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