Observation of universal dynamics in a spinor Bose gas far from equilibrium

Abstract: The dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics. While the evolution 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 spatiotemporal 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 cosmology, the dynamics of nuclear collision experiments described by quantum chromodynamics, or the post-quench dynamics in dilute quantum gases in non-relativistic quantum field theory. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi one-dimensional spinor Bose-Einstein condensate. 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 transport of an emergent conserved quantity 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 signaling the existence of non-thermal fixed points. We confirm that the non-thermal scaling phenomenon involves no fine-tuning, by preparing different initial conditions and observing the same scaling behaviour. Our analog quantum simulation approach provides the basis to reveal the underlying mechanisms and characteristics of non-thermal universality classes. One may use this universality to learn, from experiments with ultra-cold gases, about fundamental aspects of dynamics studied in cosmology and quantum chromodynamics.

Universal Dynamics in Spinor Bose Gases Far From Equilibrium

The study outlined in the paper presents a methodical investigation into the dynamics of a spinor Bose-Einstein condensate (BEC) positioned far from equilibrium. It demonstrates the emergence of universal scaling behavior, a theoretical concept previously challenging to observe experimentally. The efforts of Prüfer et al. leverage a quasi-one-dimensional spinor BEC containing approximately 70,000 rubidium atoms to explore the characteristics of non-thermal fixed points.

In systems far from equilibrium, universality is characterized by the spatio-temporal evolution of the system described via universal exponents and scaling functions, independent of the initial conditions and microscopic parameters of the system. This work explores the non-linear evolution of quantum systems by observing spin correlations spatially across different regimes of system dynamics. The spinor BEC serves as an analog quantum simulator, exploring the scaling phenomena typically analyzed in cosmological reheating processes, dynamics in nuclear collision events as per quantum chromodynamics, and post-quench quantum gas dynamics.

In the methodology, the spinor BEC was initialized in a ferromagnetic interaction regime with zero spin length, prompting spin dynamics via microwave dressing to induce energy splitting. Over extended evolution periods, the universal scaling properties were examined by analyzing the spatial correlations of spin excitations. Notably, the angular orientation of the transverse spin becomes the critical dynamical degree during the evolution time. The researchers identified the collective conserved quantity's transport towards low momentum, crucially demonstrating that the observed scaling dynamics can occur without fine-tuning through repeated observations across various initial conditions.

The empirical results presented expose a class of non-stationary systems characterized by time-independent scaling exponents and functions, indicative of non-thermal fixed points. The experiment confirmed the presence of a scaling regime, wherein the structure factor scales uniformly when plotted against the rescaled momentum variable. Specifically, the universal scaling exponents were deduced as $\alpha = 0.33 \pm 0.08$ and $\beta = 0.54 \pm 0.06$. This empirical confirmation paves the way to employ ultracold gases in understanding fundamental dynamics from both theoretical cosmology and quantum chromodynamics perspectives.

Ultimately, this paper illustrates that the universal dynamics pertaining to non-thermal fixed points exhibit impressive robustness, essential for theoretical modeling. It provides empirical access to universal scaling functions needed to compare against various theoretical models within the non-thermal universality class framework. This experiment advances theoretical and practical comprehension of out-of-equilibrium dynamics with implications across scientific disciplines.