Solitons in a Spin-Orbit-Coupled Spin-1 Bose-Einstein Condensate
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ATOMIC PHYSICS
Solitons in a Spin-Orbit-Coupled Spin-1 Bose-Einstein Condensate Sandeep Gautam1 · S. K. Adhikari2 Received: 1 September 2020 / Accepted: 2 September 2020 © Sociedade Brasileira de F´ısica 2020
Abstract After the pioneering studies on spinor Bose-Einstein condensate (BEC) and after the realization of spin-orbit (SO) coupling in a spinor BEC of 87 Rb and 23 Na atoms, it is now realized that an SO-coupled BEC may reveal new physical phenomena not possible in a scalar BEC. For example, a new class of two- or three-dimensional vector soliton can be stabilized and observed in an SO-coupled BEC, whereas such a soliton is unstable in a scalar BEC. In this paper, we present a review on solitons in an SO-coupled spin-1 spinor BEC in one, two, and three space dimensions. In addition to the static properties of these solitons, we also consider their dynamics of motion with a constant velocity and collision between two solitons. Keywords Spinor Bose-Einstein condensate · Spin-orbit coupling · Soliton
1 Introduction A bright soliton or a localized solitary wave is a selfreinforcing wave packet that maintains its shape while travelling with a constant velocity [1, 2]. This localized hump in the amplitude of the order parameter is the result of balancing of the dispersive kinetic energy with the focussing nonlinearity in the Hamiltonian. The wide range of the systems in which bright solitons have been studied include shallow water waves, non-linear optical systems [1, 2], and both scalar [3–9] and spinor [10–16] Bose-Einstein condensates (BECs). After the realization of a multi-component spinor BEC [17] with non-zero hyperfine spin, there has been interest to introduce a spin-orbit (SO) coupling in the bosonic atoms [18–20] as in the case of charged electron. Although there cannot be a natural SO coupling in a neutral atom, it is possible to introduce an artificial synthetic SO coupling by tuned Raman lasers coupling the different spin states [18–20]. Two such possible SO couplings are due to Dresselhaus [21] S. K. Adhikari
[email protected] Sandeep Gautam [email protected] 1
Department of Physics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India
2
Instituto de F´ısica Te´orica, UNESP - Universidade Estadual Paulista, 01.140-070 S˜ao Paulo, S˜ao Paulo, Brazil
and Rashba [22]. In the last decade, an important milestone in the field of spinor BECs has been the experimental realization of equal strength Rashba and Dresselhaus SO couplings in a pseudo spin-1/2 BEC of 87 Rb [23] and 23 Na [24] atoms containing two spin components Fz = 0, −1 of spin F = 1 bosons and in a spin-1 BEC of 87 Rb [25] atoms containing all the three spin components Fz = ±1, 0. The generation of non-Abelian gauge fields leading to a variety of SO couplings is discussed in refs. [18–20, 26–28]. This has also spurred theoretical studies on the solitary waves in SOcoupled pseudo spin-1/2 BECs in quasi-one-dimensional (quasi-1D) [29], quasi-two-dimensional (quasi-2D) [30– 34], and three-dimensional (3D) [35] geome
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