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

Abstract

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various systems 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 modes 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 for the simultaneous determination of the critical exponents ν and z for a continuous phase transition.

Universality of miscible–immiscible phase separation dynamics in two-component Bose–Einstein condensates

“…From the non-equilibrium dynamics far from the critical point, we numerically extract two universal scalings for the average domain number and the average bifurcation delay with respect to the quench rate, and we find the critical exponents derived from the numerical results consist well with the analytical exponents. These scaling exponents in the phase separation induced by tuning the atom-atom interaction are different from the ones [5][6][7][8], in which the phase separation is induced by tuning the Rabi coupling strength.…”

“…Although all this work and the previous ones [5][6][7][8] study miscible-immiscible transitions, there are significant differences between their KZ scalings. Firstly, the miscible-immiscible transitions are induced by different sources.…”

“…in which q is the excitation quasimomentum, ω is the excitation frequency, u j,q and v j,q , ( j=1, 2) are the Bogoliubov amplitudes. Inserting equation (9) into the linearized equation equation (7), (8) and comparing the coefficients for the terms of e iqx−iωt and e iqx+iωt , one obtains the BdG equations…”

“…The non-equilibrium dynamics of quantum phase transitions have attracted great interest in many branches of physics, including cosmology, particle physics and condensed matter physics [1][2][3]. When a system is driven across a phase transition and enters a symmetry broken phase, one of the most nontrivial results is the creation of topological defects, such as domains [4][5][6][7][8][9][10][11][12][13], vortices [14][15][16] and solitons [17][18][19]. The possibility to engineer a quantum phase transition and recover its universality from topological defects is of great significance in non-equilibrium physics [20].…”

“…Up to now, great efforts have been made to create multi-component BECs with different atomic species [38,39], isotopes [40] or spin states [41][42][43]. Multi-component BECs exhibit rich physics not accessible in a single-component BEC, including phase separation with symmetry breaking [5,[44][45][46][47][48][49], Josephon oscillation [51] and domain walls [6][7][8][9][10][11]. Remarkably, the phase separation in multicomponent BECs has been observed in several experiments [38][39][40][41]43].…”