Considerations on Rydberg transport for antihydrogen formation

1. Considerations on Rydberg transport for antihydrogen formation Daniel Comparat Laboratoire Aimé Cotton Orsay FRANCE

2. Outlook • Consideration with OUR Rybderg atoms n=20-40, k,m=-40-40 • Energy level in F and B • Lifetime in F and B • Decelerator or Transport ? • Force acting on Rydberg, scalling laws, lifetime • Example with time independent electric field F • Example with time dependent electric field • Toward a single well define level ? • Easy to transport • Easy to trap and to accumulate • Trapping Rybderg or Hbar (1s) • What are the possible traps ?

3. Energy levels of Rybderg atoms Approximation (see J. Phys. B 21 3499 (1988), Rev. Mod. Phys. 65 115 (1993)) F // B Values (K) : 15 K, 10 K, 1 K (n=30 ; k~m~l~15, B=1T, Fion=400 V/cm) B=0, n=20-40 B=1T, n=20-40 B=1T, n=30 B=0, n=30 B=0, n=30 B=1T, n=30

4. Lifetime of Rydberg atoms • Typical value 0.1 ns * n^3 m^2 • |k|<n and n>l>|m| • 10-1000µs for m=1-n • F=0, B=0 n l m good numbers • F≠0, B=0 n k m good • F≠0, B ≠ 0 but // m good ~n • F≠0, B ≠ 0 not // ~n • Small lifetime 20 µs PHYSICAL REVIEW A 72, 033405 2005

5. Outlook • Consideration with OUR Rybderg atoms n=20-40, k,m=-40-40 • Energy level in F and B • Lifetime in F and B • Decelerator or Transport ? • Force acting on Rydberg, scalling laws, lifetime • Example with time independent electric field F • Example with time dependent electric field • Toward a single well define level ? • Easy to transport • Easy to trap and to accumulate • Trapping Rybderg or Hbar (1s) • What are the possible traps ?

6. Rydberg Transport • 2 possible schemes • Create Rydberg with velocity -> Deceleration • Difficult to produce cold pbar at 1000m/s • Rydberg and then Hbar (1s or 2s) directly in flight -> Gravity • Create Rydberg at rest -> Transport (acceleration+deceleration) • Much simpler ? to have low temperature for pbar • Simpler design ? due to “symmetry” between acceleration and deceleration (Same final energy that at the beginning) 2 main problems ? Hbar (nl) not trapped (in flight) and not well define single levels 1 VERY good point • Check with high flux normal matter • pbar (proton) + Ps -> Hbar (Hydrogen)

7. Effect on B on Rydberg transport No good numbers • Equation of motion under B and F // fields 1) F and B are time independent N=30, F=0 Ekin, fin - Ekin, in = Epot, fin - Epot, in MAJOR PROBLEM due to the 10 K energy at 1 Tesla for m=15 Solutions: Compensate with Electric field F (no : affect n k not m) Time dependent magnetic field ?? (1T in 100µs ?) Final B = Initial B: YES ? (in the magnetic trap)

8. Static Stark Transport m R''(t) = -3/2 n k a(t) Grad.F(R(t)) with a(t) constant here To simplify with no magnetic field E=3/2 n k F FORCE=3/2 n k dF/dR Position of the Rybderg After few µs Rydberg created at r=0 with v=0 Final Trapping Region after Radiative decay Rlimit = Border of the Penning trap nk=1 nk=2 nk=3 nk=4 R F=Instantaneous Electric Field Electric Field Ionization limit R Pb 1cm travel During lifetime 30µs 4K -> 300 m/s =1cm in 30µs

9. Lifetime limitation on Rydberg transport Only the gradient of F (and B) are importantnot their value (neutral particlules) 1) With Bfinal = Binitial I neglect the paramagnetic term 2) I will neglect after the diamagnetic term in B2 ERROR OF 1 KELVINS ? F Cloud of Rybderg s~3mm Maximum motion during lifetime 10 cm R Ionisation limit Possibility to move 5 cm in 30 µs (n=30; k~10)

10. Time dependent Stark Transport Potential= n k * Instantaneous Electric Field Large nk, oscillate Large nk Rlimit = Border of the Penning trap Rydberg created at r=0 with v=0 R Small nk R Small nk t>0 , constant acceleration for Same motion + oscillation for F=Instantaneous Electric Field Electric Field Ionization limit R R

11. Outlook • Consideration with OUR Rybderg atoms n=20-40, k,m=-40-40 • Energy level in F and B • Lifetime in F and B • Decelerator or Transport ? • Force acting on Rydberg, scalling laws, lifetime • Example with time independent electric field F • Example with time dependent electric field • General case • Toward a single well define level ? • Easy to transport • Easy to trap and to accumulate • Trapping Rybderg or Hbar (1s) • What are the possible traps ?

12. n~20 15µs 1550nm 820 nm 365 nm=730/2 nm 4l 3s 3p 475ns 656 nm 6ns 45ns 2p 2s 1/7 s 1.5ns 121.5 nm = 243/2 nm 1s Creating Single level: Reduce Rydberg lifetime 300 µs for n~m~20. Problems high m radiative decay in Dm=+/- 1 1) Efficient l,m mixing * in electric and crossed magnetic fields (V. Danilov, A.Drozhdin and W. Chou, R. J. Damburg and V. V. Kolosov it.sns.ornl.gov/asd/public/doc/sns0054/sns0054.doc) * RF or µ-wave Second order Stark effect l mixing (same n,m) 3) fs laser n~30->n=3 2) Black body radiation ! Cooke & Gallagher PRL 21 588 (1980) Use of (mercury) lamp 4000 K 1) few mm3 high temperature region 2) Broad band (fs or µ-wave) laser MgH+ Drewsen J. Phys. B: At. Mol. Opt. Phys. 37 4571(2004) 20 µs ; 300 K for n~20. Independent of m !

13. Conclusion • Problem with 1T field (10 K for m~15) • Solution ? Transport toward magnetic trap with same 1T field ? • Create Rydberg at rest • Design to push the pbar -> Fast ? rethermalisation • Transport the « slow » (m,k small) Rydberg the « fast » follow. Few cm in 10 µs-> few mm cloud. Accelerate the deexcitation after the transport • Create Rydberg in well define state • Accelerate the deexcitation with F and B + ? Laser • Excite with laser in a well define nkm Rydberg state • Easy to design a decelerator for this particular state and calculate the coupling toward a magnetic trap (best ? m=0) • Use the 3D picture and clever desing, check for anticrossings