No Arabic abstract
We study the ground state phases for a mixture of two atomic spin-1 Bose-Einstein condensates (BECs) in the presence of a weak magnetic (B-) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intra- and inter-species spin exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single species spin- 1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intra-species ferromagnetic interaction. All other remaining ground state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground state phase diagram and calculate their Bogoliubov excitation spectra. For the BA phase, there exist three Goldstone modes attempting to restore the broken U(1) and SO(2) symmetries.
The spinor dynamics of Bose-Einstein condensates of 87Rb atoms with hyperfine spins 1 and 2 were investigated. A technique of simultaneous Ramsey interferometry was developed for individual control of the vectors of two spins with almost the same Zeeman splittings. The mixture of spinor condensates is generated in the transversely polarized spin-1 and the longitudinally polarized spin-2 states. The time evolution of the spin-1 condensate exhibits dephasing and rephasing of the Larmor precession due to the interaction with the spin-2 condensate. The scattering lengths between spin-1 and -2 atoms were estimated by comparison with the numerical simulation using the Gross-Pitaevskii equation. The proposed technique is expected to facilitate the further study of multiple spinor condensates.
We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating box-like circular trap, i.e. states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully-analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying them their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.
We investigate the polarons formed by immersing a spinor impurity in a ferromagnetic state of $F=1$ spinor Bose-Einstein condensate. The ground state energies and effective masses of the polarons are calculated in both weak-coupling regime and strong-coupling regime. In the weakly interacting regime the second order perturbation theory is performed. In the strong coupling regime we use a simple variational treatment. The analytical approximations to the energy and effective mass of the polarons are constructed. Especially, a transition from the mobile state to the self-trapping state of the polaron in the strong coupling regime is discussed. We also estimate the signatures of polaron effects in spinor BEC for the future experiments.
Excited-state quantum phase transitions (ESQPTs) extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for ESQPTs poses however a major challenge. We introduce spinor Bose-Einstein condensates as a versatile platform for studies of ESQPTs. Based on the mean-field dynamics, we define a topological order parameter that distinguishes between excited-state phases, and discuss how to interferometrically access the order parameter in current experiments. Our work opens the way for the experimental characterization of excited-state quantum phases in atomic many-body systems.
We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition at zero quadratic Zeeman shift q. Both the rate of instability and the associated finite wavevector of the unstable modes - show good agreement with predictions based upon numerical solutions to the Bogoliubov de-Gennes equations. A key feature of this work is inclusion of magnetic field inhomogeneities that smooth the phase transition. Once these were removed, we observed a dramatic sharpening of the transition point, which could then be resolved within a quadratic Zeeman shift of only 1-2 Hz. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.