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

We theoretically establish the mean-field phase diagram of a homogeneous spin-1, spin-orbit coupled Bose gas as a function of the spin-dependent interaction parameter, the Raman coupling strength and the quadratic Zeeman shift. We find that the interplay between spin-orbit coupling and spin-dependent interactions leads to the occurrence of ferromagnetic or ferronematic phases which also break translational symmetry. For weak Raman coupling, increasing attractive spin-dependent interactions (as in 87 Rb or 7 Li) induces a transition from a uniform to a stripe XY ferromagnet (with no nematic order). For repulsive spin-dependent interactions however (as in 23 Na), we find a transition from an XY spin spiral phase ( Sz = 0 and uniform total density) with uniaxial nematic order, to a biaxial ferronematic, where the total density, spin vector and nematic director oscillate in real space. We investigate the stability of these phases against the quadratic Zeeman effect, which generally tends to favor uniform phases with either ferromagnetic or nematic order but not both. We discuss the relevance of our results to ongoing experiments on spin-orbit coupled, spinor Bose gases.

We study the physics of interacting spin-1 bosons in an optical lattice using a variational Gutzwiller technique. We compute the mean-field ground state wave-function and discuss the evolution of the condensate, spin, nematic, and singlet order parameters across the superfluid-Mott transition. We then extend the Gutzwiller method to derive the equations governing the dynamics of low energy excitations in the lattice. Linearizing these equations, we compute the excitation spectra in the superfluid and Mott phases for both ferromagnetic and antiferromagnetic spin-spin interactions. In the superfluid phase, we recover the known excitation spectrum obtained from Bogoliubov theory. In the nematic Mott phase, we obtain gapped, quadratically dispersing particle and hole-like collective modes, whereas in the singlet Mott phase, we obtain a non-dispersive gapped mode, corresponding to the breaking of a singlet pair. For the ferromagnetic Mott insulator, the Gutzwiller mean-field theory only yields particle-hole like modes but no Goldstone mode associated with long range spin order. To overcome this limitation, we supplement the Gutzwiller theory with a Schwinger boson mean-field theory which captures super-exchange driven fluctuations. In addition to the gapped particle-hole-like modes, we obtain a gapless quadratically dispersing ferromagnetic spin-wave Goldstone mode. We discuss the evolution of the singlet gap, particle-hole gap, and the effective mass of the ferromagnetic Goldstone mode as the superfluid-Mott phase boundary is approached from the insulating side. We discuss the relevance and validity of Gutzwiller mean-field theories to spinful systems, and potential extensions of this framework to include more exotic physics which appears in the presence of spin-orbit coupling or artificial gauge fields.

We explain the spin segregation seen at Duke in a two-component gas of 6 Li ͓X. Du, L. Luo, B. Clancy, and J. E. Thomas, Phys. Rev. Lett. 101, 150401 ͑2008͔͒ as a mean-field effect describable via a collisionless Boltzmann equation. As seen in experiments, we find that slight differences in the trapping potentials in the two spin states drive small spin currents. The Hartree-Fock-type interactions convert these currents into a redistribution of populations in energy space, and consequently a long-lived spin texture develops. We explore the interaction strength dependence of these dynamics, finding nontrivial dependence on system parameters and close agreement with experiment.

We study the dynamics of a non-degenerate, harmonically trapped Fermi gas following a sudden ramp of the spin-orbit coupling strength using a Boltzmann equation approach. In the absence of interactions and a Zeeman field, we solve the spin-orbit coupled Boltzmann equation analytically, and derive expressions for the phase-space and temporal dynamics of an arbitrary initial spin state. For a fully spin polarized initial state, the total magnetization exhibits collapse and revival dynamics in time with a period set by the trapping potential. In real space, this corresponds to oscillations between a fully polarized state and a spin helix. To make predictions relevant to current experiments on spin-orbit coupled Fermi gases, we then numerically study the dynamics in the presence of an additional momentum independent Zeeman field. We find that the spin helix is robust for weak magnetic fields but disappears for stronger field strengths. Finally, we explore the spin dynamics in the presence of interactions and find that weak interactions enhance the amplitude of the spin helix.

We calculate the dynamics of one-and two-body correlation functions in a homogeneous Bose gas at zero temperature following a sudden change in the interaction strength, in the continuum and in a lattice. By choosing suitable examples, we highlight features in the correlation functions that emerge due to the interactions and the band structure. We find that interactions dramatically change the way correlations build up and subsequently decay following a quench. For example, the Bogoliubov dispersion induces a crossover from diffusive spreading of short-range correlations to ballistic spreading of longer-range correlations. In the lattice, the correlation functions develop additional features absent in the continuum. Most strikingly, the lattice induces an additional velocity scale and some features propagate with that velocity. Finally, we discuss the ultra-short-range properties of the density-density correlation function following a quench, and the implications for experiments using this quantity to probe the "contact." Our calculations, which can be readily tested in current experiments, suggest that the dynamics of correlations may be a useful tool for extracting many-body parameters.