Dynamical localization in the microwave ionization of Rydberg

atoms

Jiahao ChenMay 2, 2006http://www.gull.us/photos/misc/cd.jpg

rydberg statesstructure 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 andcore electrons

100 nm

Energy continuum

Rydberg states

n = 3

n = 2

n = 1

low-lyingelectronicstates

0

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.

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

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

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

hydrogen atoma simple classical model explains its behavior well

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

Field ionization mechanism

R* + n! R+ + e-

Combined potential

Potential due to applied electric field

Coulomb bindingpotential

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

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

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

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

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)

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

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

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

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

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

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

Acknowledgments

Prof. Jim LisyMatt AckermanChristine CecalaJason Rodriguez

Prof. Todd MartínezThe Martínez Group

for valued feedback and suggestions