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Understanding Rydberg Atoms: Theory, Experiments, and Applications

Learn about Rydberg atoms, their properties, and experimental setups. Discover the fascinating world of Rydberg atoms in various quantum states and how they interact with electric fields. Explore theoretical concepts and practical applications in quantum physics.

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Understanding Rydberg Atoms: Theory, Experiments, and Applications

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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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