Chaos
and dynamical localization in Rydberg atoms
The pioneering experiment of
Bayfield and Koch performed in 1974
[1] attracted a great interest in the ionization of highly excited
hydrogen and Rydberg atoms in a microwave field. The main reason of
this interest is due to the fact that such ionization requires the
absorption of a large number of photons (about 20-70) and can be
explained only as a result of the appearence of dynamical chaos and
diffusive energy excitation in the corresponding classical system.
Quantum interference effects can suppress this diffusion leading
to
quantum localization of chaos [2].
Chaotic
enhancement in the microwave ionization of Rydberg atoms
We have studied analytically and numerically the microwave ionization
of internally chaotic Rydberg atoms [3]. The internal chaos is induced
by magnetic or static electric fields. This leads to a chaotic
enhancement of microwave excitation. The dynamical localization
theory gives a detailed description of the excitation process
even in a regime where up to few
thousands photons are required to ionize one atom. We have also
discussed possible laboratory experiments.
Magnetic-field induced
enhancement of the localization length.
The same chaotic enhancement mechanism has been found in:
(i) the weak
interaction enhancement due to a complex structure of ergodic
eigenfunctions in nuclei [4].
(ii) the enhancement of the localization
length for two interacting particles in a random potential [5].
Quantum
Poincare recurrences for hydrogen atoms in a microwave field
We have studied the time
dependence of the ionization probability of
Rydberg atoms driven by a microwave field, both in classical and in
quantum mechanics [6]. The quantum survival probability follows the
classical one up to the Heisenberg time and then decays algebraically
as P(t) proportional to 1/t. This decay law derives from the
exponentially long times required to escape from some region of the
phase space, due to tunneling and localization effects. This result
implies that correlations in practice do not decay up to very long
times and has analogies with the 1/f noise found, for instance, in the
resistance fluctuations of different solid state devices. This
phenomenon indicates a broad distribution of time scales in the system:
In the case of quantum Poincare recurrences this property stems from
the exponentially low escape rate from some regions of the phase space.
1/t decay of the quantum survival
probability for realistic experimental conditions
Classical density plot (left)
and Husimi function (right) in action-angle variables, for
50<t<60 (top) and 2000<t<10000 (right). At long times the
quantum diffusion is slowed down due to localization effects
We have also shown that quantum fractal fluctuations of the
survival probability can be observed in the deep quantum regime of
strong localization, due to the slow, purely quantum algebraic decay in
time [P(t) proportional to 1/t] produced by dynamical localization [7].
References
[1] J.E. Bayfield and P.M. Koch Phys. Rev. Lett. 33, 258 (1974); P.M. Koch and
K.A.H.van Leeuwen, Phys. Rep. 255,
289 (1995).
[2] G. Casati, I. Guarneri, and D.L. Shepelyansky, IEEE Journal of
Quantum Electronics 24, 1420
(1988).
[3] G. Benenti, G. Casati and D.L. Shepelyansky, Chaotic enhancement in microwave
ionization of Rydberg atoms, Eur. Phys. J. D 5, 311 (1999).
[4] O.P.Sushkov and V.V.Flambaum, Usp. Fiz. Nauk 136, 3 (1982) [ Sov. Phys.
Usp. 25, 1 (1982)].
[5] D.L.Shepelyansky, Phys. Rev. Lett. 73,
2607 (1994).
[6] G. Benenti, G. Casati, G.
Maspero and D.L. Shepelyansky, Quantum
Poincare recurrences for a hydrogen atom in amicrowave field,
Phys. Rev. Lett. 84, 4088
(2000).
[7] G. Benenti, G. Casati, I.
Guarneri and M. Terraneo, Quantum
fractal fluctuations, Phys. Rev. Lett. 87, 014101 (2001).
