To extract directed transport from random fluctuations is a
problem
at the heart of statistical mechanics with a long history, including
links to the Maxwell demon. In far from equilibrium systems, in
presence,
for instance, of unbiased ac-driving, noise and dissipation, a directed
transport, also known as ratchet effect, can be generated.
The appearance of ratchet transport has recently gained renewed
attention
due to its possible relevance for biological transport, molecular
motors
and the prospects of nanotechnology.
We demonstrate [1] a quantum chaotic dissipative ratchet appearing
for particles in a pulsed asymmetric potential in the presence of
a dissipative environment. The system is characterized by directed
transport emerging from a quantum strange attractor. This model
exhibits,
in the limit of small effective Planck constant, a transition from
quantum to classical behavior, in agreement with the correspondence
principle. We also discuss a model, consisting of two series of
spatially
periodic kicks, that offers a clear-cut way to implement directed
transport
with cold atoms in optical lattices [2].
Finally, we study the dynamics of a dilute Bose-Einstein condensate
confined
in a toroidal trap and exposed to a pair of periodically flashed
optical
lattices. We first prove that in the noninteracting case this system
can
present a quantum symmetry which forbids the ratchet effect classically
expected. We then show how many-body atom-atom interactions, treated
within
the mean-field approximation, can break this quantum symmetry, thus
generating
directed transport [3].
Refs
:
[1] G.G. Carlo, G. Benenti, G. Casati, and D.L. Shepelyansky,
``Quantum ratchets in dissipative chaotic systems'',
Phys. Rev. Lett. 94, 164101 (2005).
[2] G.G. Carlo, G. Benenti, G. Casati, S. Wimberger, O. Morsch,
R. Mannella, and E. Arimondo,
``Quantum ratchet with cold atoms in a pair of
pulsed optical lattices'', Phys. Rev. A 74, 033617 (2006).
[3] D. Poletti, G. Benenti, G. Casati, and B. Li,
``Interaction-induced quantum ratchet in a Bose-Einstein condensate'',
preprint cond-mat/0611262, Phys. Rev. A (in press).