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.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.

Oct 1, 20150 citations

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

Jun Xu, Shuyuan Wu, Xizhou Qin +4 more

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 broken-symmetry 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, b 1 = ν / ( 1 + ν z ) and b 2 = 1 / ( 1 + ν z ) , 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.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 broken-symmetry 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, b 1 = ν / ( 1 + ν z ) and b 2 = 1 / ( 1 + ν z ) , 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.

arXiv:1510.00138Europhysics Letters (EPL)Mar 1, 201611 citations

Spontaneous symmetry breaking in Bose–Einstein condensates

Roger A. Hegstrom

Chemical Physics LettersMay 1, 19987 citations

Dynamics of spontaneous symmetry breaking in a space-time crystal

J.N. Stehouwer, Henk T. C. Stoof, Jasper Smits +1 more

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The nonequilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the Fokker-Planck formulations. We consider a semiclassical and a fully quantum approach, depending on the dissipation being either frequency independent or linearly dependent on frequency, respectively. For both cases, the Langevin equation and Fokker-Planck equation are derived, and the resulting equilibrium distribution is studied. We also study the time evolution of the space-time crystal and focus in particular on its formation and the associated dynamics of the spontaneous breaking of a ${Z}_{2}$ symmetry out of the symmetry-unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The nonequilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the Fokker-Planck formulations. We consider a semiclassical and a fully quantum approach, depending on the dissipation being either frequency independent or linearly dependent on frequency, respectively. For both cases, the Langevin equation and Fokker-Planck equation are derived, and the resulting equilibrium distribution is studied. We also study the time evolution of the space-time crystal and focus in particular on its formation and the associated dynamics of the spontaneous breaking of a ${Z}_{2}$ symmetry out of the symmetry-unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.

arXiv:2107.14505Physical Review AOct 27, 20215 citations

Nonlinear dynamics of a Bose condensed gas

F. Dalfovo, C. Minniti, S. Stringari +1 more

arXiv:cond-mat/9612175Physics Letters AMar 1, 199769 citations

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.

{Z}_{2}

symmetry out of the symmetry-unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.