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Register a new userBidirectional dynamic scaling in an isolated Bose gas far from equilibrium
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Understanding and classifying nonequilibrium many-body phenomena, analogous to the classification of equilibrium states of matter into universality classes, is an outstanding problem in physics. Any many-body system, from stellar matter to financial markets, can be out of equilibrium in a myriad of ways; since many are also difficult to experiment on, it is a major goal to establish universal principles that apply to different phenomena and physical systems. At the heart of the classification of equilibrium states is the universality seen in the self-similar spatial scaling of systems close to phase transitions. Recent theoretical work, and first experimental evidence, suggest that isolated many-body systems far from equilibrium generically exhibit dynamic (spatiotemporal) self-similar scaling, akin to turbulent cascades and the Family-Vicsek scaling in classical surface growth. Here we observe bidirectional dynamic scaling in an isolated quench-cooled atomic Bose gas; as the gas thermalises and undergoes Bose-Einstein condensation, it shows self-similar net flows of particles towards the infrared (smaller momenta) and energy towards the ultraviolet (smaller lengthscales). For both infrared (IR) and ultraviolet (UV) dynamics we find that the scaling exponents are independent of the strength of the interparticle interactions that drive the thermalisation.
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We provide experimental evidence of universal dynamics far from equilibrium during the relaxation of an isolated one-dimensional Bose gas. Following a rapid cooling quench, the system exhibits universal scaling in time and space, associated with the approach of a non-thermal fixed point. The time evolution within the scaling period is described by a single universal function and scaling exponent, independent of the specifics of the initial state. Our results provide a quantum simulation in a regime, where to date no theoretical predictions are available. This constitutes a crucial step in the verification of universality far from equilibrium. If successful, this may lead to a comprehensive classification of systems based on their universal properties far from equilibrium, relevant for a large variety of systems at different scales.
The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum entropy principle put forward in 1957 by E. T. Jaynes suggests what quantum states one should expect in equilibrium but does not hint as to how closed quantum many-body systems dynamically equilibrate. A number of theoretical and numerical studies accumulate evidence that under specific conditions quantum many-body models can relax to a situation that locally or with respect to certain observables appears as if the entire system had relaxed to a maximum entropy state. In this work, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we are able to prepare the system in a well-known initial state with high fidelity. We then follow the dynamical evolution of the system in terms of quasi-local densities, currents, and coherences. Numerical studies based on the time-dependent density-matrix renormalization group method are in an excellent quantitative agreement with the experimental data. For very long times, all three local observables show a fast relaxation to equilibrium values compatible with those expected for a global maximum entropy state. We find this relaxation of the quasi-local densities and currents to initially follow a power-law with an exponent being significantly larger than for free or hardcore bosons. For intermediate times the system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms based on matrix product states can efficiently keep track of.
We propose experimentally feasible means for non-destructive thermometry of homogeneous Bose Einstein condensates in different spatial dimensions ($din{1,2,3}$). Our impurity based protocol suggests that the fundamental error bound on thermometry at the sub nano Kelvin domain depends highly on the dimension, in that the higher the dimension the better the precision. Furthermore, sub-optimal thermometry of the condensates by using measurements that are experimentally feasible is explored. We specifically focus on measuring position and momentum of the impurity that belong to the family of Gaussian measurements. We show that, generally, experimentally feasible measurements are far from optimal, except in 1D, where position measurements are indeed optimal. This makes realistic experiments perform very well at few nano Kelvin temperatures for all dimensions, and at sub nano Kelvin temperatures in the one dimensional scenario. These results take a significant step towards experimental realisation of probe-based quantum thermometry of Bose Einstein condensates, as it deals with them in one, two and three dimensions and uses feasible measurements applicable in current experimental setups.
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 $eta$. The approach of the non-thermal fixed point is, in particular, found to involve a rescaling of momenta in time $t$ by $t^{beta}$, with $beta=1/z$, within our kinetic approach independent of $eta$. 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.
We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the forcing at high wave numbers, and study propagation of the turbulent spectrum toward the low wave numbers. Our primary goal is to compare the results for the evolving spectrum with the previous results obtained for the kinetic equation of weak wave turbulence. We demonstrate existence of a regime for which good agreement with the wave turbulence results is found in terms of the main features of the previously discussed self-similar solution. In particular, we find a reasonable agreement with the low-frequency and the high-frequency power-law asymptotics of the evolving solution, including the anomalous power-law exponent $x^* approx 1.24$ for the three-dimensional waveaction spectrum. We also study the regimes of very weak turbulence, when the evolution is affected by the discreteness of the Fourier space, and the strong turbulence regime when emerging condensate modifies the wave dynamics and leads to formation of strongly nonlinear filamentary vortices.
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