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Physical Review A

Three-dimensional solitons in Bose-Einstein condensates with spin-orbit coupling and Bessel optical lattices

Hong Li, Si-Liu Xu, Milivoj R. Belić, Jiaxi Cheng

Published Sep 26, 2018• 52 citations
Publisher

Abstract

Applying a variational approach and numerical analysis to the system of Gross-Pitaevskii equations, we find three-dimensional (3D) stable solitons in binary atomic Bose-Einstein condensates with spin-orbit coupling (SOC) and out-of-phase linear and nonlinear Bessel optical lattices. We discuss the stability of 3D solitons by utilizing their norm and energy. The introduction of Bessel potentials makes the evolution and collisions of solitons more stable and improves their resistance to collapse. Depending on the strength of the intra- and intercomponent spatial modulation of the nonlinearity and SOC, we find stable solitons of the semivortex and mixed-mode structures. Furthermore, we show that the solitons are stable against small perturbations in propagation and collisions.

DOI
10.1103/physreva.98.033827

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Applying a variational approach and numerical analysis to the system of Gross-Pitaevskii equations, we find three-dimensional (3D) stable solitons in binary atomic Bose-Einstein condensates with spin-orbit coupling (SOC) and out-of-phase linear and nonlinear Bessel optical lattices. We discuss the stability of 3D solitons by utilizing their norm and energy. The introduction of Bessel potentials makes the evolution and collisions of solitons more stable and improves their resistance to collapse. Depending on the strength of the intra- and intercomponent spatial modulation of the nonlinearity and SOC, we find stable solitons of the semivortex and mixed-mode structures. Furthermore, we show that the solitons are stable against small perturbations in propagation and collisions.
By means of variational methods and systematic numerical analysis, we demonstrate the existence of metastable solitons in three dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and spin-orbit coupling, which can be engineered by available experimental techniques. Depending on the relative strength of the intra- and intercomponent attraction, the stable solitons feature a semivortex or mixed-mode structure. In spite of the fact that the local cubic self-attraction gives rise to the supercritical collapse in 3D, and hence the setting produces no true ground state, the solitons are stable against small perturbations, motion, and collisions.
Applying an imaginary time evolution method (AITEM) to the system of Gross–Pitaevskii equations, we find two-dimensional stable solitons in binary atomic Bose–Einstein condensates with spin–orbit coupling (SOC) and the Rydberg–Rydberg interaction (RRI). The stability of 2D solitons by utilizing their norm and energy is discussed in detail. Depending on the SOC and Rydberg–Rydberg interaction, we find stable zero-vorticity and vortical solitons. Furthermore, we show that the solitons can be effectively tuned by the local and nonlocal nonlinearities of this system.
We elaborate a mechanism for the creation of stable three-dimensional (3D) solitons in spin-orbit-coupled (SOC) atomic-molecular Bose-Einstein condensate, modeled by the mean-field equations with the quadratic three-wave interaction, characterized by mismatch ααα. The planar (effectively two-dimensional) SOC is applied to the soliton's atomic component, structuring it as a mixed mode (MM) or semi-vortex (SV). The molecular component of the SV soliton is shaped as a 3D vortex, while the molecular component in the MM soliton is an MM too. The solitons exist up to a critical value of ααα. The system demonstrates a relatively large norm share of the vortex components, exceeding 50%50\%50% of the total norm, which is an essential feature of SOC-supported solitons. This is scheme for realizing stable vortex solitons in free space with the quadratic nonlinearity.
ABSTRACT We address three‐dimensional (3D) solitons maintained by spin‐orbit coupling (SOC) in the binary self‐interacting Bose‐Einstein condensate (BEC) held in the 3D optical lattice (OL). The analysis reveals that the SOC‐OL interplay results in the formation of stable full‐vortex (FV) solitons, built as sets of four density peaks residing in neighboring wells of the lattice potential, with the superimposed global vortical phase, and site‐centered semi‐vortices (SVs), in which the vorticity is present in only one component. The FV solitons, with their specific phase textures, do not exist in a uniform BEC with SOC. FV and SV states in the binary self‐attractive BEC are stable despite the possibility of the supercritical collapse in the 3D system. Such states also exist, as gap solitons, in the self‐repulsive 3D system. In terms of the chemical potential and number of particles, the stability regions of the 3D FV solitons and SVs expand with the increase of the SOC strength and OL depth. The results open the route to the creation of 3D complexes of vorticity‐carrying condensates that can be realized with existing experimental techniques.
The existence and stability of solitons in Bose-Einstein condensates with attractive interatomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of 7Li^{7}\mathrm{Li}7Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is $\ensuremath{\approx}6$ recoil energies in the lattice. The respective energy versus norm diagram features two cuspidal points, resulting in a typical swallowtail pattern, which is a generic feature of 3D solitons supported by quasi-two-dimensional or fully dimensional lattice potentials.
Excited states (ESs) of two- and three-dimensional (2D and 3D) solitons of the semivortex (SV) and mixed-mode (MM) types, supported by the interplay of the spin-orbit coupling (SOC) and local nonlinearity in binary Bose-Einstein condensates, are unstable, on the contrary to the stability of the SV and MM solitons in their fundamental states. We propose a stabilization strategy for these states in 3D, combining SOC and long-range Rydberg-Rydberg interactions (RRI), in the presence of a spatially-periodic potential, that may include a parity-time (PT)-symmetric component. ESs of the SV solitons, which carry integer vorticities S and S+1 in their two components, exhibit robustness up to S= 4. ESs of MM solitons feature an interwoven necklace-like structure, with the components carrying opposite fractional values of the orbital angular momentum. Regions of the effective stability of the 3D solitons of the SV and MM types (both fundamental ones and ESs), are identified as functions of the imaginary component of the PT-symmetric potential and strengths of the SOC and RRI terms.