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Register a new userObservation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
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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.
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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.
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 theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.
For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalise at late times. We show that the full thermalising dynamics can be described by the generalised hydrodynamics with diffusion and force terms, and we compare these predictions with numerical simulations. Finally, we provide an explanation for the slow thermalisation rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterised by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalisation can display pre-thermal plateau and relaxation dynamics with long polynomial finite-time corrections.
Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times, these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.
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