Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

Abstract

The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase-space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the PeierlsNabarro energy landscape, we deduce the various regimes in the (Ω, u) parameter-space, where u is the interaction, and Ω is the superfluid rotation-velocity. We thus characterize the superfluidstability and chaoticity of the many-body eigenstates throughout the Hilbert space.

Chaos and two-level dynamics of the atomtronic quantum interference device

“…We have verified using Poincare sections (see below) that for large u the border is in agreement with 1 c a = . For completeness we also show that for very largeu (of order N 2 ) the value of  for the ground-state becomes of orderM, reflecting the Mott transition [17].…”

“…Namely for 1 * g > superfluidity is diminished if n is close to integer. In addition we can define the 'classical' dimensionless parameter which is analogous to u L of equation (17) as…”

“…The key issue is the meta-stability of the flow-states. We follow [18], while some preliminaries regarding the energy landscape and the dynamical stability issues can be found in [17] and [34] respectively.…”

Stability and stabilization of unstable condensates

“…Now we can also understand what is the reason for the failure of Eq. (15). The firstorder treatment involves the substitution λ = 1 + , and then the product is expanded.…”

“…The stability of such stationary state is due to the interaction. This presentation is based on [10][11][12][13][14][15][16] and further references therein [17].…”