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Critical Dynamics in an Array of Coupled Binary Bose-Einstein Condensates

Jun Xu, Shuyuan Wu, Xizhou Qin, Jiahao Huang, Yongguan Ke, Honghua Zhong, Chaohong Lee

Published Oct 1, 2015• 0 citations
OpenAlex

Abstract

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.

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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.
We investigate the non-equilibrium dynamics across the miscible–immiscible phase separation in a binary mixture of Bose–Einstein condensates. The excitation spectra reveal that the Landau critical velocity vanishes at the critical point, where the superfluidity spontaneously breaks down. We analytically extract the dynamical critical exponent z = 2 and static correlation length critical exponent v = 1/2 from the Landau critical velocity. Moreover, by simulating the real-time dynamics across the critical point, we find the average domain number and the average bifurcation delay show universal scaling laws with respect to the quench time. We then numerically extract the static correlation length critical exponent v = 1/2 and the dynamical critical exponent z = 2 according to Kibble–Zurek mechanism. The scaling exponents ( v = 1/2, z = 2) in the phase separation driven by quenching the atom–atom interaction are different from the ones ( v = 1/2, z = 1) in the phase separation driven by quenching the Rabi coupling strength (2009 Phys. Rev. Lett. 102 070401; 2011 Phys. Rev. Lett. 107 230402). Our study explores the connections between the spontaneous superfluidity breakdown and the spontaneous defect formation in the phase separation dynamics.
We investigate the universal dynamics of a continuous magnetic phase transition from a unmagnetized phase to a ferromagnetic phase in a spin-1 spin-orbit-coupled Bose-Einstein condensate. When the system approaches the critical point, the Landau critical velocity gradually decreases to zero and so the correlation length diverges. Therefore, during the slow passage through the critical point, ferromagnetic domains are spontaneously created according to the Kibble-Zurek mechanism. Through calculating the Bogoliubov excitations, we give the Landau critical velocity and the correlation length, from which we derive the Kibble-Zurek scalings. Furthermore, we numerically simulate the critical spatial-temporal dynamics of the bifurcation delay and spontaneous domain formation, and extract the universal scaling exponents. The numerical scalings extracted from the critical spatial-temporal dynamics are very consistent with the scalings derived from the correlation length.
According to the famous Kibble-Zurek mechanism (KZM), the universality of spontaneous defect generation in continuous phase transitions (CPTs) can be understood by the critical slowing down. In most CPTs of atomic Bose-Einstein condensates (BECs), the universality of spontaneous defect generations has been explained by the divergent relaxation time associated with the nontrivial gapless Bogoliubov excitations. However, for atomic BECs in synthetic gauge fields, their spontaneous superfluidity breakdown is resulted from the divergent correlation length associated with the zero Landau critical velocity. Here, by considering an atomic BEC ladder subjected to a synthetic magnetic field, we reveal that the spontaneous superfluidity breakdown obeys the KZM. The Kibble-Zurek scalings are derived from the Landau critical velocity which determines the correlation length. In further, the critical exponents are numerically extracted from the critical spatial-temporal dynamics of the bifurcation delay and the spontaneous vortex generation. Our study provides a general way to explore and understand the spontaneous superfluidity breakdown in CPTs from a single-well dispersion to a double-well one, such as, BECs in synthetic gauge fields, spin-orbit coupled BECs, and BECs in shaken optical lattices.
According to the famous Kibble-Zurek mechanism (KZM), the universality of spontaneous defect generation in continuous phase transitions (CPTs) can be understood by the critical slowing down. In most CPTs of atomic Bose-Einstein condensates (BECs), the universality of spontaneous defect generations has been explained by the divergent relaxation time associated with the nontrivial gapless Bogoliubov excitations. However, for atomic BECs in synthetic gauge fields, their spontaneous superfluidity breakdown results from the divergent correlation length associated with the zero Landau critical velocity. Here, by considering an atomic BEC ladder subjected to a synthetic magnetic field, we reveal that the spontaneous superfluidity breakdown obeys the KZM. The Kibble-Zurek scalings are derived from the Landau critical velocity which determines the correlation length. Furthermore, the critical exponents are numerically extracted from the critical spatiotemporal dynamics of the bifurcation delay and the spontaneous vortex generation. Our study provides a general way to explore and understand the spontaneous superfluidity breakdown in CPTs from a single-well dispersion to a double-well one, such as BECs in synthetic gauge fields, spin-orbit-coupled BECs, and BECs in shaken optical lattices.
We investigate defect formation and the universal critical dynamics of two-dimensional two-component Bose-Einstein condensates (BECs) confined in both box and harmonic traps. Our focus is on the nonequilibrium universal dynamics of the miscible-immiscible phase transition, considering both linear and nonlinear quenching protocols. The general condition for a phase transition, g11g22=g122{g}_{11}{g}_{22}={g}_{12}^{2}g11​g22​=g122​, depends exclusively on inter- and intraspecies interactions. In this system, simultaneous phase transitions occur in both the box and harmonic traps. Consequently, the nonequilibrium critical dynamics can still be described using the homogeneous Kibble-Zurek mechanism. Through an analysis of Bogoliubov excitations, we establish a power-law relationship linking the domain correlation length, phase transition delay, and quench time. Additionally, real-time simulations of phase transition dynamics demonstrate the formation of domain defects and the delay of phase transitions in nonequilibrium conditions. These simulations also reveal the universal scaling of the correlation length and phase transition delay across various quench times and nonlinear coefficients, showing well agreement with our analytical predictions. Our study confirms that the universality class of two-component BECs is independent of dimensionality. Additionally, larger nonlinear coefficients effectively suppress the growth of nonadiabatic excitations, offering a fresh perspective on achieving quasiadiabatic evolution.