Infinite barriers and symmetries for a few trapped particles in one dimension
Abstract
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and interwell tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of fewparticle, fewwell systems. Extended attention is given to a simple but flexible threeparameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hardcore repulsion and no interwell tunneling, can both be treated as emergent symmetries of the fewparticle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in fewparticle, fewwell systems with ultracold atoms in optical traps.
 Publication:

Physical Review A
 Pub Date:
 May 2017
 DOI:
 10.1103/PhysRevA.95.053616
 arXiv:
 arXiv:1608.07189
 Bibcode:
 2017PhRvA..95e3616H
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases;
 Mathematical Physics
 EPrint:
 17 pages in twocolumn format, 9+ figures