Kibble-Zurek dynamics in an array of coupled binary Bose con- densates

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 brokensymmetry 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 b1 = ν/(1 + νz) and b2 = 1/(1 + νz), which give the static correlation-length critical exponent ν and the dynamic critical exponent z. Our approach provides an efficient way to simultaneous determination of the critical exponents ν and z for a continuous phase transition. Introduction. Symmetry, one of the most important concepts in physical sciences, describes the invariance of geometric configurations or intrinsic laws under specified transformations. Spontaneous symmetry breaking (SSB) [1] plays a significant role in many fundamental phenomena. Through a SSB, the state of a system evolves from symmetric to asymmetric, even though the underlying dynamic equations are still invariant under the symmetry transformation. It has been demonstrated that the critical dynamics of continuous SSB obeys the KibbleZurek (KZ) mechanism [2–7], in which defect excitations are spontaneously generated. Universal critical dynamics obeying KZ mechanism have been found in various systems, such as, the early universe [8], superfluid helium [9], electronic unstable crystal [10], multiferroic hexagonal ma(a)E-mail: [email protected] ganites [11], nematic liquid crystal [12], ion crystal [13,14], and atomic Bose-Einstein condensates (BECs) [15–30]. Attribute to their high controllability and robust quantum coherence, beyond testing KZ mechanism in thermodynamic phase transitions [16, 18–20, 27, 28, 30], atomic BECs provide new opportunities for exploring KZ mechanism in quantum phase transitions [15,17,21–26,29]. To extract universal scalings, several local or global quantities are analyzed. The most used quantity is the total number of generated defects, such as, solitons [18–20,28], vortices [16] and domains [15, 21–23, 29, 30]. The total number of generated defects is a global quantity dependent on the whole system. Usually, the scaling of a global quantity may only give one KZ exponent, which is a combination of the static correlation-length critical exponent ν and the dynamic critical exponent z. There are also some