Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling

Abstract

We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for existence of stable propagating solitons. Such states are found in the rotating frame, where the helicoidal SO coupling is reduced to a homogeneous one. In the absence of the Zeeman splitting the coupled Gross-Pitaevskii equations describing localized states feature many properties of the integrable systems. In particular, four-parametric families of solitons can be obtained in the exact form. Such solitons interact elastically. Zeeman splitting still allows for the existence of two families of moving solitons, but makes collisions of solitons inelastic. PACS numbers:When parameters of a continuous medium vary periodically the translational invariance is broken and nonlinear localized excitations cannot propagate freely. This is at variance with the linear systems, where the Bloch theory allows for quantum particles or waves to move without backscattering. The well-known examples are electrons in solids, atoms in optical latices, electromagnetic waves in photonic crystals, and many others. Physical understanding of the interplay between the nonlinearity and periodicity is simple. Since the nonlinear excitations are localized, in the presence of a periodic potential their energy depends on the spatial location of the wavepacket. Respectively, a steady forward motion is impossible because of the potential barriers causing radiative losses of moving localized wavepackets.. These facts are well documented, both theoretically and experimentally, in the physics of Bose-Einstein condensates (BECs) [1] and in nonlinear optics [2]. Several approaches to obtaining moving solitons in periodic media were suggested. Radiation is reduced for sufficiently wide and small-amplitude solitons in linear lattices (described using envelope function approach in photonics [3] or effective mass approximation in the meanfield theory [4]), as well as in nonlinear lattices [5]. Mobility of strongly localized solitons can be enhanced in lattices with saturable, quadratic or nonlocal nonlinearities, as well as in materials with competing linear and nonlinear lattices (see [6] for a review). However, in all these models radiation is not arrested completely: it becomes detectable at large propagation distances.In this Letter we show that freely moving nonlinear waves can exist if a system obeys special symmetries. In contrast to all previous studies, the solitons reported here do not radiate and propagate over infinitely long distances for any peak amplitude or any ratio of soliton width to system period. As the case example we consider a spin-orbit (SO) coupled BEC which is well accessible in laboratories [7,8] and represents a versatile tool for study of the nonlinear physics of synthetic fields [9] and gauge potentials [10,11]. We consider a SO-BEC described by the Hamiltonian, whose linear part reads2 /2 + ∆σ ...

Spin dynamics in helical molecules with nonlinear interactions

“…j j j j j 0 1 1 around the movable singularity manifold f(x, t)=0. By means of this test, it can also be proved that equation (21) is the only integrable case of a model very recently put forward by Kartashov and Konotov to study the dynamics of Bose-Einstein condensates with helical SOC [40]. Furthermore, it reduces to the Manakov nonlinear system when the SOC vanishes [41,42].…”

Solitons in a nonlinear model of spin transport in helical molecules

“…The result is that the model has the Painlevé property and, therefore, it can be considered as an integrable model, as opposed to different generalizations that have not such property (e.g. model introduced by Kartashov and Konotop with non-vanishing Zeeman splitting [31]). …”

Formation, stability, and dynamics of vector bright solitons in a trapless Bose–Einstein condensate with spin–orbit coupling

“…Recently, the successfully experimental realization of artificial spin-orbit coupling (SOC) in BEC has broadened the frontier of ultracold atomic gases used for quantum simulations [19][20][21][22][23][24][25][26][27]. This degree of freedom opens up a new avenue to study the fundamental properties of various topologic defects due to the close relationship between the spin and motional degrees of freedom [28][29][30][31][32][33][34][35][36][37][38][39][40]. In the presence of SOC, a variety new types of solitons, such as half-vortex gap solitons [41], discrete and continuum composite solitons [42], and many others, have been predicted.…”