRA 78, 043410 (2008) and more Phase XUV ~ - I IR

15. Frequency comb up-conversion IR DUV frequency VUVXUV X-RAY harmonic conversion XUV UV f n = f 0 + n f rep f n = p f 0 + m f rep p th harmonic: Near-Infrared:

16. XUV comb generation methods HHG in resonator (MPQ, JILA, Arizona, etc.) C. Gohle et al. Nature 436, 234 2005 A. Ozawa et al., PRL 100, 253901 (2008) R.J. Jones et al. PRL 94, 193201 (2005) I.Hartl et al. Opt. Lett. 32, 2870 (2007), Etc. A. Cingoz et al., Nature 842, 68 (2012) Argon spectroscopy at 82 nm, 3 MHz acc. HHG after amplification (LaserLaB Amsterdam) S. Witte et al. Science 30, 400 (2005) Zinkstok et al. PRA 73, 061801(R) (2006) T.J. Pinkert et al. OL 36, 2026 (2011) (argon 85 nm, neon 60 nm, helium 51 nm) D. Kandula et al. PRA 84, 062512 (2011) D. Kandula et al. PRL 105, 063001 (2010) Helium spectroscopy at 51 nm, 6 MHz acc.

17. Frequency comb lasers – infinite pulse train frequency Int. 0 f n = f 0 + n. f rep f rep = 1/T f 0 = f rep x  φ CE / 2  time φ CE =  /2 φ CE = 0 v g ≠ v φ T

18. Frequency comb lasers - two pulses frequency Int. 0 f n = f 0 + n. f rep f rep = 1/T f 0 = f rep x  φ CE / 2  time φ CE =  /2 φ CE = 0 v g ≠ v φ T

19.  p, k p pump idler signal c (2) fluorescence cone seed  s, k s   ss pp ii  i =  p –  s Parametric chirped pulse amplification BBO crystals pumped by 532 nm at intensities of 7 GW/cm 2  Tuning over 700-1000 nm with little effort  Bandwidth adjustable from 300 nm to 5 nm  No memory effect  Two comb pulses amplified by two synchronized equal pump pulses; microradian pointing sensitivity!

20. HHG of two pulses IR pulses – mJ level XUV pulses few nJ level Divergence <2 mrad <10 14 W/cm 2 f=50 cm I XUV ~ I IR 9

21. At the 15 th harmonic to excite He 15  HHG 15  f CE ~ /300 6 MHz 6.6 ns Helium 1S 2 1S2S 51.6 nm 1S5P (51 nm)

22. Principle and setup schematic overview

23. Ramsey comb excitation of helium at 51 nm Contrast up to 60% at higher rep-rate: 50 as jitter 121 MHz D. Kandula et al. PRL 105, 063001 (2010) D. Kandula et al. PRA 84, 062512 (2011)

24. He ground state measurement systematics  IR phase shifts in OPA  Pulse phase front tilt  Spectral/temporal phase difference between pulses  Doppler shift: varying speed using He, He/Ne, He/Ar & tune angle  Ionization: varying density, pulse intensity ratio  Adiabatic shift in HHG  shift in HHG due to excitation  AC Stark shifts (IR, XUV, ioniz. l.),  DC Stark (field free)  Self-phase modulation (pulse ratio).  Recoil shift 18.5 MHz for 5p  Many more efects!: Tests of chirp, HHG focus position, f 0, out-of-centre phase,....etc.

25. Theory and experiment blue = experiments and red = theory Drake Pachucki S. Bergeson et al. Eikema et al. Accuracy 6 MHz (8 fold improvement)

26. History of the He ground state energy accuracy Blue = experiment Red = theory

27. Tunable XUV Ramsey frequency comb Argon Neon Helium ~84 nm (9 th harm. in Xe) ~51 nm (15 th harm. in Kr) ~60 nm (13 th harm. in Kr) T.J. Pinkert et al. OL 36, 2026 (2011)

28. View of the lab

29. HHG and excitation apparatus

30. Apparent two-pulse limitation: T and  s Signal = cos(  tr T –  s ) T ss An error in  s gives a frequency error in  tr of  tr =  s / T

31. The magic of Fourier transformation Signal = cos(  tr T –  s ) T ss FFT  tr

32. The magic of Fourier transformation Signal = cos(  tr T –  s ) T ss FFT  tr T ss 2T FFT  tr  rep  rep = 2/T ss

33. FC-FTS vs. FC Full-rep-rate excitation T ss 2T FFT  tr  rep  rep = 2/T T 2T  tr  rep  rep = 2/T Full rep. rate coherent addition Two-pulse incoherent addition ss ss ss ss

34. AC-Stark shift T  Stark 2T FFT  tr  rep  rep = 2/T T 2T  tr  rep  rep = 2/T Full rep. rate coherent addition Two-pulse incoherent addition  Stark  Stark  Stark

35. FC-FTS features and requirements  Accuracy and resolution equivalent to full-rep rate excitation  FC-FFT more easily tunable at extreme wavelengths  AC-Stark shift 'free', in contrast to full-rep rate excitation  With more than 1 transition: ’interference’ effects, but possible to model. Simulations for T=160 ns show ~10 kHz accuracy Requirements:  IR FC pulses must be amplified with constant phase and energy, ideally < /1000 and <1% energy fluctuation, irrespective of the time delay between the pulses!

