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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Dynamical localization in the microwave ionization of Rydberg atoms Jiahao Chen May 2, 2006 http://www.gull.us/photos/misc/cd.jpg
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rydberg states structure of a highly-excited atom
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 .
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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
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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
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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
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hydrogen atom a simple classical model explains its behavior well
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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
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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
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
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Features in phase space show nature of trajectories P. M. Koch, K. A. H. van Leeuwen, Phys. Rep. 255 (1995) 289-403.
P. M. Koch, Physica D 83 (1995), 178-205. weak field strong field
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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
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)
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
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