The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attracting atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolution of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse while the collapse is observed only in a single pseudospin component. It is demonstrated that for cross-spin-coupling only double spin-components collapse can occur.
The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attracting atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolution of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse while the collapse is observed only in a single pseudospin component. It is demonstrated that for cross-spin-coupling only double spin-components collapse can occur.
We study the collective dynamics of the spin-orbit coupled two pseudospin components of a Bose-Einstein condensate trapped in a quasi-one-dimensional harmonic potential, by using variational and directly numerical approach of binary mean-field Gross-Pitaevskii equations. The results show that, because of strong coupling of spin-orbit coupling (SOC), Rabi coupling, and atomic interaction, the collective dynamics of the system behave as complex characters. When the Rabi coupling is absent, the density profiles of the system preserve the Gauss type and the wave packets do harmonic oscillations. The amplitude of the collective oscillations increases with SOC. Furthermore, when the SOC strength increases, the dipole oscillations of the two pseudospin components undergo a transition from in-phase to out-of-phase oscillations. When the Rabi coupling present, there will exist a critical value of SOC strength (which depends on the Rabi coupling and atomic interaction). If the SOC strength is less than this critical value, the density profiles of the system can preserve the Gauss type and the wave packets do anharmonic (the frequency of dipole oscillations depends on SOC) oscillations synchronously (i.e., in-phase oscillations). However, if the SOC strength is larger than this critical value, the wave packets are dynamically fragmented and the stable dipole oscillations of the system can not exist. The collective dynamics of the system can be controlled by adjusting the atomic interaction, SOC, and Rabi-coupling strength.
In this paper, we present a theoretical study of a two-component Bose-Einstein condensate composed of ytterbium (Yb) isotopes in a three-dimensional anisotropic harmonic potential. The condensate consists of a mixture of 176Yb atoms which have a negative s-wave scattering length and 174Yb atoms having a positive s-wave scattering length. We study the ground-state as well as dynamic properties of this two-component condensate. Due to the attractive interactions between 176Yb atoms, the condensate of 176Yb undergoes a collapse when the particle number exceeds a critical value. The critical number and the collapse dynamics are modified due to the presence of 174Yb atoms. We use coupled two-component Gross-Pitaevskii equations to study the collapse dynamics. The theoretical results obtained are in reasonable agreement with the experimental results of Fukuhara et al. [Phys. Rev. A 79, 021601(R) (2009)].
We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin–orbit coupled Bose–Einstein condensates (BECs) with Rabi coupling. The analysis is performed for equal densities of pseudo-spin components. Different combination of the signs of intra- and intercomponent interaction strengths are considered, with a particular emphasis on repulsive interactions. We observe that the unstable modulation builds from originally miscible condensates, depending on the combination of the signs of the intra- and intercomponent interaction strengths. The repulsive intra- and intercomponent interactions admit instability and the MI immiscibility condition is no longer significant. The influence of interaction parameters such as spin–orbit and Rabi coupling on MI are also investigated. The spin–orbit coupling (SOC) inevitably contributes to instability regardless of the nature of the interaction. In the case of attractive interaction, SOC manifests in enhancing the MI. Thus, a comprehensive study of MI in two-dimensional spin–orbit coupled BECs of pseudo-spin components is presented.
We study the role of coupling parameters on the ground state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus coupling strength with Rabi mixing using quasi-one-dimensional coupled Gross-Pitaevskii equations. By considering weak repulsive inter- and intra-species interactions between the condensate atoms, we investigate the contribution of spin-orbit and Rabi coupling parameters on the phases. We find that for a finite Rabi coupling strength, the system undergoes a phase transition from double plane-wave phase to stripe wave phase at a critical spin-orbit coupling strength.
We present the collective excitation spectrum analysis of binary Bose-Einstein condensates (BECs) with spin-orbit (SO) and Rabi couplings in a quasi-two-dimensional system. In particular, we investigate the role of SO and Rabi coupling strengths in determining the dynamical stability of the coupled BECs using Bogoliubov--de Gennes (BdG) theory. Using the eigenenergy of the BdG spectrum, we confirm the existence of phonon, roton, and maxon modes with weak repulsive intra- and interspecies contact interactions. The depth of the minimum corresponding to the roton mode strongly depends on the coupling strength. We find that the increase of the SO coupling leads to instability, while the increase in the Rabi coupling stabilizes the system. Also, the eigenvectors of the BdG spectrum indicate the presence of a densitylike mode in the stable regime and spinlike modes in the unstable regimes. A phase diagram demonstrating the stability regime in the plane of SO and Rabi coupling strengths is obtained. Finally, we complement the observation of the excitation spectrum with the direct numerical simulation results of coupled Gross-Pitaevskii equations.
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.