We study the dynamics of domain formation and coarsening in a binary Bose-Einstein condensate that is quenched across a miscible-immiscible phase transition. The late-time evolution of the system is universal and governed by scaling laws for the correlation functions. We numerically determine the scaling forms and extract the critical exponents that describe the growth rate of domain size and autocorrelations. Our data is consistent with inviscid hydrodynamic domain growth, which is governed by a universal dynamical critical exponent of 1/z = 0.68 (2). In addition, we analyze the effect of domain wall configurations which introduce a nonanalytic term in the short-distance structure of the pair correlation function, leading to a high-momentum "Porod"-tail in the static structure factor, which can be measured experimentally.The thermodynamic ground state of a system that consists of multiple species is not always spatially homogeneous. Indeed, as the thermodynamic state variables or the interspecies couplings are tuned, often a transition between a miscible and an immiscible ground state takes place [1]. A system that is quenched across such a transition does not phase-separate instantly but exhibits highly nontrivial dynamics which generally proceed in two stages [2][3][4][5]: first, domains of one species nucleate over a short time-scale. In the second stage, these domains merge and coarsen until in the infinite-time limit, only one large domain of each species remains. In certain cases, the dynamics in the latter stage can be universal in that they do not depend on the microscopic details of the system and are only constrained by symmetries and conservation laws [5,6]. The time evolution is then self-similar, i.e., the time dependence of any ensemble averaged-quantity is captured by a simple rescaling of units by a characteristic length scale L(t) (for example, the average domain size). In classical theories of phase ordering kinetics, this scale diverges with time according to a characteristic power law L(t) ∼ t 1/z . The phase ordering dynamics of different systems can thus be separated into distinct dynamical universality classes that are characterized by the dynamical critical exponent z. The concept of scaling applied to the late-time coarsening is truly universal and has found its application to a wide variety of distinct problems in physics: originally developed to describe the growth of metallic grain boundaries [7] and the spinoidal decomposition of a binary alloys below a critical phase-coexistence temperature [8], scaling concepts are now used to describe to formation of galaxies, the domain growth of liquid membranes [9], or even sociopysics [10]. Here, we extend the classical paradigm of phase ordering kinetics to quantum systems by presenting an example of a quantum system that exhibits classical late-time scaling: we calculate the dynamical critical exponent for domain coarsening in a binary superfluid in two dimensions, finding a dynamical scaling exponent that is consistent with inviscid hydrod...

We study the timescales for adiabaticity of trapped cold bosons subject to a time-varying lattice potential using a dynamic Gutzwiller mean-field theory. We explain apparently contradictory experimental observations by demonstrating a clear separation of timescales for local dynamics (∼ ms) and global mass redistribution (∼ 1s). We provide a simple explanation for the short and fast timescales, finding that while density/energy transport is dominated by low energy phonons, particle-hole excitations set the adiabaticity time for fast ramps. We show how mass transport shuts off within Mott domains, leading to a chemical potential gradient that fails to equilibrate on experimental timescales.Introduction.-A wide range of experiments have forced us to confront questions of dynamics in strongly correlated systems. These include studies of high density nuclear matter at the Relativistic Heavy Ion Collider (RHIC) [1], transport through metal-insulator interfaces [2], and femtosecond spectroscopy [3] of quantum dots after sudden changes in gate voltages [4]. This is a conceptually rich area where computation is difficult, and where it is hard to devise experiments which are straightforward to analyze. Experiments in cold atoms are beginning to play an important role in this areathey have started providing a framework for understanding the non-equilibrium dynamics of strongly correlated materials [5][6][7][8][9][10]. In cold gas experiments, not only is the Hamiltonian known, but one can dynamically tune between weak and strong interactions, readily producing highly non-equilibrium situations that allow one to explore both linear and nonlinear responses, the reestablishment of equilibrium, and the generation of topological defects during rapid quenches [11]. The latter physics is relevant to astrophysical models of the early universe. Here we theoretically explore the timescales governing local and global transport of bosons in optical lattices, the prototypical example of strongly correlated cold atom physics.Adding further interest to this area, initial experiments [5][6][7] probing the dynamics of bosons in optical lattices have found adiabaticity/relaxation timescales that differ by two orders of magnitude. The shortest of these timescales was particularly noteworthy, as it was an order of magnitude smaller than the inverse of the single particle tunneling energy, t ∼ 0.1J −1 [6]. How can the system adjust itself on a timescale which is short compared to the tunneling time? Conversely, experiments on a nearly identical system at Chicago [5], found that the global density profile didn't attain it's equilibrium value even on times t ∼ 10J −1 ! Here we resolve this contradiction by demonstrating a separation of timescales for global transport and local equilibration, and show that the timescale for adiabiaticity is largely set by the gap towards particle-hole excitations in the strongly correlated superfluid.

We explore how correlations evolve in a gas of lattice bosons when the lattice depth is rapidly reduced. We find a simple closed form expression for the static structure factor in the limit of vanishing interactions. The corresponding real-space density correlation function shows multiple spatial oscillations which linearly disperse as a function of time. By perturbatively including the effects of the interactions we calculate how the boson quasi-momentum evolves following the quench.Comment: 10 pages, 6 figures thoroughly expanded version of earlier manuscrip