Nonlinear dynamics of Rydberg-dressed Bose-Einstein condensates in a triple-well potential

Abstract

We study nonlinear dynamics of Rydberg-dressed Bose-Einstein condensates (BECs) trapped in a triple-well potential in the semiclassical limit. The Rydberg-dressed BECs experience a long-range soft-core interaction, giving rise to strong nearest and next-nearest neighbor interactions in the triple-well system. Using mean-field Gross-Pitaevskii (GP) equations, we show that lower branches of the eigenspectra exhibit loops and level-crossings when the soft-core interaction is strong. The direct level-crossings eliminate the possibility of adiabatic Landau-Zener transitions when tilting of the triple-well potential. We demonstrate that the long-range interaction allows for self-trapping in one, two, or three wells, in a far more controllable manor than BECs with short-range or dipolar interactions. Exact quantum simulations of the three-well Bose-Hubbard model indicate that selftrapping and nonadiabatic transition can be observed with less than a dozen bosons. Our study is relevant to current research into collective excitation and nonlinear dynamics of Rydberg-dressed atoms.

Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions

“…Though the Hamiltonian ( 2) is Hermitian, the density-dependent nonlinearity prevents us from calculating the eigenenergy through conventional diagonalization. To overcome this, a shooting method will be employed to numerically evaluate the eigenstate Ψj = [ ψ1 , ψ2 , • • • , ψL ] and the corresponding eigenenergy ε j self-consistently [71]. A trial solution is seeded into the semiclassical Hamiltonian.…”

“…Scheme I: First, we consider a linear quench of the potential bias [71]. The bias between two neighboring sites is given by the following function:…”

“…The majority of the condensate is located on the first (leftmost) site [n 1 (0) = |ψ 1 | 2 ≈ 1] initially (Figure 4a). In the adiabatic limit and without the nonlinear interaction, the condensate will move to the third well, n 3 (τ) ≈ 1, after the quench [71]. The population at this adiabatic limit is shown with a black dot in each panel.…”

“…By increasing the interaction strength, we note that the localized state returns to a stable configuration when |γ| is small. This means that the localized state becomes a stable, self-trapped state [71]. When L = 5, the dynamical stability now depends heavily on tilt γ.…”

“…In Ref. [71], we showed that the self-trapping dynamics of Rydberg-dressed BECs can be controlled in a triple-well potential through mean-field and quantum mechanical analyses.…”