Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent h - 3 and, related to this, a large dynamical exponent  z 5 are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phaseordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a close connection between the anomalous scaling exponent η, introduced in a quantum-field theoretic approach, and conservation-law induced scaling in classical phase-ordering kinetics is revealed. Moreover, the relation to superfluid turbulence as well as to driven stationary systems is discussed. analysis as well as a comprehensive classification scheme of far-from-equilibrium universal dynamics are lacking so far.Here we consider possible universal scaling behavior of a time-evolving isolated two-dimensional (2D) quantum-degenerate Bose gas quenched far out of equilibrium. We discuss the numerically found scaling in time and in the spatial degrees of freedom in the framework of non-thermal fixed points [34][35][36][37][38]. This approach builds on a scaling analysis of non-perturbative dynamic equations for field correlation functions in the spirit of a renormalization-group approach to far-from-equilibrium dynamics [35,[39][40][41][42][43][44]. Close to a non-thermal fixed point, correlation functions show a time evolution which takes the form of a rescaling in space and time [38]. In consequence, the relaxation is critically slowed down, while correlations evolve as a power law rather than exponentially in time.We prepare far-from-equilibrium states by imprinting phase defects, i.e., quantum vortex excitations, into an otherwise strongly phase-coherent condensate. Different kinds of initial states are realized by varying the number of defects, their arrangement, and their winding numbers. Independently of the microscopic details of the initial state, such as the statistics of fluctuations, the system is attracted to one or more non-thermal fixed points where the information about these details gets lost. Close to such a fixed point the correlations exhibit and evolve according to universal power laws [45][46][47][48][49][50].More than one attractor can exist for the dynamical evolution of the system, as we will demonstrate being the case for the 2D Bose gas studied here. Consequently, different types of universal evolution wit...

We report on the experimental observation of scaling in the time evolution following a sudden quench into the vicinity of a quantum critical point. The experimental system, a two-component Bose gas with coherent exchange between the constituents, allows for the necessary high level of control of parameters as well as the access to time-resolved spatial correlation functions. The theoretical analysis reveals that when quenching the system close to the critical point, the energy introduced by the quench leads to a short-time evolution exhibiting crossover reminiscent of the finite-temperature critical properties in the system's universality class. Observing the time evolution after a quench represents a paradigm shift in accessing and probing experimentally universal properties close to a quantum critical point and allows in a new way benchmarking of quantum many-body theory with experiments.

Quasi-stationary far-from-equilibrium critical states of a two-component Bose gas are studied in two spatial dimensions. After the system has undergone an initial dynamical instability it approaches a non-thermal fixed point. At this critical point the structure of the gas is characterised by ensembles of (quasi-)topological defects such as vortices, skyrmions and solitons which give rise to universal power-law behaviour of momentum correlation functions. The resulting power-law spectra can be interpreted in terms of strong-wave-turbulence cascades driven by particle transport into longwave-length excitations. Scaling exponents are determined on both sides of the miscible-immiscible transition controlled by the ratio of the intra-species to inter-species couplings. Making use of quantum turbulence methods, we explain the specific values of the exponents from the presence of transient (quasi-)topological defects.

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