Abstract
We show that attractive two-dimensional (2D) spinor Bose–Einstein condensates with helicoidal spatially periodic spin–orbit coupling (SOC) support a rich variety of stable fundamental solitons and bound soliton complexes. Such states exist with chemical potentials belonging to the semi-infinite gap in the band spectrum created by the periodically modulated SOC. All these states exist above a certain threshold value of the norm. The chemical potential of fundamental solitons attains the bottom of the lowest band, whose locus is a ring in the space of Bloch momenta, and the radius of the non-monotonous function of the SOC strength. The chemical potential of soliton complexes does not attain the band edge. The complexes are bound states of several out-of-phase fundamental solitons whose centers are placed at local maxima of the SOC-modulation phase. In this sense, the impact of the helicoidal SOC landscape on the solitons is similar to that of a periodic 2D potential. In particular, it can compensate repulsive forces between out-of-phase solitons, making their bound states stable. Extended stability domains are found for complexes built of two and four solitons (dipoles and quadrupoles, respectively). They are typically stable below a critical value of the chemical potential.
Highlights
Spin-orbit coupling (SOC) is a fundamentally important effect in physics of semiconductors, whose theoretical models [1, 2] and experimental manifestations [3, 4] have been known for a long time
Much interest was drawn to emulation of SOC in binary ultracold gases [these are two-component Bose-Einstein condensates (BEC)] [5, 6, 7, 8]
We demonstrate that stable solitons form sets of states, generated from a seed one by symmetry transformations
Summary
Spin-orbit coupling (SOC) is a fundamentally important effect in physics of semiconductors, whose theoretical models [1, 2] and experimental manifestations [3, 4] have been known for a long time. The total effect of a SOC gauge field can lead to the enhanced stability of solitons in media with attractive interactions, and to the existence of novel stable localized modes – quasisolitons – in purely repulsive condensates, both in the free space and in the presence of traps [48]. This system, with a helicoidal orientation of the local SOC [see equation (1)], gives rise to a vast stability region for fundamental 2D pseudo-spinor solitons It produces stable dipole and quadrupole bound states of fundamental solitons with opposite signs, which cannot be found in the absence of the spatially-periodic modulation.
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