transport in microscopic systems
A great challenge for the future
technology on microscopic scale is the design and construction of
microscopic motors that can use input energy to drive directed motion
in the face of inescapable thermal and other noise. Driving such
directed motion is what protein motors -perfected over the course of
millions of years by evolution- do in every cell in our bodies [1-3].
Modern technologies go down to smaller and smaller scales, where
quantum effects are expected to play a very important role. Indeed,
along with thermal activation, quantum tunneling provides an
alternative mechanism to overcome energy barriers and lead to directed
motion. Therefore, for future technological progress it is very
important to be able to create directed transport and to be able to
control its direction in the presence of noise, decoherence, thermal
fluctuations, and quantum effects. Such systems with directed
transport, called ratchets,
find applications in a very broad range of physical systems: mesoscopic
systems with antidot lattices, experimental realization of quantum
ratchets in semiconductor heterostructures, directed transport of cold
atoms, thermal rectifiers in molecular chains, biomotors and directed
transport in molecular wires and proteins.
Quantum ratchets are potentially useful in a number of
technological applications such as novel rectifiers, pumps, molecular
switches, and transistors.
The understanding of the physics of such systems might also bring
important insights for the treatment and operation of quantum
information at the nanoscale.
ratchets in dissipative chaotic systems
Using the method of quantum
trajectories we have studied  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
The role of transporting islands in the chaotic sea for the
corresponding classical model has been investigated in 
We have also studied a model, consisting of two series of
periodic kicks, that offers a clear-cut way to implement directed
transport with cold atoms in optical lattices .
Phase space pictures for the model discussed in Ref.  after 100
kicks: classical Poincare sections (left) and quantum Husimi functions
at effective Planck constant equal to 0.012 (right).
The strange attractor is asymmetric and leads, independently of the
initial conditions, to stationary directed transport (<p>
different from zero).
Magnifications of the plots are shown in the second and third rows (the
phase-space area is reduced by a factor 1/9 and 1/81,
respectively): the fractal structure of the classical strange
attractor is smoothed on the scale of Planck's cell.
The color is proportional to the density: blue for zero and red for
quantum ratchet in a Bose-Einstein condensate
Quantum Hamiltonian ratchets are
relevant in systems such as cold
atoms in which the high degree of quantum control may allow
experimental implementations near to the dissipationless limit.
Moreover, the realization of Bose-Einstein condensates (BECs) of dilute
gases has opened new opportunities for the study of dynamical systems
in the presence of many-body interactions. Indeed, it is possible to
prepare initial states with high precision and to tune over a wide
range the many-body atom-atom interaction. From the viewpoint of
directed transport, the study of many-body quantum system is, to our
knowledge, at the very beginning.
We have studied  the dynamics of a dilute Bose-Einstein
confined in a toroidal trap and exposed to a pair of periodically
flashed optical lattices. We first proved that in the noninteracting
case this system can present a quantum symmetry which forbids the
ratchet effect classically expected. We then showed how the interaction
between atoms in the condensate, studied in the mean-field
approximation, can break the quantum symmetry present in our model in
the noninteracting limit, thus giving rise to the ratchet effect. The
role of noise, the validity of the mean-field description and the
possibility to observe experimentally our ratchet model have been
discussed as well.
Momentum versus time for different values of the
dimensionless atom-atom interaction strength g: g=0 (dashed line), g=0.5 (continuous curve), g=1(dotted curve). Note that
directed transport is induced by interactions (see Ref. ).
Steering Bose-Einstein condensates
despite time symmetry
We have considered
 a non-dissipative, i.e. Hamiltonian system in which the time-reversal symmetry is not broken and
the system is driven smoothly. We have show that, starting out from
initial conditions symmetric both in momentum and space, interactions,
treated in the limits of a mean-field approximation, induce directed
current in a BEC. In a full many-body analysis of the system, symmetry
considerations imply that this directed current is asymptotically
decaying. Despite this fact we show that a finite current persists over
a time scale which increases with increasing atom number in
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