Quantum Scattering in Confined Geometries

In the past decades remarkable progress has been achieved in our understanding of the physics of low-dimensional systems. It is now possible to fabricate mesoscopic structures in which at least one or two transversal dimensions are of the order of the deBroglie wavelength of the particles, for which the degrees of freedom in transversal direction are forced to occupy only one or very few states of the confining potential. Such systems can be well approximated as quasi-1 or -2 dimensional system. Some examples are quantum wires, atom waveguides, and 2-dimensional electron gases. To control the propagation of particle beams through these systems we need a good understanding of the effects of the geometric confinement on atom-atom collisions. In such systems, the free-space scattering theory is no longer valid, and a new theory is needed. For example, it has been shown that in the low energy limit of the scattering process in quasi-1D systems, when the system is in the ground state of the confinement potential, the coupling constant between colliding atoms shows a resonance, which is independent of the shape of the interaction potential. In the vicinity of the resonance the coupling constant can be tuned from -∞ to +∞ by varying the strength of the confinement potential over a small range. In this case a total reflection may take place between the colliding atoms even in the case of an attractive interaction. This is not possible in 3D free-space. This kind of resonance, has been known as confinement-induced resonance (CIR)[1]. CIR might be useful, e.g., as an alternative gating mechanism in low-power transistor-like devices.


Atom-Atom collision in a waveguide


Resonant behaviour in the collisional process

Our Focus

We focus on several aspects of quantum scattering in waveguides with harmonic or anharmonic cylindrical confinement. Specifically this covers

· The effects of the quantum interference of different partial wave amplitudes on the scattering process. Our wave-packet dynamical simulation predicts that scattering of particles strongly interacting in 3D can be suppressed at low energies in a quasi-1D confinement. In this case an almost lossless total transmission is observed [2].

· Confinement-induced resonances for multi-channel scattering processes. Our goal is to find CIRs when the incident atoms have enough energy to occupy excited states of the confining potential. We assume the two atoms to be identical. This allows us to separate the center of mass and relative motions.

References

[1] M. Olshanii, Phys. Rev. Lett. 81, 938 (1998).
[2] J.I. Kim, V.S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 (2006).