considerations on rydberg transport for antihydrogen formation daniel comparat laboratoire aimé...
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Considerations on Rydberg transport Considerations on Rydberg transport for antihydrogen formationfor antihydrogen formation
Daniel
Comparat
Laboratoire Aimé Cotton
Orsay FRANCE
Outlook
1) Consideration with OUR Rybderg atoms n=20-40, k,m=-40-401) Energy level in F and B2) Lifetime in F and B
2) Decelerator or Transport ?1) Force acting on Rydberg, scalling laws, lifetime2) Example with time independent electric field F3) 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 ?
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, Fion=400 V/cm)
10000 20000 30000 40000Vm
400
300
200
100
K
10000 20000 30000 40000Vm
400
300
200
100
K
10000 20000 30000 40000Vm
30
20
10
10
20
30
K
10000 20000 30000 40000Vm
40
20
20
40
K
100 200 300 400Vm
20
10
10
20
K
100 200 300 400Vm
0.3
0.2
0.1
0.1
0.2
0.3
K
B=0, n=30
B=0, n=30
B=0, n=20-40 B=1T, n=20-40
B=1T, n=30
B=1T, n=30
Lifetime of Rydberg atoms
PHYSICAL REVIEW A 72, 033405 2005
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
Outlook
1) Consideration with OUR Rybderg atoms n=20-40, k,m=-40-401) Energy level in F and B2) Lifetime in F and B
2) Decelerator or Transport ?1) Force acting on Rydberg, scalling laws, lifetime2) Example with time independent electric field F3) 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 ?
Rydberg Transport2 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 pointCheck with high flux normal matter pbar (proton) + Ps -> Hbar (Hydrogen)
1 0.8 0.6 0.4 0.2T
10
5
5
10
K
Effect on B on Rydberg transport
Equation of motion under B and F // fields
1) F and B are time independent
Ekin, fin - Ekin, in = Epot, fin - Epot, 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)
Static Stark Transport
R
FORCE=3/2 n k dF/dR
R
F=Instantaneous Electric Field
nk=1
nk=3nk=2
nk=4
To simplify with no magnetic field E=3/2 n k F
Rlimit = Border of the Penning trap
Final TrappingRegion 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 RybdergAfter few µs
Electric FieldIonization limit
Pb 1cm travelDuring lifetime 30µs
4K -> 300 m/s =1cm in 30µs
Lifetime limitation on Rydberg transport
1) With Bfinal = Binitial I neglect the paramagnetic term2) I will neglect after the diamagnetic term in B2
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 limitPossibility to move 5 cm in 30 µs (n=30; k~10)
Time dependent Stark Transport
R
Potential= n k * Instantaneous Electric Field
Rlimit = Border of the Penning trap
Large nk, oscillate
R
t>0 , constant acceleration forSame motion + oscillation for
Small nkR
Rydberg created at r=0 with v=0
Large nk
Small nk
R
F=Instantaneous Electric Field
Electric FieldIonization limit
Outlook
1) Consideration with OUR Rybderg atoms n=20-40, k,m=-40-401) Energy level in F and B2) Lifetime in F and B
2) Decelerator or Transport ?1) Force acting on Rydberg, scalling laws, lifetime2) Example with time independent electric field F3) Example with time dependent electric field4) 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 ?
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-waveSecond 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 K1) few mm3 high temperature region 2) Broad band (fs or µ-wave) laser
1s
2s
3s 3p
n~20
2p
121.5 nm = 243/2 nm
1.5ns1/7 s
15µs
475ns
45ns6ns
820 nm
656 nm
365 nm=730/2 nm4l
1550nm
3) fs laser n~30->n=3
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 rest1) Design to push the pbar -> Fast ? rethermalisation2) 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 + ? Laser2) Excite with laser in a well define nkm Rydberg state3) 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