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Dynamical localization in the microwave ionization of Rydberg atoms

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

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