Brenton J. Knuffman- Rydberg Atoms in Ponderomotive Potentials
Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2:...
Transcript of Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2:...
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Rydberg atoms
Tobias Thiele
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References
• T. Gallagher: Rydberg atoms
Content
• Part 1: Rydberg atoms
• Part 2: A typical beam experiment
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Introduction – What is „Rydberg“?
• Rydberg atoms are (any) atoms in state with high principal quantum number n.
![Page 4: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/4.jpg)
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
![Page 5: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/5.jpg)
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!
![Page 6: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/6.jpg)
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
![Page 7: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/7.jpg)
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
![Page 8: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/8.jpg)
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
![Page 9: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/9.jpg)
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
![Page 10: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/10.jpg)
Introduction – Rydberg formula?
• Energy follows Rydberg formula:
2)( ln
hRyEE
![Page 11: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/11.jpg)
Introduction – Rydberg formula?
• Energy follows Rydberg formula:
2)( ln
hRyEE
13.6 eV
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• Energy follows Rydberg formula:
22)( n
hRy
n
hRyEE
l
Introduction – Hydrogen?
0
0
13.6 eV
Ener
gy
0
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• Energy follows Rydberg formula:
2)( ln
hRyEE
Quantum Defect?
Quantum Defect
Ener
gy
0
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Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
A
e
![Page 15: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/15.jpg)
Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
A
e
![Page 16: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/16.jpg)
Rydberg Atom Theory
• Rydberg Atom
• Almost like Hydrogen
– Core with one positive charge
– One electron
• What is the difference?
A
e
![Page 17: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/17.jpg)
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
![Page 18: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/18.jpg)
Radial parts-Interesting regions W
r
rrV
1)(
0
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Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
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Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
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Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
Interesting Region For Rydberg Atoms
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Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
H
![Page 23: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/23.jpg)
Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
nH
H
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Radial parts-Interesting regions W
r
rrV
1)(
0
)(1
)( rVr
rV core
0rr Ion core
lδ
nH
H
![Page 25: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/25.jpg)
(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
![Page 26: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/26.jpg)
(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
![Page 27: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/27.jpg)
(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
![Page 28: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/28.jpg)
(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
![Page 29: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/29.jpg)
(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
![Page 30: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/30.jpg)
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
![Page 31: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/31.jpg)
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
![Page 32: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/32.jpg)
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(
![Page 33: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/33.jpg)
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
![Page 34: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/34.jpg)
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
![Page 35: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/35.jpg)
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
![Page 36: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/36.jpg)
• 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
![Page 37: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/37.jpg)
• 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
![Page 38: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/38.jpg)
n=12
n=11
n=13
Stark Map Hydrogen
![Page 39: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/39.jpg)
Levels degenerate
n=12
n=11
n=13
Stark Map Hydrogen
![Page 40: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/40.jpg)
n=12
n=11
n=13
k=-11 blue
k=11 red
Stark Map Hydrogen
![Page 41: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/41.jpg)
Cross perfect Runge-Lenz vector conserved
Levels degenerate
n=12
n=11
n=13
Stark Map Hydrogen
![Page 42: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/42.jpg)
n=12
n=11
n=13
Stark Map Helium
![Page 43: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/43.jpg)
Levels not degenerate
n=12
n=11
n=13
Stark Map Helium
![Page 44: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/44.jpg)
n=12
n=11
n=13
k=-11 blue
k=11 red
Stark Map Helium
![Page 45: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/45.jpg)
n=12
n=11
n=13
k=-11 blue
k=11 red
s-type
Stark Map Helium
![Page 46: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/46.jpg)
Do not cross! No coulomb-potential
Levels degenerate
n=12
n=11
n=13
Stark Map Helium
![Page 47: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/47.jpg)
Stark Map Helium
n=12
n=11
n=13
Inglis-Teller Limit n-5
![Page 48: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/48.jpg)
• 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
![Page 49: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/49.jpg)
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
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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
![Page 51: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/51.jpg)
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
![Page 52: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/52.jpg)
• 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
![Page 53: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/53.jpg)
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
![Page 54: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/54.jpg)
• 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
![Page 55: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/55.jpg)
• 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
![Page 56: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/56.jpg)
Hydrogen Atom in an electric Field
classic
Red states
Blue states
Inglis-Teller
![Page 57: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/57.jpg)
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
![Page 58: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/58.jpg)
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
![Page 59: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/59.jpg)
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
![Page 60: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/60.jpg)
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
![Page 61: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/61.jpg)
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
![Page 62: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/62.jpg)
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
![Page 63: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/63.jpg)
Part 2- Generation of Rydberg atoms
• Typical Experiments:
– Beam experiments
– (ultra) cold atoms
– Vapor cells
![Page 64: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/64.jpg)
ETH physics Rydberg experiment
Creation of a cold supersonic beam of Helium. Speed: 1700m/s, pulsed: 25Hz, temperature atoms=100mK
![Page 65: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/65.jpg)
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.
![Page 66: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/66.jpg)
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.
![Page 67: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/67.jpg)
Dye/Yag laser system
![Page 68: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/68.jpg)
Dye/Yag laser system
Experiment
![Page 69: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/69.jpg)
Dye/Yag laser system
Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser
Experiment
![Page 70: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/70.jpg)
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
![Page 71: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/71.jpg)
Dye laser
Nd:Yag pump laser
DCM dye
cuvette
Frequency doubling
![Page 72: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/72.jpg)
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) .
![Page 73: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/73.jpg)
Results TOF 100ns
![Page 74: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/74.jpg)
Results TOF 100ns Inglis-Teller limit
![Page 75: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/75.jpg)
Results TOF 100ns Adiabatic Ionization- rate ~ 70% (fitted)
41
0
161250
F
cmV
nd
![Page 76: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/76.jpg)
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
![Page 77: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/77.jpg)
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
![Page 78: Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)](https://reader030.fdocuments.us/reader030/viewer/2022021423/5ac939ab7f8b9a42358d01b8/html5/thumbnails/78.jpg)
Results TOF 15ms
lifetime
41
0 2
91250
F
cmV
nd
41
0
161250
F
cmV
nd
3n
32 nr
From ground state