1. Rydberg atoms part 1
Tobias Thiele

2. Content References Part 1: Rydberg atoms
Part 2: typical (beam) experiments
T. Gallagher: Rydberg atoms
References

3. 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!

4. 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:

5. 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:

6. Introduction – Rydberg atom?
Hydrogen
Energy follows Rydberg formula:
=13.6 eV
Energy

7. Quantum Defect? Energy follows Rydberg formula: Hydrogen n-Hydrogen
Energy

8. 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

9. Radial parts-Interesting regionsW
Ion core r
Interesting Region
For Rydberg Atoms

10. (Helium) Energy Structure
usually measured
Only large for low l (s,p,d,f)
He level structure
is big for s,p
Excentric orbits penetrate into core.
Large deviation from Coulomb.
Large phase shift-> large quantum defect

11. (Helium) Energy Structure
usually measured
Only large for low l (s,p,d,f)
He level structure
is big for s,p

12. 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:

13. Hydrogen Atom in an electric Field
Rydberg Atoms very sensitive to electric fields
Solve: in parabolic coordinates
Energy-Field dependence: Perturbation-Theory

14. Stark Effect For non-Hydrogenic Atom (e.g. Helium)
„Exact“ solution by numeric diagonalization of
in undisturbed (standard) basis ( ,l,m)
Numerov

15. Stark Map Hydrogen Levels degenerate Cross perfect
Runge-Lenz vector conserved
n=11

16. Stark Map Hydrogen
n=13
k=-11
blue
n=12
k=11
red
n=11

17. Stark Map Helium Levels not degenerate s-type Do not cross!
No coulomb-potential
n=11

18. Stark Map Helium
n=13
k=-11
blue
n=12
k=11
red
n=11

19. Stark Map Helium
Inglis-Teller
Limit α n-5
n=13
n=12
n=11

20. 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

21. 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

22. (Hydrogen) Atom in an electric Field
When do Rydberg atoms ionize?
No field applied
Electric Field applied
Quasi-Classical ioniz.:
red
blue

23. (Hydrogen) Atom in an electric Field
When do Rydberg atoms ionize?
No field applied
Electric Field applied
Quasi-Classical ioniz.:
red
blue

24. (Hydrogen) Atom in an electric Field
Blue states
Red states
classic
Inglis-Teller

25. Lifetime From Fermis golden rule Einstein A coefficient for two states

26. Lifetime From Fermis golden rule Einstein A coefficient for two states
For l≈0:
Overlap of WF
For l≈0:
Constant (dominated
by decay to GS)

27. Lifetime From Fermis golden rule Einstein A coefficient for two states
For l ≈ n:
For l ≈ n:
Overlap of WF

28. Lifetime 7.2 μs 70 ms ms State Stark State 60 p small Circular state
60 l=59 m=59
Statistical mixture
Scaling
(overlap of )
Lifetime
7.2 μs
70 ms ms

29. Rydberg atoms part 2
Tobias Thiele

30. Part 2- Rydberg atoms Typical Experiments: Beam experiments
(ultra) cold atoms
Vapor cells

31. Cavity-QED systems

32. Goal: large g, small G Couple atoms to cavities
Realize Jaynes-Cummings Hamiltonian
Single atom(dipole) - coupling to cavity:
𝑔= 𝑑 𝐹 0 ℏ = 𝜔 0 𝑑 𝜖 0 ℏ 𝑉
Reduce mode volume
Increase resonance frequency
Increase dipole moment

33. Coupling Rydberg atoms
Couple atoms to cavities
Realize Jaynes-Cummings Hamiltonian
Single atom(dipole) - coupling to cavity:
Scaling with excitation state n?
𝑔= 𝑑 𝐹 0 ℏ = 𝜔 0 𝑑 𝜖 0 ℏ 𝑉 =2 𝜋 𝑘𝐻𝑧
S. Haroche
(Rydberg in microwave cavity)
∝𝑛 2
𝑔= 𝑑 𝐹 0 ℏ = 𝜔 0 𝑑 𝜖 0 ℏ 𝑉 ≈2 𝜋 6∗ 𝑛 −4
∝𝑛 −3
∝𝑛 9

34. Advantages microwave regime for strong coupling g>> G,k
Coupling to ground state of cavity
l~0.01 m (microwave, possible) for n=50
l ~10-7 m (optical, n. possible),
Typical mode volume: 1mm *(50 mm)2
Linewidth:
G ~ 10 Hz (microwave)
G ~ MHz (optical)

35. Summary coupling strength
Microwave:
Optical:
What about G?
Optical G6p~ 2.5 MHz
Rydberg G50p~300 kHz, G50,50~100 Hz
h=𝑔/Gnp ∝ 1/n, h=𝑔/Gn,n-1 ∝ n
𝑔~2𝜋 40 𝑘𝐻𝑧, κ ~2𝜋 10 𝐻𝑧
frequency limited
Mode volume limited
𝑔~2𝜋 5 𝑀𝐻𝑧, κ ~2𝜋 1 𝑀𝐻𝑧
n-4
Optimal n when g >> G ~ κ
n-3
n-5

36. Cavity-QED from groundstates to Rydberg-states
Hopefully we
in future!
BEC in cavity
Single atoms in
optical cavities
Haroche

37. Cavity-QED systems
Combine best of
both worlds - Hybrid

38. Hybrid system for optical to microwave conversion

39. ETH physics Rydberg experiment
Creation of a cold supersonic beam of Helium.
Speed: 1700m/s, pulsed: 25Hz, temperature atoms=100mK

40. 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.

41. ETH physics Rydberg experiment
Actual experiment consists of 5 electrodes. Between the first 2 the atoms
get excited to Rydberg states up to Ionization limit with a dye laser.

42. Dye/Yag laser system

43. Dye/Yag laser system
Experiment

44. Dye/Yag laser system Experiment
Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!)
Provides energy for dye laser

45. Dye/Yag laser system
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
Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!)
Provides energy for dye laser

46. Dye laser
cuvette
Nd:Yag pump laser
Frequency doubling
DCM dye

47. ETH physics Rydberg experiment
Detection: 1.2 kV/cm electric field applied in 50 ns. Rydberg atoms ionize and electrons are
detected at the MCP detector (single particle multiplier) .

48. Results TOF 100ns

49. Results TOF 100ns
Inglis-Teller limit

50. Results TOF 100ns
Adiabatic Ionization-
rate ~ 70% (fitted)

51. Pure diabatic Ionization- rate:
Results TOF 100ns
Adiabatic Ionization-
rate ~ 70% (fitted)
Pure diabatic Ionization rate:

52. Pure diabatic Ionization- rate:
Results TOF 100ns
Adiabatic Ionization-
rate ~ 70% (fitted)
Pure diabatic Ionization rate:
saturation
From ground state

53. Results TOF 15 ms
From ground state
lifetime

54. Rabi oscillations over a distance of 1.5 mm between Rydberg states