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 [1,2]. 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 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 cosmology [3,4], the dynamics of nuclear collision experiments described by quantum chromodynamics [5,6], or the postquench dynamics in dilute quantum gases in nonrelativistic quantum field theory [7][8][9][10][11]. However, an experimental demonstration of such scaling evolution in space and time in a quantum many-body system is lacking so far. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi one-dimensional spinor Bose-Einstein condensate [12][13][14][15][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 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 [10,17,18]. 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.Isolated quantum many-body systems offer particularly clean settings for studying fundamental properties of the underlying unitary time evolution [19]. For sys-tems initialised far from equilibrium different scenarios have been identified, including the occurence of manybody oscillations [20] and revivals [21], the manifestation of many-body localisation [22], and quasi-stationary behaviour in a prethermalised stage of the evolution [23].Here we observe a new scenario associated to the notion of non-thermal fixed points. This is illustrated schematically in Fig. 1a: Starting from a class of farfrom-equilibrium initial conditions, the system develops a universal scaling behaviour in time and space. This is a consequence of the effective loss of details about initial conditions and system parameters long before a quasistationary or equilibrium situation may be reached. The transient scaling behaviour is found to be governed by the transport of an emergent collectiv...

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

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Highly occupied gauge theories in 2+1 dimensions: A self-similar attractor

“…Examples have been found with classical field methods in various theories in three spatial dimensions (3D) including non-Abelian gauge theories, relativistic and non-relativistic scalar field theories [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], and in two-dimensional scalar systems [17][18][19][20]. Nonthermal fixed points have recently also been found experimentally in ultra-cold atom experiments [21,22]. A kinetic theory description of the underlying theory is often a natural way to explain the existence and properties of such fixed points [1,14,[23][24][25][26][27].…”

Violation of single-length-scaling dynamics via spin vortices in an isolated spin-1 Bose gas

“…Dissipative coarsening forms a special case of more general spatio-temporal universal dynamical phenomena far from equilibrium which can occur in both, open and isolated (quantum) many-body systems [4,[27][28][29]. Following a quench far out of equilibrium, a system can in general approach a non-thermal fixed point [10,[30][31][32][33][34][35]. Such fixed points have been discussed and experimentally observed with [35][36][37][38][39][40] and without [10,[30][31][32][33][41][42][43] reference to ordering patterns and kinetics as well as topological defects.…”