dynamical localization in the microwave ionization of rydberg atoms
DESCRIPTION
Literature seminar in physical chemistry (CHEM 545, Spring 2006) at UIUCTRANSCRIPT
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Dynamical localization in the microwave ionization of Rydberg
atoms
Jiahao ChenMay 2, 2006http://www.gull.us/photos/misc/cd.jpg
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rydberg statesstructure of a highly-excited
atom
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What Rydberg states are
• Loosely bound electrons, i.e. n À 1• Just below ionization threshold
– Classical-like behavior
n À 1
nucleus andcore electrons
100 nm
Energy continuum
Rydberg states
n = 3
n = 2
n = 1
low-lyingelectronicstates
0
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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.
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Bohr model of the hydrogen atom
n = 3, E = -1.5 eV
n = 12E = -0.09 eVE = -9 kJ/molE = -2 kcal/molE = -800 cm-1
E = -20 THz
n = 1E = -13.6 eV
10 a.u. = 5.3 Å
Rydberg electronsare weakly bound
core electronsare tightly bound
Microwave ionizationinvolves ~ 200 photonsat 10 GHz
distances are to scale
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Rydberg electrons are very sensitive to core electrons
Accurate polarizabilities from Stark EffectH. Gould, T. M. Miller, Adv. At. Mol. Opt. Phys. 51 (2005), 343-361E. L. Snow et. al., Phys. Rev. A 71 (2005), art. no. 022510
Molecular fingerprintingJ. L. Gosselin, P. M. Weber, J. Phys. Chem. A 109 (2005), 4899-4904
Electricfield
Energy
same n,different l
Electronenergy/eV
Intensity/a.u.
Theory review: W. Clark, C. H. Greene, Rev. Mod. Phys. 71 (1999), 821-833
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Rydberg atoms as single-photon microwave detectors
• Monitor Rydberg transition in 85Rb 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.
Ph
oto
n c
ou
nt
F/Vcm-1
3.24.5 6.5
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hydrogen atoma simple classical model explains its behavior well
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The Bayfield-Koch experiment
prepareRydberg
state
take atomsout of storage
microwavethe atoms
removeelectrons
Detectand
record
microwaveresonator
atomic beamexcitation
laser, e.g. CO2 AC oscillator
ion detector, e.g.mass spectrometer
anodeDC bias
laserresonator
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 recombiningwith electrons
H: electric dischargeAlkali atoms: laser ablation
Interaction time~ 10 ns
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Field ionization mechanism
R* + n! R+ + e-
Combined potential
Potential due to applied electric field
Coulomb bindingpotential
Classical energy of Rydberg electron
position
Energy
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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
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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.
KAM torus•quasiperiodic orbits•bound trajectories•Localized in phase space
Chaotic layer•diffusive transport•“ionized trajectories”
0 Angle
Action
80
65
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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
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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 chaoticWrong scaling behavior
Experiment and classical modelagree well at low frequencies:Transition from regular to chaoticNegligible effect from tunneling
There exists a frequency at whichRydberg H atoms ionize mosteasily!
Experiment shows suppressed ionization threshold due to dynamical localization
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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)
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alkali metal atoms
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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
nucleuscore electronsvalence 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 = 0Li, l = 0.002129Na, l = 0.015543
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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.
Electricfield
Energy
same n,different l
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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.pdfL. Perotti, Phys. Rev. A 71, (2005) art. no. 033405.
H, expt., = 36 GHz , = 4 nsH, expt., = 36 GHz , = 4 nsRb, calc., = 36 GHz , = 4 nsRb, calc., = 8.87 GHz , = 4 nsRb, expt., = 8.87 GHz, = 5 µs
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Calculations for Li, Na, Rb v. H atoms
A. Krug, A. Buchleitner, Phys. Rev. A 72 (2005), art. no. 061402
H, expt. #2H, expt. #1 H, calc.
H, expt. #2Li, 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 thresholdalkali thresholdchaotic
fieldionization
• Alkali atoms show same threshold different from H• Core scattering enhances dynamical localization
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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
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Acknowledgments
Prof. Jim LisyMatt AckermanChristine CecalaJason Rodriguez
Prof. Todd MartínezThe Martínez Group
for valued feedback and suggestions