Flipping-shuttle oscillations of bright one- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with Rabi mixing

Abstract

We analyze a possibility of macroscopic quantum effects in the form of coupled structural oscillations and shuttle motion of bright two-component spin-orbit-coupled striped (one-dimensional, 1D) and semi-vortex (two-dimensional, 2D) matter-wave solitons, under the action of linear mixing (Rabi coupling) between the components. In 1D, the intrinsic oscillations manifest themselves as flippings between spatially even and odd components of striped solitons, while in 2D the system features periodic transitions between zero-vorticity and vortical components of semi-vortex solitons. The consideration is performed by means of a combination of analytical and numerical methods. I. INTRODUCTIONAtomic Bose-Einstein condensates (BEC), in addition to exhibiting a great deal of their own dynamical regimes [1-3], have drawn a lot of interest as testing grounds for the emulation of various effects from condensed-matter physics [4], a prominent example provided by the spin-orbit coupling (SOC). Although the true spin of bosonic atoms, such as 87 Rb, used for the SOC emulation in BEC, is zero, the wave function of the condensate may be composed as a mixture of two components representing different hyperfine atomic states. The resulting pseudospin 1/2 makes it possible to map the spinor wave function of electrons in solids into the two-component bosonic wave function of the atomic BEC. Breakthrough experiments [5,6] have demonstrated the real possibility to simulate the SOC effect in the bosonic gas, in the form of the linear interaction between the momentum and pseudospin of coherent matter waves. Two fundamental types of the SOC, well known from works on physics of semiconductors, which are represented by the Dresselhaus [9] and Rashba [8] Hamiltonians, as well as the Zeeman-splitting effect [7], may be simulated in the atomic BEC. While the initial experiments on the SOC emulation realized effectively one-dimensional (1D) settings [10,11], the implementation of the SOC in an effectively 2D geometry was reported too [12].The SOC being a linear effect by itself, its interplay with the intrinsic nonlinearity of the BEC, which is usually induced, in the mean-field approximation, by contact inter-atomic collisions or long-range dipole-dipole interactions, produces various localized structures, such as vortices [13][14][15][16][17], monopoles [18], skyrmions [19,20], and dark solitons [21,22]. The use of periodic potentials, induced by optical lattices, offers additional possibilities -in particular, the creation of gap solitons [23,24,57].The conventional repulsive sign of inter-atomic forces can be switched to attraction by means of the Feshbach resonance [26,27], which suggests possibilities for the creation of bright matter-wave solitons [28][29][30][31], in addition to the well-known dark ones [32]. In particular, the modulational instability [33] and various options for the making of effectively 1D bright solitons under the action of SOC in attractive condensates have been theoretically analyzed in detail [34]- [44]. A challengi...

Topological excitations in rotating Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling in a two-dimensional optical lattice

“…Recent experimental realization of artificial spin-orbit coupling (SOC) [4][5][6][7][8] which couples the internal states and the orbit motion of the atoms not only offers a platform to simulate the response of charged particles to external electromagnetic field, but also give opportunities to search of novel quantum states [9][10][11][12][13][14][15][16][17][18]. Relevant investigations show that the SOC can lead to many new quantum phases such as plane-wave phase [19], stripe phase [20][21][22], bright soliton [23,24], dark soliton [25], half-quantum vortex configuration [22,26,27], and topological superfluid phase [6], which enrich the phase diagram and physics of BEC system. In particular, the combined effects of SOC and rotation on the BECs are predicted to generate various novel features.…”

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.…”

Bright solitons in a spin-tensor-momentum-coupled Bose-Einstein condensate

“…The lack of Galilean invariance in spin-orbit-coupled systems [24] makes that it is nontrivial to find movable solitons, one can not directly obtain a movable soliton from its stationary correspondence. Different aspects of bright solitons with the SOC have been investigated a lot [25][26][27][28][29][30], ranging from with long-ranged dipole interactions [31][32][33] to in optical lattices [34][35][36][37][38][39][40].…”