Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.
Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, for example, in early universe inflation or quark-gluon plasma dynamics.
In this thesis the non-equilibrium dynamics of ultracold quantum gases is studied numerically and analytically in one, two, and three spatial dimensions. We focus on the regime of large occupation numbers, where the system can be described by an ensemble of non-linear waves. A goal of this work is to investigate the existence of non-thermal fixed points in the dynamics of ultracold Bose gases. It is shown that a two- or three-dimensional Bose gas features a non-thermal fixed point which is characterised by a dilute random distribution of vortices or vortex lines. This state is accompanied by particle and energy fluxes and decays via the formation of vortex-antivortex correlations. By making use of superfluid turbulence methods, we give a detailed analysis of the underlying vortex dynamics. Furthermore, we focus on the relevance of the non-thermal fixed point for the dynamics of phase ordering kinetics and Bose-Einstein condensation. Then, we explore the possibility of a non-thermal fixed point in a one-dimensional ultracold Bose gas as well as a two-component Bose gas in two dimensions. Finally, we discuss the realisation of a non-thermal fixed point in a relativistic scalar field theory as well as for the case of a two-component Bose gas in two dimensions. After a brief discussion of experimental prospects, we summarise our results and close with an outlook.
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas are analyzed in two and three spatial dimensions. For such systems, universal power-law distributions, previously found within a nonperturbative quantum-field theoretic approach, are shown to be related to vortical dynamics and superfluid turbulence. The results imply an interpretation of the momentum scaling at the nonthermal fixed points in terms of independent vortex excitations of the superfluid. Long-wavelength acoustic excitations on the top of these are found to follow a nonthermal power law. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, e.g., in early-universe inflation or quark-gluon plasma dynamics.
Using a non-perturbative quantum kinetic framework, we develop a unified description of the far-from-equilibrium dynamics of three-dimensional Bose gases following cooling quenches across the Bose-Einstein condensation transition. By tracking the spatio-temporal evolution of the momentum distribution, we show that the equilibrium condensation threshold simultaneously acts as a dynamical critical point, separating distinct far-from-equilibrium universality classes governed by different non-equilibrium attractors. While quenches above the transition exhibit a single-timescale relaxation toward a thermal fixed point, quenches below the transition display a crossover from a transient weak-turbulence regime to a coarsening fixed point governed by the diffusive recombination of vortex lines. Quenches directly to the condensation threshold, finally, are controlled by a previously unidentified critical fixed point characterized by the superdiffusive spreading of critical fluctuations and a distinct set of dynamical exponents. Together, these dynamical scaling laws establish a far-from-equilibrium counterpart of the condensation phase transition, in which the equilibrium critical point also organizes the long-time non-equilibrium dynamics.
Abstract Using a non-perturbative quantum kinetic framework, we develop a unified description of the far-from-equilibrium dynamics of three-dimensional Bose gases following cooling quenches across the Bose-Einstein condensation transition. By tracking the spatio-temporal evolution of the momentum distribution, we show that the equilibrium condensation threshold simultaneously acts as a dynamical critical point, separating distinct far-from-equilibrium universality classes governed by different non-equilibrium attractors. While quenches above the transition exhibit a single-timescale relaxation toward a thermal fixed point, quenches below the transition display a crossover from a transient weak-turbulence regime to a coarsening fixed point governed by the diffusive recombination of vortex lines. Quenches directly to the condensation threshold, finally, are controlled by a previously unidentified critical fixed point characterized by the superdiffusive spreading of critical fluctuations and a distinct set of dynamical exponents. Together, these dynamical scaling laws establish a far-from-equilibrium counterpart of the condensation phase transition, in which the equilibrium critical point also organizes the long-time non-equilibrium dynamics.
Abstract This chapter considers nearly coherent Bose gases brought far out of equilibrium and their behavior in the context of connections between universal properties, (quasi-)topological field configurations, and turbulent dynamics. The isolated Bose gas, on its way back to thermal equilibrium, can approach metastable nonequilibrium configurations and spend a long time in their vicinity. In such configurations, termed nonthermal fixed points, the system shows universal long-range properties manifest through scaling, i.e. self-similar correlations. The time evolution near such fixed points undergoes critical slowing down. The spatial field pattern, at the same time, is characterized by the appearance of defects and domain formation whose geometry gives rise to the particular scaling laws seen in the correlation functions. An overall picture is obtained that connects well-known concepts for describing universal dynamics such as wave turbulence, superfluid turbulence, and (quasi-)topological excitations. The extension to fermionic and gauge fields should reveal many interesting new aspects.