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How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving, we realize a dipolar XY spin-1/2 model in an external field. Starting from a spin-polarized state, we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation is density dependent relaxation of the total magnetization much faster than typical decoherence rates. To determine the processes governing this relaxation, we employ different theoretical approaches that treat quantum effects on initial conditions and dynamical laws separately. This allows us to identify an intrinsically quantum component to the relaxation attributed to primordial quantum fluctuations.

We outline a kinetic theory of non-thermal 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 non-equilibrium 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 non-thermal fixed point. We identify such fixed points using a non-perturbative 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 non-perturbative 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 η. The approach of the non-thermal fixed point is, in particular, found to involve a rescaling of momenta in time t by t β , with β = 1/z, within our kinetic approach independent of η. We confirm our analytical predictions by numerically evaluating the kinetic scattering integral as well as the non-perturbative 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.

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We explore the far-from-equilibrium dynamics of Bose gases in a universal regime associated to nonthermal fixed points. While previous investigations concentrated on scaling functions and exponents describing equal-time correlations, we compute the additional scaling functions and dynamic exponent z characterizing the frequency dependence or dispersion from unequal-time correlations. This allows us to compare the characteristic condensation and correlation times from a finite-size scaling analysis depending on the system's volume. arXiv:1612.03038v1 [cond-mat.quant-gas]

An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase space methods such as the Truncated Wigner Approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [1]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations [2] to our coupled spin-boson model. This allows in principle to study how systematically adding higher order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one-and two-point correlation functions in several dimensions and for arbitrary number of bosonic modes.

Many-body quantum systems far from equilibrium can exhibit universal scaling dynamics which defy standard classification schemes. Here, we disentangle the dominant excitations in the universal dynamics of highly-occupied N -component scalar systems using unequal-time correlators. While previous equal-time studies have conjectured the infrared properties to be universal for all N , we clearly identify for the first time two fundamentally different phenomena relevant at different N . We find all N ≥ 3 to be indeed dominated by the same Lorentzian "large-N " peak, whereas N = 1 is characterized instead by a non-Lorentzian peak with different properties, and for N = 2 we see a mixture of two contributions.

We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D longrange interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased. arXiv:1806.02347v2 [cond-mat.quant-gas]