Post on 21-Jun-2020
Rydberg atoms
Tobias Thiele
References
• T. Gallagher: Rydberg atoms
Content
• Part 1: Rydberg atoms
• Part 2: A typical beam experiment
Introduction – What is „Rydberg“?
• Rydberg atoms are (any) atoms in state with high principal quantum number n.
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
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
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
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
Introduction – Rydberg formula?
• Energy follows Rydberg formula:
2)( ln
hRyEE
Introduction – Rydberg formula?
• Energy follows Rydberg formula:
2)( ln
hRyEE
13.6 eV
• Energy follows Rydberg formula:
22)( n
hRy
n
hRyEE
l
Introduction – Hydrogen?
0
0
13.6 eV
Ener
gy
0
• Energy follows Rydberg formula:
2)( ln
hRyEE
Quantum Defect?
Quantum Defect
Ener
gy
0
Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
A
e
Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
A
e
Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
A
e
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 regions W
r
rrV
1)(
0
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
Interesting Region For Rydberg Atoms
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
H
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
nH
H
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
lδ
nH
H
(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
(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
(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
(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
3)(
1
lndn
dW
2)(2
1
lnW
Electric Dipole Moment
• Electron most of the time far away from core
– Strong electric dipole:
– Proportional to transition matrix element
red
3)(
1
lndn
dW
2)(2
1
lnW
Electric Dipole Moment
• Electron most of the time far away from core
– Strong electric dipole:
– Proportional to transition matrix element
red
3)(
1
lndn
dW
2)(2
1
lnW
ififif rered )cos(
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
3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
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
Stark Effect
• For non-Hydrogenic Atom (e.g. Helium)
– „Exact“ solution by numeric diagonalization of
in undisturbed (standard) basis ( ,l,m)
FdHH ififif
0
n~
3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n
EFdHH
0
• 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
3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n
Stark Effect EFdHH
0
• 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
n=12
n=11
n=13
Stark Map Hydrogen
Levels degenerate
n=12
n=11
n=13
Stark Map Hydrogen
n=12
n=11
n=13
k=-11 blue
k=11 red
Stark Map Hydrogen
Cross perfect Runge-Lenz vector conserved
Levels degenerate
n=12
n=11
n=13
Stark Map Hydrogen
n=12
n=11
n=13
Stark Map Helium
Levels not degenerate
n=12
n=11
n=13
Stark Map Helium
n=12
n=11
n=13
k=-11 blue
k=11 red
Stark Map Helium
n=12
n=11
n=13
k=-11 blue
k=11 red
s-type
Stark Map Helium
Do not cross! No coulomb-potential
Levels degenerate
n=12
n=11
n=13
Stark Map Helium
Stark Map Helium
n=12
n=11
n=13
Inglis-Teller Limit n-5
• 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
Hydrogen 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
Hydrogen 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
Hydrogen 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
4
2
16
1
4
1
n
WF
Fzr
V
cl
416
1
nFcl
416
1 nFcl3)(
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
Hydrogen 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
Hydrogen Atom in an electric Field
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Quasi-Classical ioniz.:
2
20
2
2
2
4
44
12)(
Z
WF
FmZV
m
416
1
nFcl
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Quasi-Classical ioniz.:
Hydrogen Atom in an electric Field
4
2
20
2
2
2
9
1
4
44
12)(
nZ
WF
FmZV
m
416
1
nFcl
49
1
nFr
red
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
• When do Rydberg atoms ionize?
– No field applied
– Electric Field applied
– Quasi-Classical ioniz.:
416
1
nFcl
49
1
nFr
Hydrogen Atom in an electric Field
4
4
2
2
2
2
2
9
29
1
4
44
12)(
n
nZ
WF
FmZV
red
blue
49
2
nFb
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT
Hydrogen Atom in an electric Field
classic
Red states
Blue states
Inglis-Teller
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 ,,
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
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 l0: Overlap of WF
23
n
30, nn
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 ln: Overlap of WF
2n
53, ,nnln
For ln: Overlap of WF
3 n
Lifetime 2
3
3
,,,
2
,,,12
),max(
3
4nlrln
l
ll
c
eA
lnln
lnln
1
,,
,,,,
lnln
lnlnln A
State Stark State
60 p small
Circular state 60 l=59 m=59
Statistical mixture
Scaling (overlap of )
Lifetime 7.2 ms 70 ms ms
3n 5n 5.4n
)1,1(),( lnln)l,n(
23
n2nr
416
1 nFcl3)(
1
lndn
dW
2)(2
1
lnW
2
0nad
4n 5 nFIT53
, , nnln
Part 2- Generation of Rydberg atoms
• Typical Experiments:
– Beam experiments
– (ultra) cold atoms
– Vapor cells
ETH physics Rydberg experiment
Creation of a cold supersonic beam of Helium. Speed: 1700m/s, pulsed: 25Hz, temperature atoms=100mK
ETH physics Rydberg experiment
Excite electrons to the 2s-state, (to overcome very strong binding energy in the xuv range) by means of a discharge – like a lightning.
ETH physics Rydberg experiment
Actual experiment consists of 5 electrodes. Between the first 2 the atoms get excited to Rydberg states up to n=inf with a dye laser.
Dye/Yag laser system
Dye/Yag laser system
Experiment
Dye/Yag laser system
Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser
Experiment
Dye/Yag laser system
Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser
Dye laser with DCM dye: Dye is excited by Yag and fluoresces. A cavity creates light with 624 nm wavelength. This is then frequency doubled to 312 nm.
Experiment
Dye laser
Nd:Yag pump laser
DCM dye
cuvette
Frequency doubling
ETH physics Rydberg experiment
Detection: 1.2 kV/cm electric field applied in 10 ns. Rydberg atoms ionize and electrons are Detected at the MCP detector (single particle multiplier) .
Results TOF 100ns
Results TOF 100ns Inglis-Teller limit
Results TOF 100ns Adiabatic Ionization- rate ~ 70% (fitted)
41
0
161250
F
cmV
nd
41
0 2
91250
F
cmV
nd
Adiabatic Ionization- rate ~ 70% (fitted) )exp( t
Pure diabatic Ionization- rate:
41
0
161250
F
cmV
nd
Results TOF 100ns
Results TOF 100ns 32 nr
41
0 2
91250
F
cmV
nd
Adiabatic Ionization- rate ~ 70% (fitted) saturation )exp( t
Pure diabatic Ionization- rate:
41
0
161250
F
cmV
nd
From ground state
Results TOF 15ms
lifetime
41
0 2
91250
F
cmV
nd
41
0
161250
F
cmV
nd
3n
32 nr
From ground state