36. The old situation with a delay line D. Kandula et al., Opt. Express, 16, 7071-7082 (2008) power amp. 2 x 200 mJ SHG sync. 7 ps osc. 1064 nm comb laser ~780 nm f rep =150 MHz 2x 2 mJ 200 fs @ 30 Hz Relay imaging 3-stage NOPCPA regen amp. 2 mJ

37. The old situation with a delay line SHG sync. comb laser ~780 nm f rep =125 MHz 3-stage NOPCPA

38. The new system SHG sync. comb laser ~780 nm f rep =125 MHz 2x 2 mJ 10-200 fs, T=8 ns to >10 s rep. rate 300 Hz 3-stage NOPCPA 10 ps osc. 1064 nm power amp. 2 x 120 mJ 'bounce' amp 2 x 1 mJ EOM/AOM pulse picking & scaling T J. Morgenweg and K.S.E. Eikema, OL 37, 208 (2012) J. Morgenweg and K.S.E. Eikema, Las. Phys. Lett. 5, 1 (2012)

39. New pump laser front-end t = 8 ns to >10 s Rep. rate < 1 kHz 30 Hz rep. rate (300 Hz in prep.) 2x 1 mJ 2x 100 mJ

40. (Bounce) amplifier performance (n=7; T osc ~ 8 ns) (n=35) (n=160)

41. Amplified comb pulses - phase measurement  Single shot differential spectral interferometry  Single shot SNR sufficient for 10-20 mrad rms stability  Inaccuracy < 5mrad BS 50 % BS 10% OPCPA NG CCD Camera Oscillator BS 5% PC HHG Spectr. MZ-Interferometer Pulse separation Analysis SP-Filter Fiber

42. Phase of the amplified comb pulses Average phase equal within 5 mrad (/1200) and pulse energy equal within 1% for a 2-pulse delay (16 ns) to 32-pulse delay (256 ns) Laser shots Delay

43. Doppler-’free’ comb excitation in Rb CW lasers: Hansch et al., OC 11, 1 (1974) Nanosecond pulses: Biraben et al., PRL 32, 12 (1974) Picosecond pulses: Fendel et al., OL 32, 6 (2007) Femtosecond pulses, and with spatial coherent control: I. Barmes et al., to be published in Nature Photonics

44. V-shaped phase 100µm Transform-limited Elimination of background by coherent control

45. Two-photon two-pulse Fourier-Ramsey-Comb Excitation of Rb (5S – 7S) Inter-pulse delay T in femtoseconds n=2; T=15.9 ns n=4; T=31.8 ns n=2; T=63.5 ns Fluorescence signal

46. Summary and Outlook  XUV frequency comb metrology demonstrated, 85-50 nm Ground state energy of helium with an accuracy of 6 MHz  Fourier-Ramsey Frequency Comb Excitation with 2 pulses New system and first spectroscopy in Rb shown Few mrad variation over 256 ns; potentially <kHz XUV accuracy  Outlook: He + in an ion trap with Be + cooling for 1S-2S spectr., Two-photon (2*120 nm) in Helium with coherent control, Two-photon in H2 to improve ionization potential to <100 kHz Delay extension up to 100’s of s for Hz-level accuracy? D. Kandula et al. PRL 105, 063001 (2010) D. Kandula et al. PRA 84, 062512 (2011) T.J. Pinkert et al. Opt. Lett. 36, 2026 (2011) J. Morgenweg et al. Opt. Lett. 37, 208 (2011) I. Barmes et al., Nature Photonics, to be published Ions in a Paul trap

47. The people Itan Barmes Tjeerd Pinkert Jonas Morgenweg Wim Ubachs Christoph Gohle Roel Zinkstok Axel Ruehl Stefan Witte Dominik Kandula Amandine Renault Anne Lisa Wolf

48. From here on additional slides

49. Coherent control for Doppler-reduced excitation

50. Full spatial coherent control

51. Spatial and atom selective excitation To be published in Nature Photonics

52. Enhanced signal to noise 15 kHz absolute accuracy Abs. calibration 2.6x better than previous measurements Hyperfine & Isotope shift up to 10x better than before Flat phase V-phase 85 Rb(3-3) 87 Rb(1-1) 85 Rb(2-2) 87 Rb(2-2)

53. Full measurement series, f rep =121.5 MHz Pure He Ne seeded Ar seeded

54. OPA: Pump laser influence on phase Requirements: –Pump pulse wave fronts equal to </20 –Pump pulse intensity equal within few % Then: –Comb amplified wave fronts equal to /300 k = k p – k s - k i

55. 2-pulse ‘Ramsey’ comb principle Phase coherent pulse excitation: Ramsey (1949), Hänsch and coworkers (1976/77), Chebotayev et al. (1976), Snadden et al. (1996), Bellini et al. (1997, 1998),.... Time domainFrequency domain T  = 1/T t t

56. He ground state ionization energy Theory position (Pachucki, PRA 2010)

57. Direct comb spectroscopy in Ca+ for a search of  variation Dipole allowed: 4s 2 S 1/2 -4p 2 P 1/2 or 3/2 Forbidden: 4s 2 S 1/2 -3d 2 D 5/2 All wavelengths of interest accessible with frequency comb at full repetition rate: equilibrium! Ca + ion

58. Relative to: 411 042 129 776 393.2 (1.0) Hz as measured by Chwalla et al, PRL 102, 023002 (2009) Lifetime 3d 2 D 5/2 = 1 second Comb excitation of the 729 nm clock transition A.L. Wolf et al., Opt. Lett. 36, 49 (2011)