Abstract Here, we study the collapse process of quasi-two-dimensional Bose–Einstein condensate with symmetrized Dresselhaus spin–orbit coupling. We show that at a sufficiently strong spin–orbit coupling the arising spin-dependent velocity compensates the attraction between particles and can prevent the collapse of the condensate. As a result, spin–orbit coupling can lead to a stable condensate rather than the collapse process.
Abstract Here, we study the collapse process of quasi-two-dimensional Bose–Einstein condensate with symmetrized Dresselhaus spin–orbit coupling. We show that at a sufficiently strong spin–orbit coupling the arising spin-dependent velocity compensates the attraction between particles and can prevent the collapse of the condensate. As a result, spin–orbit coupling can lead to a stable condensate rather than the collapse process.
A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent ``anomalous'' velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.
Attractive Bose-Einstein condensates of dilute alkali gases are unstable against collapse in two- and three-dimensional free space. Nevertheless, we demonstrate that the spin-orbit coupling of the two-component condensates counteracts the tendency of collapse and makes the system preferable to an extended spatial distribution in the three-dimensional case. Furthermore, stable topological objects can be formed in the condensates, which are shown to be the lowest energy states. Two configurations of the density profiles, called three-dimensional skyrmion and three-dimensional dimeron, respectively, are identified depending on the strength of the spin-orbit coupling.
We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudospinor system of Gross-Pitaevskii equations with self- and cross attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semivortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by ∼1.5×10^{4}. The results are obtained by means of combined analytical and numerical methods.
By variational analysis and direct numerical simulation, we study the phase transition and stability of a trapped D-dimensional Bose-Einstein condensate with spin-orbit coupling. The complete phase and stability diagrams of the system are presented in full parameter space, while the collapse dynamics induced by the mean-filed attraction and the mechanism for stabilizing the collapse by spin-orbit coupling are illustrated explicitly. Particularly, a full and deep understanding of the dependence of phase transition and stability mechanism on geometric dimensionality and external trap potential is revealed. It is shown that the spin-orbit coupling can modify the dispersion relations, which can balance the mean-filed attractive interaction and result in a spin polarized or overlapped state to stabilize the collapse, then changes the collapsing threshold dependent on the geometric dimensionality and external trap potential. Moreover, from 2D to 3D system, the mean-field attraction for inducing the collapse is reduced and the collapse speed is enhanced, namely, the collapse can be more easily stabilized in 2D system. That is, the collapse can be manipulated by adjusting the spin-orbit coupling, Raman coupling, geometric dimensionality and the external trap potential, which can provide a possible way for elaborating the collapse dynamics experimentally.
Cold atomic Bose-Einstein systems in the presence of simulated Rashba- Dresselhaus spin-orbit coupling exhibit novel physical features. With pure in-plane Rashba coupling the system is predicted in Bogoliubov-Hartree-Fock to have a stable Bose condensate below a critical temperature, even though the effective density of states is two-dimensional. In addition the system has a normal state at all temperatures. We review here the new physics when the system has such spin-orbit coupling, and discuss the nature of the finite temperature condensation phase transition from the normal to condensed phases.
Abstract We demonstrate the formation of stable spatially-ordered states in a uniform and also trapped quasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin–orbit (SO) coupled pseudo spin-1/2 Bose–Einstein condensate using the mean-field Gross–Pitaevskii equation. For weak SO coupling, one can have a circularly-symmetric (0, +1)- or (0, −1)-type multi-ring state with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses denote the net angular momentum projection in the two components, in addition to a circularly-asymmetric degenerate state with zero net angular momentum projection. For intermediate SO couplings, in addition to the above two types, one can also have states with stripe pattern in component densities with no periodic modulation in total density. The stripe state continues to exist for large SO coupling. In addition, a new spatially-periodic state appears in the uniform system: a superlattice state, possessing some properties of a supersolid , with a square-lattice pattern in component densities and also in total density. In a trapped system the superlattice state is slightly different with multi-ring pattern in component density and a square-lattice pattern in total density. For an equal mixture of Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only stripe states are found for all strengths of SO couplings. In a uniform system all these states are quasi-2D solitonic states.