Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various system from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs mode whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents $b_{1}=\nu/(1+\nu z)$ and $b_{2}=1/(1+\nu z)$, which give the static correlation-length critical exponent $\nu$ and the dynamic critical exponent $z$. Our approach provides an efficient way to simultaneous determination of the critical exponents $\nu$ and $z$ for a continuous phase transition.Comment: 6 pages, 4 figures, accepted for publication in EPL (Europhysics Letters

Bis[μ-2-(2-naphth­oxy)acetato]bis­{aqua[2-(2-naphth­oxy)acetato]zinc(II)}

The title binuclear ZnII compound, [Zn2(C12H9O3)4(H2O)2], is centrosymmetric. Each Zn atom is coordinated by two bridging 2-naphthoxyacetate anions, one terminal 2-naphth­oxy­acetate anion and one water mol­ecule in a distorted ZnO4 tetra­hedral geometry. The naphthalene system of the bridging ligand is nearly perpendicular to the naphthalene of the terminal ligand, with a dihedral angle of 78.26 (6)°. Within the binuclear mol­ecule the Zn⋯Zn separation is 3.815 (5) Å. In the crystal structure, inter­molecular O—H⋯O hydrogen bonding between the water mol­ecule and carboxyl­ate groups helps to stabilize the crystal structure