Scattering Problem in Bose-Einstein Condensates with Magnetic Domain Wall

Abstract

We present a comprehensive theoretical study of linear wave scattering from magnetic domain walls with varied twist angles $Θ$ in spin-$1/2$ Bose-Einstein condensates (BECs). Using a gauge transformation, we show that scattering observables depend solely on the total twist $Θ$, independent of chirality. Within the Bogoliubov-de Gennes (BdG) framework, we develop a transfer-matrix method to compute reflection and transmission coefficients for incident phonons and free particles. Our results reveal a scattering threshold at the Zeeman energy $E = \hbarΩ_0$, separating a pure phonon regime from multi-channel scattering involving both collective and single-particle excitations above threshold. For large twist angles, competition between kinetic and Zeeman energies reduces the effective spin rotation, leading to comb-like density modulations and Fano-like resonances below threshold. The transition probability between phonon and particle channels is strongly tunable with $Θ$, enhanced for odd multiples of $π$ but suppressed for even multiples. These findings establish twist-engineered domain walls as a versatile platform for controlling quantum transport, with implications for atomtronic devices and quantum simulation.

Figures (7)

• Figure 1: Spatial profiles of the domain wall's spin rotation angle $\theta(x)$ and its derivative $\theta'(x)$ for a total twist $\Theta = \pi$, and schematic of the multi-channel scattering process for a linear wave incident from the left on the magnetic domain wall. An incident phonon (or particle) can be reflected as a phonon ($|A_2|^2$) or a particle ($|A_6|^2$), and transmitted as a phonon ($|A'_1|^2$) or a particle ($|A'_5|^2$). Evanescent waves ($|A_4|^2$, $|A_8|^2$ on the left and $|A'_3|^2$, $|A'_7|^2$ on the right) are also indicated. The scattering is governed by synthetic spin-orbit coupling induced by the domain wall texture and the mean-field background field.
• Figure 2: (Top) Ground-state properties for a $\Theta=\pi$ domain wall: BEC density profile, wavefunction components (imaginary parts vanish), and spin texture. (Bottom) Energy-dependent scattering probabilities for phonon/particle incidence with $E \in [0.01,2]\Omega_0$. The scattering probabilities are defined as follows: $|A_1'|^2$ (phonon transmission), $|A_2|^2$ (phonon reflection), $|A_5'|^2$ (particle transmission), and $|A_6|^2$ (particle reflection). Current conservation is verified via $F=1$. The ground state is obtained for a system of length $L=20$ with total particle number $N=80$, discretized on a uniform grid with spacing $\Delta x=0.0\dot{3}$.
• Figure 3: Ground-state profile and scattering probabilities for linear waves incident on a domain wall with twist $\Theta = 3\pi/2$.
• Figure 4: Ground-state profile and scattering probabilities for linear waves incident on a domain wall with twist $\Theta = 2\pi$.
• Figure 5: Ground-state profile and scattering probabilities for linear waves incident on a domain wall with twist $\Theta = 3\pi$.