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.
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.
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, we study numerically critical dynamics in the ultracold Bose gas in one and two spatial dimensions. We concentrate on two specific setups, both amenable for experimental realisation: Hamiltonian parameter quenches in a two-component Bose gas in one spatial dimension and a driven-dissipative single-component gas in two spatial \ndimensions. The setups are chosen to excite critical dynamics, either via quenches close to a quantum critical point or via nucleation of vortex defects. The goal is to identify critical scaling and universal scaling forms in the time evolution of the respective systems. The analysis for the two-component Bose gas reveals that short-time quench dynamics can be described by a universal crossover function, where the quench-induced energy appears as the relevant energy scale. For the single-component gas, we find a new universal phase of time evolution, characterised by an anomalously slow phase ordering process of vortex defects. We discuss our results in the light of concepts of prethermalisation, generalised Gibbs ensembles and non-thermal fixed points, for universal critical \nphenomena far from thermal equilibrium.
Abstract Closed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behaviour in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarise corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarise the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates.
We review turbulence in ultracold quantum gases, using the scalar contact-interaction Bose-Einstein condensate as the reference system for quantized circulation, compressibility, vortices, sound, and cascades. We focus on the quantitative diagnostics that connect helium and classical phenomenology to microscopic wave-function dynamics: incompressible and compressible kinetic-energy spectra, wave-occupation spectra, spectral fluxes, vortex-resolved correlations, and velocity statistics. These diagnostics distinguish equilibrium vortex organization, decaying turbulent relaxation, forced cascade dynamics, and weak-wave turbulence, and show why power laws alone are insufficient evidence for a cascade. We survey experiments on two-dimensional Onsager clustering, three-dimensional vortex-line turbulence, box-trap wave cascades, engineered dissipation, and turbulent equations of state. We close by briefly placing the contact-interaction scalar superfluid system in a broader landscape of nonlocal, multicomponent, fermionic, and driven-dissipative quantum fluids, where turbulence concepts can be tested for universality.
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.