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

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

GBAR overview Gravitational Behaviour of Antimatter at Rest

g 30 cm Time of flight measurment of g H initial velocity  v 0 < 1 m/s Accurate measurment of g < 1 % T ~ 100 µK What does v 0 = 1m/s mean for a trapped H ? Quantum harmonic oscillator m = kg  v 0 < 1 m/s  < 2  x 5 MHz Ground state State-of-the-art in quantum particle confinement

Could we use H laser cooling at = 121 nm ? Doppler limit Recoil limit  = 2  100 MHz T D = 2400 µK T R = 650 µK v D ~ 8 m/s v R ~ 3,3 m/s > 1 m/s The idea of J. Walz and T. Hänsch 1.Produce H + ions 2.Trap and cool H + ions to the µK range 3.Photodetach the excess positron to get H at rest 4.Observe the free fall General Relativity and Gravitation 36, pp (2004) A Proposal to Measure Antimatter Gravity Using Ultracold Antihydrogen Atoms H + = p e + e +

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

H + cooling method ?  Buffer gas cooling Direct laser cooling Sympathetic cooling by laser cooled Be + through Coulomb interaction 2 mm H+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

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

Step 1 H + capture and Doppler sympathetic cooling time

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

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

Plasma physics n = 3 x m -3 q 1 = q 2 = 1,6 x C m H + = 1,67 x kg m r = 9/10 m H +

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

Numerical simulations Time dependant RF trapping forces Exact Coulomb interaction N 2 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 ions

Small  t Too large  t NFlopCPU 20 cores 100 Gflop/s GPU Titan 1,3 Tflop/s Multi GPU days 7 hrs days18 days18 days /N GPU Time steps < 0,2 ns for 13 MHz RF adaptative time step down to 1 ps for Coulomb collisions 10 ms  t> = 10 ps

vzvz 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 600 Be +

H 2 + ion, 232 meV stopping time ~ 8 ms 1 eV 144 ms 10 eV 14 s a th = a exp =

Conclusion on Doppler cooling Should work with < 10 eV projectile ions Sligthly faster with bigger Be + ion clouds Experimental evidence 40 Ar 13+ / Be + J. Crespo, Heidelberg tests with Ca + /Be + in Mainz Be + /H + in Paris 600 → 6000 → L ~ N 1/3 Lisa Schmöger,….. and J. R. Crespo López-Urrutia Review of Scientific Instruments 86 (2015)

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

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

m lc /m sc b12b12 z motion x,y motion Precision trap – motional couplings m LC /m SC  1 b 1 = 50 % b 2 = 50 % m LC /m SC = 9/1 b 1 = %b 2 = 1.69 % Efficient sympathetic cooling x,y ? L. Hilico & al, Int. J. of Modern Physics, Conference Series 30, (2014)

Relevant Be + energy levels nm 2 S 1/2 2 P 1/2 2 P 3/2 F=0, 1, 2, 3 F=1, 2  hfs = 1.25 GHz Electronic levels Motional levels n=1 n=0 … Harmonic oscillator Objective : prepare F=2 F=1 few 100 kHz to few MHz Ion pair motional ground state

Raman side band cooling, NIST nm 2 S 1/2 2 P 1/2 2 P 3/2 F=0, 1, 2, 3 F=1, 2 Stimulated Raman transition Spontaneous Raman transitions n=3 n=2       hfs -  i   hfs = 1.25 GHz  ~ tens of GHz Be + H+H+  vibr

Raman side band cooling Stimulated Raman transition no spontaneous emission coherent process n=3 n=2 Population transfert probability Lamb Dicke parameter For n → n-1,  pulse duration Single ionb 1 = 13 modes  ~ 100 µs /n/mode Be + /H + b 1z = modesx 4 b 1x,y = modesx 80 ~ 10 ms < 0.84 s  Rabi oscillation

Step 3 Trapping potential adiabatic ramp down

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  ’s ~ 10 … 100 kHz To be tested in Mainz on Ca + ions

Experimental progress

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

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 ANR BESCOOL ITN ComiQ