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Dynamical localization in the microwave ionization of Rydberg atoms Jiahao Chen May 2, 2006 http://www.gull.us/photos/misc/cd.jpg
rydberg states structure of a highly-excited atom
What Rydberg states are ,[object Object],[object Object],[object Object],n  À  1 nucleus and core electrons 100 nm Energy continuum Rydberg states  n  = 3 n  = 2 n  = 1 low-lying electronic states 0
Quantum defect in Rydberg spectra ,[object Object],[object Object],[object Object],[object Object],T. F. Gallagher,  Rydberg Atoms , Cambridge Univ. Press,  2005 .
Bohr model of the hydrogen atom n  = 3,  E  = -1.5 eV n  = 12 E  = -0.09 eV E   = -9 kJ/mol E  =  -2 kcal/mol E  = -800 cm -1 E  = -20 THz n  = 1 E  = -13.6 eV 10 a.u. = 5.3 Å Rydberg electrons are weakly bound core electrons are tightly bound Microwave ionization involves ~ 200 photons at 10 GHz distances are to scale
Rydberg electrons are very sensitive to core electrons Accurate polarizabilities from Stark Effect H. Gould, T. M. Miller,  Adv. At. Mol. Opt. Phys.   51  (2005), 343-361 E. L. Snow  et. al. ,  Phys. Rev. A  71  (2005), art. no. 022510 Molecular fingerprinting J. L. Gosselin, P. M. Weber,  J. Phys. Chem. A   109  (2005), 4899-4904 Electron energy/eV Intensity/a.u. Theory review: W. Clark, C. H. Greene,  Rev. Mod. Phys.   71  (1999), 821-833 Electric field Energy same  n, different  l
Rydberg atoms as single-photon microwave detectors ,[object Object],[object Object],M. Tada, Y. Kishimoto, K. Kominato, A. Shibata, S. Yamada, T. Haseyama, I. Ogawa, H. Funahashi, K. Yamamoto, S. Matsuki,  Phys. Lett. A   349  (2006) 488-493. Photon count F /Vcm -1 3.2 4.5 6.5
hydrogen atom a simple classical model explains its behavior well
The Bayfield-Koch experiment prepare Rydberg state take atoms out of storage microwave the atoms remove electrons Detect and record Hydrogen: J. E. Bayfield, P. M. Koch,  Phys. Rev. Lett.   33  (1974), 258-261. Sodium: T. W. Ducas  et. al. ,  Phys. Rev. Lett.   35  (1975), 366-369. Rubidium: L. Sirko, M. Arndt, P. M. Koch, H. Walther,  Phys. Rev. A   49  (1994), 3831-3841. Lithium: C. H. Cheng, C .Y. Lee, T. F. Gallagher,  Phys. Rev. A   54  (1996), 3303-3309. T. F. Gallagher,  Rydberg Atoms , Cambridge Univ. Press,  2005 . Prevents ions from recombining with electrons H: electric discharge Alkali atoms: laser ablation Interaction time ~ 10 ns microwave resonator atomic beam excitation laser, e.g. CO 2   AC oscillator ion detector, e.g. mass spectrometer anode DC bias laser resonator
Field ionization mechanism R* +   n   !   R +  + e - Combined potential Potential due to applied  electric field Coulomb binding potential Classical energy of Rydberg electron position Energy
H is described well classically ,[object Object],[object Object],[object Object],P. M. Koch, K. A. H. van Leeuwen,  Phys. Rep.   255  (1995) 289-403. *E. Persson, S. Yoshida, X. M. Tong, C. O. Reinhold, J. Burgdorfer,  Phys. Rev. A   68  (2003) art. no. 063406
Features in phase space show nature of trajectories P. M. Koch, K. A. H. van Leeuwen,  Phys. Rep.   255  (1995) 289-403. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0   Angle Action 80 65
Destruction of KAM tori means more chaos ,[object Object],[object Object],[object Object],P. M. Koch,  Physica D   83  (1995), 178-205. weak   field strong   field
Classical model predicts onset of anomaly P. M. Koch,  Physica D   83  (1995), 178-205. Classical theory: Initial state is already chaotic Wrong scaling behavior Experiment and classical model agree well at low frequencies: Transition from regular to chaotic Negligible effect from tunneling There exists a frequency at which Rydberg H atoms ionize most easily! Experiment shows suppressed ionization threshold due to dynamical localization
How dynamical localization occurs ,[object Object],[object Object],position time time potential O. Benson  et. al. ,  Phys. Rev. A   51  (1995), 4862-4876. E. Persson  et. al. ,  Phys. Rev. A   66  (2002), art. no. 043407. No noise (solid line) Noise (all others)
alkali metal atoms
How alkali atoms differ ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],nucleus core electrons valence Rydberg electron D. Campos, M. C. Spinel, J. Madroñero,  J. Phys. A   34  (2001), 8101-8118. A. Krug, A. Buchleitner,  Phys. Rev. A   66  (2002), art. no. 053416. H,   l  = 0 Li,   l  = 0.002129 Na,   l  = 0.015543
