Order-by-disorder phenomena in cold atomic gases

• Main Author: Payrits, Matjaz
• Other Authors: Barnett, Ryan
• Published: Imperial College London 2016
• Subjects: 539.7
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.700703

This thesis presents novel theoretical results on two cold atomic systems with particular emphasis on the order-by-disorder mechanism that they exhibit. The latter selects one or a number of classically degenerate states of lowest energy as the true ground states on the basis of Helmholtz free energy contributions of fluctuations about the classical solutions. It has traditionally played an important role in solid-state systems but has so far not been conclusively observed. The first system considered is that of cold bosons hopping in the two-dimensional dice lattice in the presence of an artificial gauge field, tuned to provide half an elementary flux per plaquette. The single-particle band structure consists entirely of flat bands. Many-particle behaviour is captured by a Bose-Hubbard model with contact interactions. Mean-field analysis yields a large degeneracy of classical ground states which is lifted through Order by Disorder. A closer analysis yields a picture of free-energy-mediated interactions between domain walls separating distinct, classically degenerate regions. The second system is that of spin-2 species in a tightly confining spatial potential, with a generalised quadratic-Zeeman coupling. It is analysed by means of an exact mapping of the many-body Hamiltonian onto that of a five-dimensional rotor. The new Hamiltonian is in general non-Hermitian, but Hermitianising transforms may be found in a number of regimes. Analytical results for the ordinary quadratic Zeeman potential are presented and shown to yield qualitatively different behaviour from the mean-field analysis. In particular, there are no signs of a fluctuation-induced phase transition, predicted by mean-field theory. Motivated by this, an alternative potential, breaking less symmetry, is considered within the rotor framework and shown to display microscopic parallels of Order by Disorder.