The universal scaling of macroscopic observables tells us about the loss of information on initial conditions and microscopic system properties. By studying the time evolution of an isolated spinor Bose gas after a sudden quench into a magnetically ordered phase, it is numerically shown that universal scaling evolution at a nonthermal fixed point is possible in a purely one-dimensional geometry.
The universal scaling of macroscopic observables tells us about the loss of information on initial conditions and microscopic system properties. By studying the time evolution of an isolated spinor Bose gas after a sudden quench into a magnetically ordered phase, it is numerically shown that universal scaling evolution at a nonthermal fixed point is possible in a purely one-dimensional geometry.
Close to equilibrium, the underlying symmetries of a system determine its possible universal behavior. Far from equilibrium, however, different universal phenomena associated with the existence of multiple non-thermal fixed points can be realized for given microscopic symmetries. Here, we study this phenomenon using a quasi-one-dimensional spinor Bose-Einstein condensate. We prepare two different initial conditions and observe two distinct universal scaling dynamics with different exponents. Measurements of the complex-valued order parameter with spatial resolution allow us to characterize the phase-amplitude excitations for the two scenarios. Our study provides new insights into the phenomenon of universal dynamics far from equilibrium and opens a path towards mapping out the associated basins of non-thermal fixed points.
Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.
Abstract Predicting the dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics1, 2. While the evolution of a many-body system is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium, universality is identified through the scaling of the spatio-temporal evolution of the system, captured by universal exponents and functions. Theoretically, this has been studied in examples as different as the reheating process in inflationary Universe cosmology3, 4, the dynamics of nuclear collision experiments described by quantum chromodynamics5, 6, and the post-quench dynamics in dilute quantum gases in non-relativistic quantum field theory7–11. However, an experimental demonstration of such scaling evolution in space and time in a quantum many-body system has been lacking. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi-one-dimensional spinor Bose–Einstein condensate12–16. For long evolution times we extract the scaling properties from the spatial correlations of the spin excitations. From this we find the dynamics to be governed by an emergent conserved quantity and the transport of spin excitations towards low momentum scales. Our results establish an important class of non-stationary systems whose dynamics is encoded in time-independent scaling exponents and functions, signalling the existence of non-thermal fixed points10, 17, 18. We confirm that the non-thermal scaling phenomenon involves no fine-tuning of parameters, by preparing different initial conditions and observing the same scaling behaviour. Our analogue quantum simulation approach provides the basis with which to reveal the underlying mechanisms and characteristics of non-thermal universality classes. One may use this universality to learn, from experiments with ultracold gases, about fundamental aspects of dynamics studied in cosmology and quantum chromodynamics.
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.
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.
We outline a kinetic theory of nonthermal fixed points for the example of a dilute Bose gas, partially reviewing results obtained earlier, thereby extending, complementing, generalizing, and straightening them out. We study universal dynamics after a cooling quench, focusing on situations where the time evolution represents a pure rescaling of spatial correlations, with time defining the scale parameter. The nonequilibrium initial condition set by the quench induces a redistribution of particles in momentum space. Depending on conservation laws, this can take the form of a wave-turbulent flux or of a more general self-similar evolution, signaling the critically slowed approach to a nonthermal fixed point. We identify such fixed points using a nonperturbative kinetic theory of collective scattering between highly occupied long-wavelength modes. In contrast, a wave-turbulent flux, possible in the perturbative Boltzmann regime, builds up in a critically accelerated self-similar manner. A key result is the simple analytical universal scaling form of the nonperturbative many-body scattering matrix, for which we lay out the concrete conditions under which it applies. We derive the scaling exponents for the time evolution as well as for the power-law tail of the momentum distribution function, for a general dynamical critical exponent z and an anomalous scaling dimension $\ensuremath{\eta}$. The approach of the nonthermal fixed point is, in particular, found to involve a rescaling of momenta in time t by ${t}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\beta}}$, with $\ensuremath{\beta}=1/z$, within our kinetic approach independent of $\ensuremath{\eta}$. We confirm our analytical predictions by numerically evaluating the kinetic scattering integral as well as the nonperturbative many-body coupling function. As a side result, we obtain a possible finite-size interpretation of wave-turbulent scaling recently measured by Navon et al.