Nonadiabatic ionization threshold ,[object Object],[object Object],[object Object],P. Pillet  et. al. ,  Phys. Rev. A   30 , (1983) 280–294. L. Perotti,  Phys. Rev. A   71 , (2005) art. no. 033405. Electric field Energy same  n, different  l
Li and H data show different onsets ,[object Object],[object Object],[object Object],H, calc. H, expt. Li, calc. Li, expt. A. Krug, Ph.D. thesis,  2001 , http://edoc.ub.uni-muenchen.de/archive/00000336/01/Krug_Andreas.pdf L. Perotti,  Phys. Rev. A   71 , (2005) art. no. 033405. H, expt.,    = 36 GHz ,    = 4 ns H, expt.,    = 36 GHz ,    = 4 ns Rb, calc.,    = 36 GHz ,    = 4 ns Rb, calc.,    = 8.87 GHz ,    = 4 ns Rb, expt.,    = 8.87 GHz,    = 5 µs
Calculations for Li, Na, Rb v. H atoms A. Krug, A. Buchleitner,  Phys. Rev. A   72  (2005), art. no. 061402 H, expt. #2 H, expt. #1 H, calc. H, expt. #2 Li,   l  = 0.40, calc. Rb,   l  = 3.13, calc. Na,   l  = 1.35, calc. H, calc. Li, calc. Rb, calc. Na, calc. universal scaling/ data collapse H threshold alkali threshold chaotic field ionization ,[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Acknowledgments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Dynamical localization in the microwave ionization of Rydberg atoms

  • 1. Dynamical localization in the microwave ionization of Rydberg atoms Jiahao Chen May 2, 2006 http://www.gull.us/photos/misc/cd.jpg
  • 2. rydberg states structure of a highly-excited atom
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  • 5. Bohr model of the hydrogen atom n = 3, E = -1.5 eV n = 12 E = -0.09 eV E = -9 kJ/mol E = -2 kcal/mol E = -800 cm -1 E = -20 THz n = 1 E = -13.6 eV 10 a.u. = 5.3 Å Rydberg electrons are weakly bound core electrons are tightly bound Microwave ionization involves ~ 200 photons at 10 GHz distances are to scale
  • 6. Rydberg electrons are very sensitive to core electrons Accurate polarizabilities from Stark Effect H. Gould, T. M. Miller, Adv. At. Mol. Opt. Phys. 51 (2005), 343-361 E. L. Snow et. al. , Phys. Rev. A 71 (2005), art. no. 022510 Molecular fingerprinting J. L. Gosselin, P. M. Weber, J. Phys. Chem. A 109 (2005), 4899-4904 Electron energy/eV Intensity/a.u. Theory review: W. Clark, C. H. Greene, Rev. Mod. Phys. 71 (1999), 821-833 Electric field Energy same n, different l
  • 7.
  • 8. hydrogen atom a simple classical model explains its behavior well
  • 9. The Bayfield-Koch experiment prepare Rydberg state take atoms out of storage microwave the atoms remove electrons Detect and record Hydrogen: J. E. Bayfield, P. M. Koch, Phys. Rev. Lett. 33 (1974), 258-261. Sodium: T. W. Ducas et. al. , Phys. Rev. Lett. 35 (1975), 366-369. Rubidium: L. Sirko, M. Arndt, P. M. Koch, H. Walther, Phys. Rev. A 49 (1994), 3831-3841. Lithium: C. H. Cheng, C .Y. Lee, T. F. Gallagher, Phys. Rev. A 54 (1996), 3303-3309. T. F. Gallagher, Rydberg Atoms , Cambridge Univ. Press, 2005 . Prevents ions from recombining with electrons H: electric discharge Alkali atoms: laser ablation Interaction time ~ 10 ns microwave resonator atomic beam excitation laser, e.g. CO 2 AC oscillator ion detector, e.g. mass spectrometer anode DC bias laser resonator
  • 10. Field ionization mechanism R* + n   ! R + + e - Combined potential Potential due to applied electric field Coulomb binding potential Classical energy of Rydberg electron position Energy
  • 11.
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  • 14. Classical model predicts onset of anomaly P. M. Koch, Physica D 83 (1995), 178-205. Classical theory: Initial state is already chaotic Wrong scaling behavior Experiment and classical model agree well at low frequencies: Transition from regular to chaotic Negligible effect from tunneling There exists a frequency at which Rydberg H atoms ionize most easily! Experiment shows suppressed ionization threshold due to dynamical localization
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Editor's Notes

  1. Aluminum foil on a CD-ROM ionizing in a domestic microwave oven. Intro: Rydberg atoms are close to ionization threshold Correspondence principle => good for semiclassical theory Ionization behavior in microwave fields => good model for quantum chaos No well-defined adiabatic – nonadiabatic transition Anomalous diffusion rate in quantum chaos => dynamical localization Classical chaotic trajectories killed by interference with everything else The larger the path in phase space, the more likely it will die Compare with experiment. To do: Look up chemical applications of Anderson localization. Peter Wolynes.