Dynamics in multiple-well Bose-Einstein condensates

Abstract

We study the dynamics of three-dimensional weakly linked Bose-Einstein condensates using a multimode model with an effective interaction parameter. The system is confined by a ring-shaped four-well trapping potential. By constructing a two-mode Hamiltonian in a reduced highly symmetric phase space, we examine the periodic orbits and calculate their time periods both in the self-trapping and Josephson regimes. The dynamics in the vicinity of the reduced phase space is investigated by means of a Floquet multiplier analysis, finding regions of different linear stability and analyzing their implications on the exact dynamics. The numerical exploration in an extended region of the phase space demonstrates that two-mode tools can also be useful for performing a partition of the space in different regimes. Comparisons with Gross-Pitaevskii simulations confirm these findings and emphasize the importance of properly determining the effective on-site interaction parameter governing the multimode dynamics.

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

“…Here we present some results for the four-well trap V 1 with N = 10 4 and initial conditions given by N 1 = N −1 , N 0 = N 2 and ϕ k = 0. In this case we have found a value of α = 0.219 [26], irrespective of the rotation frequency. This choice of initial conditions allows us to analyze a particular effect of the rotation.…”

Blocked populations in ring-shaped optical lattices

“…Theoretical studies of this phenomenon has been also carried out by several authors in extended regular lattices [12][13][14][15]. More recently, the study of self-trapping has also been addressed in ringshaped optical lattices [16][17][18]. Such works treat threeand four-well systems.…”

“…A systematic study of the selftrapping regime and the crossover to the Josephson oscillations in four-well systems including non-symmetric configurations has been developed in Ref. [18]. It is worthwhile noticing that the dynamics in multiple well condensates constitutes a promising area provided that successful efforts have been performed to experimentally construct ring-shaped optical lattices [24].…”

“…If the number of wells of the lattice is a multiple of four, there exists a family of nonstationary states with constant site populations and special non-trivial phases. These states could be regarded as a special variation of a ST regime where, in contrast to that observed in twoand multiple-well condensates [1,2,7,18], the population imbalance between neighboring sites can be arbitrarily low and do not exhibit any oscillation in time. For such states the M model order parameter can be expressed as a linear combination of particular degenerate Gross-Pitaevskii (GP) stationary states.…”

“…II we briefly review the main concepts of the multimode model. In particular, we rewrite the equations of motion which include an effective onsite interaction parameter [18] and we outline the construction of the localized states in terms of the GP stationary ones. In Sec.…”