Rydberg atoms part 1 Tobias Thiele
References
• Part 1: Rydberg atoms
• Part 2: 2 typical (beam) experiments
• T. Gallagher: Rydberg atoms
Content
Introduction – What is „Rydberg“?
• Rydberg atoms are (any) atoms in state with high principal quantum number n.
• Rydberg atoms are (any) atoms with exaggerated properties
equivalent!
Introduction – How was it found?
• In 1885: Balmer series:
– Visible absorption wavelengths of H:
– Other series discovered by Lyman, Brackett, Paschen, ...
– Summarized by Johannes Rydberg:
42
2
n
bn
2
~~
n
Ry
Introduction – Generalization
• In 1885: Balmer series:
– Visible absorption wavelengths of H:
– Other series discovered by Lyman, Brackett, Paschen, ...
– Quantum Defect was found for other atoms:
42
2
n
bn
2)(
~~
ln
Ry
• Energy follows Rydberg formula:
22)( n
hRy
n
hRyEE
l
Introduction – Rydberg atom?
0
0
Ener
gy
0
Hydrogen=13.6 eV
• Energy follows Rydberg formula:
2)( ln
hRyEE
Quantum Defect?
Quantum Defect
Ener
gy
0Hydrogen n-Hydrogen
Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
– No difference in angular momentum states
A
e
Radial parts-Interesting regionsW
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
lδ
nH
H
Interesting Region For Rydberg Atoms
(Helium) Energy Structure
• usually measured
– Only large for low l (s,p,d,f)
• He level structure
• is big for s,p
2)(2
1
lnW
l
l
Excentric orbits penetrate into core.Large deviation from Coulomb.Large phase shift-> large quantum defect
(Helium) Energy Structure
• usually measured
– Only large for low l (s,p,d,f)
• He level structure
• is big for s,p
•
2)(2
1
lnW
l
l
3)(
1
lndn
dW
Electric Dipole Moment
• Electron most of the time far away from core
– Strong electric dipole:
– Proportional to transition matrix element
• We find electric Dipole Moment
–
• Cross Section:
red
ififif rered )cos(
2)cos(1 nllrd if
42nr
3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n
• For non-Hydrogenic Atom (e.g. Helium)
– „Exact“ solution by numeric diagonalization of
in undisturbed (standard) basis ( ,l,m)
FdHH ififif
0
n~
2)(2
1
lnW
Numerov
3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n
Stark Effect EFdHH
0
• Rydberg Atoms very sensitive to electric fields
– Solve: in parabolic coordinates
• Energy-Field dependence: Perturbation-Theory
k
nn 21k
nn 21
Hydrogen Atom in an electric Field
EFdHH
0
)(199)(31716
)(2
3
2
1 522
21
24
212nOmnnnn
FnnnF
nW
Rydberg Atom in an electric Field
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Classical ionization:
– Valid only for
• Non-H atoms if F is
Increased slowly
3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Classical ionization:
– Valid only for
• Non-H atoms if F is
Increased slowly
416
1
nFcl
Rydberg Atom in an electric Field
4
2
16
1
4
1
n
WF
Fzr
V
cl
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
blue
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Quasi-Classical ioniz.:
4
4
2
2
2
2
2
9
29
1
4
44
12)(
n
nZ
WF
FmZV
red
(Hydrogen) Atom in an electric Field
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
416
1
nFcl
49
1
nFr
49
2
nFb
blue
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Quasi-Classical ioniz.:
4
4
2
2
2
2
2
9
29
1
4
44
12)(
n
nZ
WF
FmZV
red
(Hydrogen) Atom in an electric Field
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
416
1
nFcl
49
1
nFr
49
2
nFb
Lifetime
• From Fermis golden rule
– Einstein A coefficient for two states
– Lifetime
2
3
3
,,,
2
,,,12
),max(
3
4nlrln
l
ll
c
eA
lnln
lnln
lnln ,,
1
,,
,,,,
lnln
lnlnln A
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
Lifetime
• From Fermis golden rule
– Einstein A coefficient for two states
– Lifetime
2
3
3
,,,
2
,,,12
),max(
3
4nlrln
l
ll
c
eA
lnln
lnln
lnln ,,
1
,,
,,,,
lnln
lnlnln A
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
For l≈0:Overlap of WF
23
n
30, nn
For l≈0:Constant (dominated by decay to GS)
Lifetime
• From Fermis golden rule
– Einstein A coefficient for two states
– Lifetime
2
3
3
,,,
2
,,,12
),max(
3
4nlrln
l
ll
c
eA
lnln
lnln
lnln ,,
1
,,
,,,,
lnln
lnlnln A
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
For l ≈ n:Overlap of WF
2n
53, ,nnln
For l ≈ n:Overlap of WF
3 n
Lifetime2
3
3
,,,
2
,,,12
),max(
3
4nlrln
l
ll
c
eA
lnln
lnln
1
,,
,,,,
lnln
lnlnln A
StateStark State
60 psmall
Circular state60 l=59 m=59
Statistical mixture
Scaling(overlap of )
Lifetime 7.2 μs 70 ms ms
3n 5n 5.4n
)1,1(),( lnln)l,n(
23
n 2nr
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT53
, ,nnln