Capture, sympathetic cooling and ground state cooling of H + ions for the project

1. Capture, sympathetic cooling and ground state cooling of H+ ions for the project Laurent Hilico Jean-Philippe Karr Albane Douillet Nicolas Sillitoe Johannes Heinrich Ferdinand Schmidt Kaler Sebastian Wolf

2. Outline • H+ motion control requirements • Capture and cooling challenges • Doppler cooling • Sideband cooling • Adiabatic ramp down of the trapping potential

3. GBAR overview Gravitational Behaviour of Antimatter at Rest

4. Time of flight measurment of g Accurate measurment of g < 1 % g H initial velocity Dv0 < 1 m/s 30 cm T ~ 100 µK What does v0 = 1m/s mean for a trapped H ? Quantum harmonic oscillator m = 1.67 10-27 kg Ground state Dv0 < 1 m/s w < 2p x 5 MHz State-of-the-art in quantum particle confinement

5. Could we use H laser cooling at l = 121 nm ? Doppler limit Recoil limit G = 2p 100 MHz TD = 2400 µK vD ~ 8 m/s > 1 m/s vR ~ 3,3 m/s TR = 650 µK The idea of J. Walz and T. Hänsch H+ = p e+e+ Produce H+ ions Trap and cool H+ ions to the µK range Photodetach the excess positron to get H at rest Observe the free fall General Relativity and Gravitation 36, pp 561-570 (2004) A Proposal to Measure Antimatter Gravity Using Ultracold Antihydrogen Atoms

6. laser p Last Gbar steps H+ Capture and cooling by laser cooled Be+ ions Threshold Photodetachment l=1.7 µm Reaction chamber H at rest H+ g e+ 30 cm Cooling challenges Trapped particule Temperature 3 neV 20 µK Kinetic energy 1 .. 6 keV Temperature 60 .. 200 eV 500 000 K ÷ 1010..11 Frontiers of Quantum world Classical world

7. H+ cooling method ? • Buffer gas cooling Direct laser cooling • Sympathetic cooling by laser cooled Be+ through Coulomb interaction H+ Step 1 Capture in a linear Paul trap and Doppler sympathetic cooling with a Be+ ion cloud → 0.47 mK Step 2 Transfer to precision trap and Raman side band cooling on a Be+/H+ ion pair → 100 µK Step 3 Adiabatic ramp down of the trapping potential → 20 µK, v << 1 m/s 2 mm

8. Timing • AD + ELENA period 100 s • Photodetachment by 313 nm Be+ cooling laser • 313 nm at saturation intensity H+ life time ~ 1 s • hollow beam ~ 10 s laser

9. Step 1 H+ capture and Doppler sympathetic cooling time

10. t H+ intake Ubiais=980 V time 0 V Capture efficiency Be+ laser cooled ions 1 keV H+ ions Biased linear RF Paul trap Output end-caps Input end-caps 1000… 0 V Versus initial temperature (eV) Versus intake delay t eV

11. Doppler sympathetic cooling time 600 Be+ H+ Axial trapping potential How long does it take ?

12. Plasma physics n = 3 x 1013 m-3 q1= q2= 1,6 x 10-19 C mH+ = 1,67 x 10-27 kg mr = 9/10 mH+

13. Oscillating projectile in a finite size plasma Harmonic axial potential T = 0,33 µs L = 0,8 mm H+ Axial trapping potential ! Stopping time ~ Conclusion

14. Numerical simulations 15360 ions • Time dependant RF trapping forces • Exact Coulomb interaction N2 terms • 37 Flop per term • Laser cooling absorption momentum kicks spontaneous emission stimulated emission • Injection of sympathetically cooled ions on the trap axis • Parallel implementation: CPU FORTRAN and GPU CUDA Thanks to Pierre Dupré

15. Time steps < 0,2 ns for 13 MHz RF adaptative time step down to 1 ps for Coulomb collisions Small dt Too large dt 10 ms <dt> = 10 ps

16. 600 Be+ Sympathetically cooled H+ trajectory Initial energy 53 meV (600 K) stopping time with 600 Be+ 53 meV ~ 2 ms 1 eV ~ 800 ms 10 eV ~ 80 s vz

17. stopping time ~ 8 ms H2+ ion, 232 meV 1 eV 144 ms 10 eV 14 s ath = 2.23 1012 aexp= 2.42 1012

18. Conclusion on Doppler cooling • Should work with < 10 eV projectile ions • Sligthly faster with bigger Be+ ion clouds • Experimental evidence • 40Ar13+ / Be+ J. Crespo, Heidelberg • tests with Ca+/Be+ in Mainz • Be+/H+ in Paris L ~ N1/3 600 → 6000 → 15000 Lisa Schmöger,….. and J. R. Crespo López-UrrutiaReview of Scientific Instruments86 (2015)

19. Step 2 Raman sideband cooling H+/Be+ ion pair 2 mm Mainz precision trap

20. Precision trap – motional couplings Two coupled oscillators in an external potential x,y • z trapping DC potentials • x,y trapping RF effective potentials • Coulomb interaction coupling z H+ Be+ Newton equations equilibrium positions small oscillations in phase mode out of phase mode normal modes individual ion modes x, y, z 1D 3D T. Hasegawa, Phys. Rev. A 83, 053407 (2011) J. B. Wübbena, S. Amairi, O. Mandel, P.O. Schmidt, Phys. Rev. A 85, 043412 (2012)

21. b12 z motion x,y motion mlc/msc Precision trap – motional couplings L. Hilico & al, Int. J. of Modern Physics, Conference Series 30, 1460269 (2014) Efficient sympathetic cooling mLC/mSC 1 b1 = 50 % b2 = 50 % mLC/mSC = 9/1 b1 = 99.986 % b2 = 1.69 % x,y ?

22. Relevant Be+ energy levels Electronic levels Motional levels Harmonic oscillator 2P3/2 F=0, 1, 2, 3 F=1, 2 2P1/2 313.13 nm … few 100 kHz to few MHz n=1 n=0 F=2 F=1 2S1/2 dhfs= 1.25 GHz Ion pair motional ground state Objective : prepare

23. Raman side band cooling, NIST w0-D+dhfs- wi w0-D Stimulated Raman transition Spontaneous Raman transitions H+ Be+ w0 D ~ tens of GHz 2P3/2 F=0, 1, 2, 3 F=1, 2 2P1/2 313.13 nm 2S1/2 n=2 dhfs= 1.25 GHz n=3 n=2 wvibr

24. Raman side band cooling Stimulated Raman transition no spontaneous emission coherent process Rabi oscillation D Population transfert probability Lamb Dicke parameter For n → n-1, p pulse duration n=2 ~ 10 ms < 0.84 s n=3 n=2

25. Step 3 Trapping potential adiabatic ramp down

26. For side band cooling as large as possible For H+ velocity as small as possible • Idea • use a tight trap for coling • slowly ramp down the trap steepness after cooling within ~ 0.1 s to get w’s ~ 10 … 100 kHz To be tested in Mainz on Ca+ ions

27. Experimental progress

28. Next steps H+ injection Capture trap / precision trap Cryo assembly design 313 nm laser : ready

29. Conclusion • Capture and Doppler cooling of < 10 eV H+ in a linear Paul trap • Transfer to precision trap • Doppler and ground state cooling in precision trap OK OK Postdoc position available • ANR BESCOOL • ITN ComiQ