Dynamical localization in the microwave ionization of Rydberg atoms


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Literature seminar in physical chemistry (CHEM 545, Spring 2006) at UIUC

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  • 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.
  • Dynamical localization in the microwave ionization of Rydberg atoms

    1. 1. Dynamical localization in the microwave ionization of Rydberg atoms Jiahao Chen May 2, 2006 http://www.gull.us/photos/misc/cd.jpg
    2. 2. rydberg states structure of a highly-excited atom
    3. 3. What Rydberg states are <ul><li>Loosely bound electrons, i.e. n À 1 </li></ul><ul><li>Just below ionization threshold </li></ul><ul><ul><li>Classical-like behavior </li></ul></ul>n À 1 nucleus and core electrons 100 nm Energy continuum Rydberg states  n = 3 n = 2 n = 1 low-lying electronic states 0
    4. 4. Quantum defect in Rydberg spectra <ul><li>In atomic units, the energy of a Rydberg state is </li></ul><ul><li>The quantum defect  l measures how much a Rydberg state resembles a hydrogenic state </li></ul><ul><ul><li>Wide range of  l : ~ 0.001 - 3 </li></ul></ul><ul><li>Each atom and angular momentum state (Z, l ) has a different spectrum </li></ul>T. F. Gallagher, Rydberg Atoms , Cambridge Univ. Press, 2005 .
    5. 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. 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. 7. Rydberg atoms as single-photon microwave detectors <ul><li>Monitor Rydberg transition in 85 Rb atomic beam </li></ul><ul><li>Sensitive to record low temperature thermal radiation (67 mK – 1 K) </li></ul>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
    8. 8. hydrogen atom a simple classical model explains its behavior well
    9. 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. 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. 11. H is described well classically <ul><li>One-dimensional projection (no centrifugal forces) </li></ul><ul><li>Analogous to planetary motion with periodic perturbation </li></ul><ul><li>1-D model is an accurate approximation of full 3-D atom* </li></ul>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
    12. 12. Features in phase space show nature of trajectories P. M. Koch, K. A. H. van Leeuwen, Phys. Rep. 255 (1995) 289-403. <ul><li>KAM torus </li></ul><ul><li>quasiperiodic orbits </li></ul><ul><li>bound trajectories </li></ul><ul><li>Localized in phase space </li></ul><ul><li>Chaotic layer </li></ul><ul><li>diffusive transport </li></ul><ul><li>“ ionized trajectories” </li></ul>0   Angle Action 80 65
    13. 13. Destruction of KAM tori means more chaos <ul><li>Strong fields destroy KAM tori </li></ul><ul><li>Less bound orbits, more unbound orbits </li></ul><ul><li>Stronger fields cause more classical ionization </li></ul>P. M. Koch, Physica D 83 (1995), 178-205. weak field strong field
    14. 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
    15. 15. How dynamical localization occurs <ul><li>Paths need not propagate the same way in time, leading to different dynamical phases </li></ul><ul><li>Noise suppresses localization effect </li></ul>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)
    16. 16. alkali metal atoms
    17. 17. How alkali atoms differ <ul><li>Theoretically: </li></ul><ul><ul><li>Electron correlations lead to ‘core scattering effect’ </li></ul></ul><ul><ul><li>Ionization depends greatly on exactly how microwave field was turned on </li></ul></ul><ul><li>Experimentally: </li></ul><ul><ul><li>Easier to prepare atomic beam </li></ul></ul><ul><ul><li>Heavier, slower atoms allow longer interactions </li></ul></ul><ul><li>Observe different ionization behavior vs. H, even for very small quantum defects </li></ul>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
    18. 18. Nonadiabatic ionization threshold <ul><li>Stark effect splits degeneracies in l </li></ul><ul><li>Incremental non-adiabatic transitions </li></ul><ul><li>n  n+1 transition is rate-limiting </li></ul>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
    19. 19. Li and H data show different onsets <ul><li>Different threshold for onset of dynamical localization </li></ul><ul><li>Alkali atoms consistently easier to ionize </li></ul><ul><li>Weak time-dependence of ionization threshold (e.g. in Rb data) </li></ul>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
    20. 20. 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 <ul><li>Alkali atoms show same threshold different from H </li></ul><ul><li>Core scattering enhances dynamical localization </li></ul>
    21. 21. Conclusions <ul><li>Rydberg states are great semiclassical systems </li></ul><ul><li>Ionization behavior of H Rydberg atoms well described by classical model </li></ul><ul><ul><li>Transition from regular to chaotic motion </li></ul></ul><ul><li>Effect electron correlation in non-H Rydberg atoms still poorly understood </li></ul><ul><ul><li>Core electrons in alkali atoms change onset of dynamical localization </li></ul></ul><ul><ul><li>Effect of angular quantum number still not well understood </li></ul></ul>
    22. 22. Acknowledgments <ul><li>Prof. Jim Lisy </li></ul><ul><li>Matt Ackerman </li></ul><ul><li>Christine Cecala </li></ul><ul><li>Jason Rodriguez </li></ul><ul><li>Prof. Todd Martínez </li></ul><ul><li>The Martínez Group </li></ul><ul><li>for valued feedback and suggestions </li></ul>