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Rydberg atoms part 1

Rydberg atoms part 1. Tobias Thiele. References. Content. Part 1: Rydberg atoms Part 2: typical (beam) experiments T. Gallagher: Rydberg atoms. Introduction – What is „Rydberg“?. Rydberg atoms are (any) atoms in state with high principal quantum number n.

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Rydberg atoms part 1

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  1. Rydberg atomspart 1 Tobias Thiele

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

  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 0 0 0 Energy

  7. Quantum Defect? • Energy follows Rydberg formula: Quantum Defect n-Hydrogen Hydrogen 0 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 regions W Ion core 0 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 n=13 Levels degenerate n=12 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 n=13 Levels not degenerate n=12 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 • Lifetime

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

  28. Lifetime

  29. Rydberg atomspart 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: 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? S. Haroche (Rydberg in microwave cavity)

  34. Advantages microwave regimefor 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=Gnp 1/n, h=Gn,n-1n frequency limited Mode volume limited n-4 Optimal n when g >> G~ 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)

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