Stephanovich V A, Kirichenko E V, Engel G, Sinner A
Institute of Physics, University of Opole, Oleska 48, 45-052, Opole, Poland.
Phys Rev E. 2024 Jan;109(1-1):014222. doi: 10.1103/PhysRevE.109.014222.
We study the ensemble of pseudo-spin 1/2 ultracold bosons, performing Lévy flights, confined in a parabolic potential. The (pseudo-) spin-orbit coupling (SOC) is additionally imposed on these particles. We consider the structure and dynamics of macroscopic pseudospin qubits based on Bose-Einstein condensates, obtained from the above "fractional" bosons. Under "fractional" we understand the substitution of the ordinary second derivative (kinetic energy term) in the Gross-Pitaevskii equation by a so-called fractional Laplacian, characterized by the Lévy index μ. We show that the joint action of interparticle interaction, SOC, and Zeeman splitting in a synthetic magnetic field makes the dynamics of corresponding qubit highly nontrivial with evident chaotic features at both strong interactions and Lévy indices μ→1 when the Lévy trajectories of bosons with long jumps dominated over those derived from ordinary Gaussian distribution, corresponding to μ=2. Using analytical and numerical arguments, we discuss the possibilities to control the above qubit using the synergy of SOC, interaction strength, and "fractionality," characterized by the Lévy index μ.
我们研究了限制在抛物形势阱中、进行 Lévy 飞行的伪自旋 1/2 超冷玻色子系综。此外，（伪）自旋轨道耦合（SOC）被施加于这些粒子上。我们考虑基于从上述“分数”玻色子获得的玻色 - 爱因斯坦凝聚体的宏观伪自旋量子比特的结构和动力学。在“分数”的情况下，我们指的是在格罗斯 - 皮塔耶夫斯基方程中用所谓的分数拉普拉斯算子替代普通的二阶导数（动能项），该分数拉普拉斯算子由 Lévy 指数 μ 表征。我们表明，在合成磁场中，粒子间相互作用、SOC 和塞曼分裂的联合作用使得相应量子比特的动力学非常复杂，在强相互作用以及 Lévy 指数 μ → 1 时具有明显的混沌特征，此时具有长跳跃的玻色子的 Lévy 轨迹比对应于 μ = 2 的普通高斯分布所导出的轨迹占主导。通过解析和数值论证，我们讨论了利用 SOC、相互作用强度和由 Lévy 指数 μ 表征的“分数性”的协同作用来控制上述量子比特的可能性。
