We predict that spatially modulated Zeeman splitting resulting in the formation of a Zeeman lattice can be used for creation of localized self-sustained excitations in spinor polariton condensates with dominant repulsive interactions. In such lattices, the phenomenon of TE-TM splitting, playing the role of effective spin-orbit interaction, leads to the emergence of the stripe phase and formation of stable gap-stripe solitons with a complex intrinsic structure resulting from the presence of two characteristic spatial scales, one of which is set by the period of the Zeeman lattice, while the other is set by the momentum in the depth of the Brillouin zone, at which such solitons bifurcate from the linear spectrum. Gap-stripe polariton solitons can be excited by a suitable resonant pump.
We predict that spatially modulated Zeeman splitting resulting in the formation of a Zeeman lattice can be used for creation of localized self-sustained excitations in spinor polariton condensates with dominant repulsive interactions. In such lattices, the phenomenon of TE-TM splitting, playing the role of effective spin-orbit interaction, leads to the emergence of the stripe phase and formation of stable gap-stripe solitons with a complex intrinsic structure resulting from the presence of two characteristic spatial scales, one of which is set by the period of the Zeeman lattice, while the other is set by the momentum in the depth of the Brillouin zone, at which such solitons bifurcate from the linear spectrum. Gap-stripe polariton solitons can be excited by a suitable resonant pump.
Topological insulators are unique materials possessing forbidden topological gap and behaving similar to usual insulators in their bulk, but at the same time supporting localized in-gap states at their edges that demonstrate exceptional robustness, because they are protected by topology of the system and cannot be destroyed by local disorder or edge perturbations. Topological insulators discovered in different areas of physics, including optics, acoustics, and physics of Bose-Einstein and polariton condensates, usually employ potential landscapes (or lattices), designed such as to feature specific degeneracies in their linear modal spectra, that can be lifted by various physical effects or controllable deformations of the potential, leading to opening of the topological gap, where edge states appear. In this work, using binary Bose-Einstein condensate we propose a type of topological insulator that does not explicitly use specially designed potential landscape, but instead utilizes spatially inhomogeneous Rabi coupling between two components, in the form of a one- or two-dimensional Su-Schrieffer-Heeger structure, combined with Zeeman splitting. Such Rabi lattices reveal the appearance of topologically nontrivial phases (including higher-order ones) controlled by spatial shift of the domains with enhanced coupling between condensates within unit cells of the structure, where localized topological states appear at the edges or in the corners of truncated Rabi lattice. We also show that the properties of edge states, their spatial localization, and location of their chemical potential within topological gap can be controlled by interatomic interactions that lead to formation of gap topological edge solitons bifurcating from linear edge states. Such solitons in condensates with inhomogeneous Rabi coupling appear as very robust nonlinear topological objects that do not require any threshold norm for their formation even in two-dimensional geometries, and that can exist in stable form for both attractive and repulsive interactions. Our results demonstrate considerable enhancement of stability of solitons in topological Rabi lattices in comparison with trivial Rabi lattices. They open additional prospects for realization of topologically nontrivial phases by spatial engineering of coupling in multicomponent systems.
We elaborate a mechanism for the formation of stable solitons of the semivortex type (with vorticities 0 and 1 in their two components), populating a finite band gap in the spectrum of the spin-orbit-coupled binary Bose-Einstein condensate with the Zeeman splitting, in the two-dimensional (2D) free space, under conditions which make the kinetic-energy terms in the respective coupled Gross-Pitaevskii equations negligible. Unlike a recent work which used long-range dipole-dipole interactions to construct stable gap solitons in a similar setting, we here demonstrate that stable solitons are supported by generic local interactions of both attractive and repulsive signs, provided that the relative strength of the cross- and self-interactions in the two-component system does not exceed a critical value $\ensuremath{\approx}0.77$. A boundary between stable and unstable fundamental 2D gap solitons is precisely predicted by the Vakhitov-Kolokolov criterion, while all excited states of the 2D solitons, with vorticities (m,1+m) in the two components, m=1,2,..., are unstable. The analysis of the one-dimensional (1D) reduction of the system produces an exact analytical solution for the family of gap solitons which populate the entire band gap, the family being fully stable. Motion of the 1D solitons in the trapping potential is considered too, showing that their effective mass is positive or negative if the cubic nonlinearity is attractive or repulsive, respectively.
We report a diversity of stable gap solitons in a spin-orbit-coupled Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is shown that the solitons can be classified by the main physical symmetries they obey, i.e., symmetries with respect to parity (P), time (T), and internal degree of freedom, i.e., spin (C), inversions. The conventional gap and gap-stripe solitons are obtained in lattices with different parameters. It is shown that solitons of the same type but obeying different symmetries can exist in the same lattice at different spatial locations. PT and CPT symmetric solitons have antiferromagnetic structure and are characterized, respectively, by nonzero and zero total magnetizations.
It was recently found that, under the action of the spin-orbit coupling (SOC) and Zeeman splitting (ZS), binary BEC with intrinsic cubic nonlinearity supports families of gap solitons, provided that the kinetic energy is negligible in comparison with the SOC and ZS terms. We demonstrate that, also under the action of SOC and ZS, a similar setting may be introduced for BEC with two components representing different atomic states, resonantly coupled by microwave radiation, while the Poisson's equation accounts for the feedback of the two-component atomic wave function onto the radiation. The microwave-mediated interaction induces an effective nonlinear trapping potential, which strongly affects the purport of the linear spectrum in this system. As a result, families of both gap and embedded solitons (those overlapping with the continuous spectrum) are found, being chiefly stable. The shape of the solitons features exact or broken skew symmetry. In addition to fundamental solitons (whose shape may or may not include a node), a family of dipole solitons is constructed too, which are even more stable than their fundamental counterparts. A nontrivial stability area is identified for moving solitons in the present system, which lacks Galilean invariance. Colliding solitons merge into a single one.
We model the nonlinear behavior of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or antiferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multicomponent structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA) frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetization, i.e., intrinsic precession of the local spin. Finally, we demonstrate that nonstationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.
We study the formation of solitons in a uniform quasi-two-dimensional (quasi-2D) spin-orbit (SO) coupled self-repulsive binary dipolar and nondipolar Bose-Einstein condensate (BEC) using the mean-field Gross-Pitaevskii equation. For a weak SO coupling, in a nondipolar BEC, one can have three types of degenerate solitons: a multiring soliton with intrinsic vorticity of angular momentum projection +1 or -1 in one component and 0 in the other, a circularly asymmetric soliton, and a stripe soliton with stripes in the density. For an intermediate SO coupling, the multiring soliton ceases to exist and a square-lattice soliton appears with a spatially periodic pattern in density on a square lattice, in addition to the degenerate circularly asymmetric and stripe solitons. In the presence of a dipolar interaction, with the polarization direction aligned in the quasi-2D plane, only the degenerate circularly asymmetric and stripe solitons appear.