Dynamical localization in the microwave ionization of Rydberg atoms

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Information about Dynamical localization in the microwave ionization of Rydberg atoms

Published on June 16, 2008

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

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 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

Loosely bound electrons, i.e. n À 1

Just below ionization threshold

Classical-like behavior

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 .

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

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 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

Monitor Rydberg transition in 85 Rb atomic beam

Sensitive to record low temperature thermal radiation (67 mK – 1 K)

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 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

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*

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

KAM torus

quasiperiodic orbits

bound trajectories

Localized in phase space

Chaotic layer

diffusive transport

“ ionized trajectories”

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

Strong fields destroy KAM tori

Less bound orbits, more unbound orbits

Stronger fields cause more classical ionization

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 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)

Paths need not propagate the same way in time, leading to different dynamical phases

Noise suppresses localization effect

alkali metal atoms

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

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

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

Stark effect splits degeneracies in l

Incremental non-adiabatic transitions

n  n+1 transition is rate-limiting

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

Different threshold for onset of dynamical localization

Alkali atoms consistently easier to ionize

Weak time-dependence of ionization threshold (e.g. in Rb data)

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

Alkali atoms show same threshold different from H

Core scattering enhances dynamical localization

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

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

Acknowledgments Prof. Jim Lisy Matt Ackerman Christine Cecala Jason Rodriguez Prof. Todd Martínez The Martínez Group for valued feedback and suggestions

Prof. Jim Lisy

Matt Ackerman

Christine Cecala

Jason Rodriguez

Prof. Todd Martínez

The Martínez Group

for valued feedback and suggestions

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