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Physics Letters A

Spin–orbit-coupled BEC in a double-well potential: Quantum energy spectrum and flat band

Wen-Yuan Wang, Hui Cao, Jie Liu, Libin Fu

Published Apr 27, 2015• 9 citations
Publisher
DOI
10.1016/j.physleta.2015.04.028

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Motivated by recent efforts in creating flat bands in ultracold atomic systems, we investigate how to probe a flat band in an optically trapped spin-orbital-coupled Bose-Einstein condensate using Bragg spectroscopy. We find that the excitation spectrum and the dynamic structure factor of the condensate are dramatically altered when the band structure exhibits various levels of flatness. In particular, when the band exhibits perfect flatness around the band minima corresponding to a near-infinite effective mass, a quadratic dispersion emerges in the low-energy excitation spectrum; in sharp contrast, for the opposite case when an ordinary band is present, the familiar linear dispersion arises. Such linear-to-quadratic crossover in the low-energy spectrum presents a striking manifestation of the transition of an ordinary band into a flat band, thereby allowing a direct probe of the flat band by using Bragg spectroscopy.
Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.
Gap solitons (GSs) bifurcating from flat bands, which may be represented in terms of Wannier functions, have garnered significant interest due to their strong localization with extremely small norms. Moiré lattices (MLs), with multiple flat bands, offer an appropriate platform for creating such solitons. We explore the formation mechanism and stability of GSs in spin-1 Bose-Einstein condensates under the combined action of the Rashba spin-orbit coupling (SOC) and an ML potential. We identify five Wannier-type GS families bifurcating from the lowest five energy bands in the spectrum induced by the ML with sufficiently large period and depth. These fundamental GSs serve as basic elements for constructing more complex Wannier-type GS states. Reducing the lattice period and depth triggers a transition from the Wannier-type GSs to those of the Bloch type, the latter exhibiting higher norm thresholds and pronounced spatial broadening near edges of the energy bands. In addition to tuning the lattice-potential parameters, adjusting the SOC strength can also modulate the flatness of energy bands and enhance the localization of gap solitons, enabling reversible transitions between the GSs of the Wannier and Bloch types. Distinctive properties of GSs in the quasiperiodic ML are uncovered too. Thus, we propose the theoretical foundation for the creation of and manipulations with strongly localized GSs.