Quantum stirring of particles in closed devices (2005-2008)
We study the quantum analog of stirring of water inside a cup using a spoon.
This can be regarded as a prototype example for quantum pumping in closed
devices. The current in the device is induced by translating a scatterer. Its
calculation is done using the Kubo formula approach. The transported charge is
expressed as a line integral that encircles chains of Dirac monopoles. For
simple systems the results turn out to be counter intuitive: e.g. as we move a
small scatterer "forward" the current is induced "backwards". One should
realize that the route towards quantum-classical correspondence has to do with
"quantum chaos" considerations, and hence assumes greater complexity of the
device. We also point out the relation to the familiar S matrix formalism
which is used to analyze quantum pumping in open geometries.
In [5,6] we propose a BEC stirring device which can be regarded as the incorporation
of a quantum pump into a closed circuit: it produces a DC circulating current
in response to a cyclic adiabatic change of two control parameters of an
optical trap. We demonstrate the feasibility of this concept and point out that
such device can be utilized in order to probe the interatomic interactions.
Figure: A scatterer (represented by a black circle) is translated
through a systems that has a Fermi occupation of spineless
non-interacting electrons. In (a) the system is a simple ring.
In (b) it is a chaotic ring (Sinai billiard). In (c) and in (d) we
have network systems that are of the same type of (a) and (b)
respectively. In (c)-(e) the scatterer is a delta function (represented
by a big circle), while the current is measured at a section
(represented by a dotted vertical line). In (e) we have an open
geometry with left and right leads that are attached to reservoirs that
have the same chemical potential.
[1] D. Cohen, T. Kottos and H. Schanz, Phys. Rev. E 71, 035202(R) (2005).
[arXiv]
[pdf]
[2] G. Rosenberg and D. Cohen, J. Phys. A 39, 2287 (2006).
[arXiv]
[pdf]
[3] I. Sela and D. Cohen, Phys. Rev. B 77, 245440 (2008).
[arXiv]
[pdf]
[4] I. Sela and D. Cohen, Phys. Rev. B 78, 155404 (2008).
[arXiv]
[pdf]
[5] M. Hiller, T. Kottos, D. Cohen, Europhysics Letters 82, 40006 (2008).
[arXiv]
[pdf]
[6] M. Hiller, T. Kottos, D. Cohen, Phys. Rev. A 78, 013602 (2008).
[arXiv]
[pdf]