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

2. Outlook 1)Consideration with OUR Rybderg atoms n=20-40, k,m=-40-40 1)Energy level in F and B 2)Lifetime in F and B 2)Decelerator or Transport ? 1)Force acting on Rydberg, scalling laws, lifetime 2)Example with time independent electric field F 3)Example with time dependent electric field Toward a single well define level ? Easy to transport Easy to trap and to accumulate 1)Trapping Rybderg or Hbar (1s) 1)What are the possible traps ?

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

4. Lifetime of Rydberg atoms PHYSICAL REVIEW A 72, 033405 2005 Typical value 0.1 ns * n^3 m^2 |k| 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

5. Outlook 1)Consideration with OUR Rybderg atoms n=20-40, k,m=-40-40 1)Energy level in F and B 2)Lifetime in F and B 2)Decelerator or Transport ? 1)Force acting on Rydberg, scalling laws, lifetime 2)Example with time independent electric field F 3)Example with time dependent electric field Toward a single well define level ? Easy to transport Easy to trap and to accumulate 1)Trapping Rybderg or Hbar (1s) 1)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 Equation of motion under B and F // fields 1) F and B are time independent E kin, fin - E kin, in = E pot, fin - E pot, in No good numbers MAJOR PROBLEM due to the 10 K energy at 1 Tesla for m=15 N=30, F=0 Solutions: 1)Compensate with Electric field F (no : affect n k not m) 2)Time dependent magnetic field ?? (1T in 100µs ?) 3)Final B = Initial B: YES ? (in the magnetic trap)

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

9. Lifetime limitation on Rydberg transport 1) With B final = B initial I neglect the paramagnetic term 2) I will neglect after the diamagnetic term in B 2 ERROR OF 1 KELVINS ? Only the gradient of F (and B) are important not their value (neutral particlules) Maximum motion during lifetime 10 cm R F Cloud of Rybderg  mm Ionisation limit Possibility to move 5 cm in 30 µs (n=30; k~10)

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

11. Outlook 1)Consideration with OUR Rybderg atoms n=20-40, k,m=-40-40 1)Energy level in F and B 2)Lifetime in F and B 2)Decelerator or Transport ? 1)Force acting on Rydberg, scalling laws, lifetime 2)Example with time independent electric field F 3)Example with time dependent electric field 4)General case 3)Toward a single well define level ? 1)Easy to transport 2)Easy to trap and to accumulate 4)Trapping Rybderg or Hbar (1s) 1)What are the possible traps ?

12. Creating Single level: Reduce Rydberg lifetime 300 µs for n~m~20. Problems high m radiative decay in  m=+/- 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) 2) Black body radiation ! 20 µs ; 300 K for n~20. Independent of m ! Cooke & Gallagher PRL 21 588 (1980) MgH + Drewsen J. Phys. B: At. Mol. Opt. Phys. 37 4571 (2004) Use of (mercury) lamp 4000 K 1) few mm 3 high temperature region 2) Broad band (fs or µ-wave) laser 1s 2s 3s3p n~20 2p 121.5 nm = 243/2 nm 1.5ns 1/7 s 15µs 475ns 45ns 6ns 820 nm 656 nm 365 nm=730/2 nm 4l 1550nm 3) fs laser n~30->n=3

13. Conclusion 1)Problem with 1T field (10 K for m~15) 1)Solution ? Transport toward magnetic trap with same 1T field ? 2)Create Rydberg at rest 1)Design to push the pbar -> Fast ? rethermalisation 2)Transport the « slow » (m,k small) Rydberg the « fast » follow. Few cm in 10 µs-> few mm cloud. Accelerate the deexcitation after the transport 3)Create Rydberg in well define state 1)Accelerate the deexcitation with F and B + ? Laser 2)Excite with laser in a well define nkm Rydberg state 3)Easy to design a decelerator for this particular state and calculate the coupling toward a magnetic trap (best ? m=0) 4)Use the 3D picture and clever desing, check for anticrossings