In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coupling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multidimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.PACS numbers: 42.50. Gy, 37.10.De, 42.25.Bs Although cold gases are typically neutral, artificial electromagnetism may be induced by several means, including rotation [1], manipulation of atoms in optical lattices [2,3,4], and the use of laser arrangements [5]. Interestingly, seminal experiments on optically created gauge fields have been recently reported [6]. Artificial electromagnetism has attracted a growing attention in recent years, partially due to the possibility of achieving nonAbelian gauge fields [4,5], which establish fascinating links between cold gases and high-energy physics [4,7,8]. A striking example is given by the possibility of inducing quasi-relativistic physics in cold atoms despite the extremely low velocities involved [9]. In particular, under proper conditions cold atoms may experience an effective spin-orbit coupling, which leads to a Dirac cone in the dispersion [10], resembling the case of yet another paradigm of modern physics, namely graphene [11,12]. Similar phenomena are expected in cold atoms and graphene including Veselago lensing [9,13,14].Interparticle interactions lead to inherent nonlinearities in Bose-Einstein condensates (BECs). At sufficiently low temperatures the BEC physics is described by a nonlinear Schödinger equation similar to that found in nonlinear optics [1]. Resemblances between both fields have been successfully explored in recent years, most remarkably in what concerns the physics of solitons [15,16,17,18,19], for which nonlinearity and dispersion compensate leading to a non-dispersing solution. Nonlinearity plays also an important role in high-energy physics. Indeed, non-linear Dirac equations (NLDEs), and more generally non-linear spinor fields, have been studied extensively, starting with the pioneering works of Ivanenko [20], Weyl [21], and Heisenberg [22]. These equations may present also localized solutions [23,24].In this Letter we explore the nonlinear physics of a multicomponent BEC (also called spinor BEC [25]) in the presence of an optically-induced spin-orbit coupling. In the low-momentum limit, the spinor BEC may be described by a particular type of two-component NLDE. We show that for the case of attractive interactions, the condensate may become self-trapped, rese...
Ultra-cold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels.
We investigate the dynamics of a spinor Bose-Einstein condensate which is governed by an optically induced non-Abelian gauge potential. Using a ring shaped trap to confine the atoms and a hydrodynamic ansatz, nonlinear Josephson type equations are found to describe the system. The degenerate eigenstates which show rotation are solved exactly. We consider a homogenous filled ring and observe population dynamics between the two quasi-spin components but also space dependent Josephson oscillations. Stable mass currents can be observed which are induced by the constant non-Abelian effective magnetic field in the limit of weak interactions. For strong interactions the appearance of two-component dark soliton-like objects are observed.
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