Quantum signatures of an oscillatory instability in the Bose-Hubbard trimer
2012 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 86, no 1, 016214- p.Article in journal (Refereed) Published
We study the Bose-Hubbard model for three sites in a symmetric, triangular configuration and search for quantum signatures of the classical regime of oscillatory instabilities, known to appear through Hamiltonian Hopf bifurcations for the "single-depleted-well" family of stationary states in the discrete nonlinear Schrodinger equation. In the regimes of classical stability, single quantum eigenstates with properties analogous to those of the classical stationary states can be identified already for rather small particle numbers. On the other hand, in the instability regime the interaction with other eigenstates through avoided crossings leads to strong mixing, and no single eigenstate with classical-like properties can be seen. We compare the quantum dynamics resulting from initial conditions taken as perturbed quantum eigenstates and SU(3) coherent states, respectively, in a quantum-semiclassical transitional regime of 10-100 particles. While the perturbed quantum eigenstates do not show a classical-like behavior in the instability regime, a coherent state behaves analogously to a perturbed classical stationary state, and exhibits initially resonant oscillations with oscillation frequencies well described by classical internal-mode oscillations.
Place, publisher, year, edition, pages
American Physical Society , 2012. Vol. 86, no 1, 016214- p.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-79982DOI: 10.1103/PhysRevE.86.016214ISI: 000306470900001OAI: oai:DiVA.org:liu-79982DiVA: diva2:544950
Funding Agencies|Swedish Research Council||Swedish Institute||2012-08-172012-08-172016-08-22