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arXiv:2411.02839 · Physical Review Research

Transfer of solitons and half-vortex solitons via adiabatic passage

Chenhui Wang, Yongping Zhang, V. V. Konotop

Published Nov 4, 2024• 3 citations

Abstract

We show that the transfer of matter-wave solitons and half-vortex solitons in a spin-orbit coupled Bose-Einstein condensate between two (or more) arbitrarily chosen sites of an optical lattice can be implemented using the adiabatic passage. The underlying linear Hamiltonian has a flat band in its spectrum, so that even sufficiently weak interatomic interactions can sustain well-localized Wannier solitons which are involved in the transfer process. The adiabatic passage is assisted by properly chosen spatial and temporal modulations of the Rabi frequency. Within the framework of a few-mode approximation, the mechanism is enabled by a dark state created by coupling the initial and target low-energy solitons with a high-energy extended Bloch state, like in the conventional stimulated Raman adiabatic passage used for the coherent control of quantum states. In real space, however, the atomic transfer between initial and target states is sustained by the current carried by the extended Bloch state, which remains populated during the whole process. The full description of the transfer is provided by the Gross-Pitaevskii equation. Protocols for the adiabatic passage are described for one- and two-dimensional optical lattices, as well as for splitting and subsequent transfer of an initial wave packet simultaneously to two different target locations. Published by the American Physical Society 2024

DOI: 10.1103/physrevresearch.6.043089

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We show that the transfer of matter-wave solitons and half-vortex solitons in a spin-orbit coupled Bose-Einstein condensate between two (or more) arbitrarily chosen sites of an optical lattice can be implemented using the adiabatic passage. The underlying linear Hamiltonian has a flat band in its spectrum, so that even sufficiently weak interatomic interactions can sustain well-localized Wannier solitons which are involved in the transfer process. The adiabatic passage is assisted by properly chosen spatial and temporal modulations of the Rabi frequency. Within the framework of a few-mode approximation, the mechanism is enabled by a dark state created by coupling the initial and target low-energy solitons with a high-energy extended Bloch state, like in the conventional stimulated Raman adiabatic passage used for the coherent control of quantum states. In real space, however, the atomic transfer between initial and target states is sustained by the current carried by the extended Bloch state, which remains populated during the whole process. The full description of the transfer is provided by the Gross-Pitaevskii equation. Protocols for the adiabatic passage are described for one- and two-dimensional optical lattices, as well as for splitting and subsequent transfer of an initial wave packet simultaneously to two different target locations. Published by the American Physical Society 2024

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We examine a scheme for the optical creation of a superfluid vortex in a trapped Bose-Einstein condensate, using the stimulated Raman adiabatic passage technique (STIRAP). By exposing an oblate, axis-symmetric condensate to two copropagating laser pulses, one can transfer external angular momentum from the light field to the matter wave, if one of the beams is the fundamental Gaussian mode and the other is a Gauss-Laguerre mode of angular momentum $1\ensuremath{\hbar}$. We demonstrate the complete transfer efficiency by numerical integration of the multicomponent Gross-Pitaevskii equation and explain the results with an intuitive and accurate approximation within the Thomas-Fermi limit. In addition, we discuss residual excitations (breathing modes) which occur in the two-dimensional regime and present the Bogoliubov excitation spectrum.

We investigate families of soliton solutions in a spin-orbit-coupled Bose-Einstein condensate embedded in an optical lattice, which bifurcate from the nearly flat lowest band. Unlike the conventional gap solitons, the obtained solutions have the shape well approximated by a Wannier function (or a few Wannier functions) of the underlying linear Hamiltonian with amplitudes varying along the family and with nearly constant widths. The Wannier solitons sharing all symmetries of the system Hamiltonian are found to be stable. Such solutions allow for the construction of Wannier breathers that can be viewed as nonlinearly coupled one-hump solitons. The breathers are well described by a few-mode model and manifest stable behavior either in an oscillatory regime with balanced average populations or in a self-trapping regime characterized by unbalanced atomic populations of the local potential minima (similarly to the conventional boson Josephson junction), with the frequencies controlled by the interatomic interactions.

We examine a scheme for the optical creation of a superfluid vortex in a trapped Bose-Einstein condensate (BEC), using the stimulated Raman adiabatic passage (STIRAP) technique. By exposing an oblate, axis-symmetric condensate to two co-propagating laser pulses, one can transfer external angular momentum from the light field to the matter wave, if one of the beams is the fundamental Gaussian mode and the other is a Gauss-Laguerre mode of angular momentum

1\hbar

. We demonstrate the complete transfer efficiency by numerical integration of the multi-component Gross-Pitaevskii equation and explain the results with an intuitive and accurate approximation within the Thomas-Fermi limit. In addition, we discuss residual excitations (breathing modes) which occur in the two-dimensional regime and present the Bogoliubov excitation spectrum.

Periodic potentials with flat bands in their spectra support strongly localized nonlinear excitations. Although a perfectly flat band cannot exist in a continuous systems, a spin–orbit–coupled Bose–Einstein condensate loaded in a Zeeman lattice can realize the quasi-flat lowest band with an extremely narrow bandwidth. In such a quasi-flat band, half-vortex solitons become confined within a single lattice cell, enabling the formation of arrays of coupled half-vortex solitons arranged of various spatial geometries. In this work, we study the existence and stability of these lattices within the framework of the two-component Gross–Pitaevskii equation. We demonstrate that, near the quasi-flat band, half-vortex solitons and their arrays can be excited with a nearly negligible number of atoms and are constrained by their local symmetries, which are isomorphic to a dihedral group of order 8. This allows observation of the respective field patterns in the nearly linear regime where they exhibit enhanced stability. The constructed lattices may have diverse geometric profiles, and in particular create a composite super-half-vortex soliton with nonlinear symmetry breaking. • A two-dimensional Zeeman lattice with a quasi-flat is obtained. • Half-vortex solitons with a negligible threshold energy are found; they can be observed in a quasi-linear regime. • Stable half-vortex soliton lattices of different shapes, as well as super-half-vortex solitons are obtained.