Memories of initial states and density imbalance in the dynamics of noninteracting and interacting disordered systems

We study the dynamics of one- and two-dimensional disordered lattice bosons/fermions initialized to a Fock state with 1 particle on a set of lattice sites (A) and 0 particles on the rest of the sites ((A) over bar). Such states have been considered in recent ultracold atomic experiments to detect many body localization. For noninteracting systems we establish a universal relation between the long time density imbalance between A and (A) over bar sites, I(infinity), the localization length xi(1), and the geometry of the initial pattern. For the alternating initial pattern of 1 and 0 particles in one dimension, I(infinity) = tanh[a/xi(l)], where a is the lattice spacing. For systems with mobility edge, we find analytic relations between I(infinity), the effective localization length (xi) over bar (l), and the fraction of localized states f(l). The imbalance as a function of disorder shows nonanalytic behavior when the mobility edge passes through a band edge. For interacting bosonic systems, we show that there is a mechanism to retain a finite long-time imbalance in the system even in presence of dissipative and stochastic processes coming from interparticle scattering. The scattering of particles, which lead to a decay of the memory of initial conditions through dissipative processes, also creates excitations in the system. For strong disorder, the excitations act as a local bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems

Particle-Hole Asymmetry in Doped Mott Insulators: Implications for Tunneling and Photoemission Spectroscopies

In a system with strong local repulsive interactions it should be more difficult to add an electron than to extract one. We make this idea precise by deriving various exact sum rules for the one-particle spectral function independent of the details of the Hamiltonian describing the system and of the nature of the ground state. We extend these results using a variational ansatz for the superconducting ground state and low lying excitations. Our results shed light on the striking asymmetry in the tunneling spectra of high Tc superconductors and should also be useful in estimating the local doping variations in inhomogeneous materials.Comment: 4 pages, no figure

Interacting Hofstadter spectrum of atoms in an artificial gauge field

Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements. The theory also provides an estimate of the critical interaction strength at the transition to the Mott insulator phase.Comment: 4+ pages, 2 figures; v2: published versio

Preparation and detection of d-wave superfluidity in two-dimensional optical superlattices

We propose a controlled method to create and detect d-wave superfluidity with ultracold fermionic atoms loaded in two-dimensional optical superlattices. Our scheme consists in preparing an array of nearest-neighbor coupled square plaquettes or ``superplaquettes'' and using them as building blocks to construct a d-wave superfluid state. We describe how to use the coherent dynamical evolution in such a system to experimentally probe the pairing mechanism. We also derive the zero temperature phase diagram of the fermions in a checkerboard lattice (many weakly coupled plaquettes) and show that by tuning the inter-plaquette tunneling spin-dependently or varying the filling factor one can drive the system into a d-wave superfluid phase or a Cooper pair density wave phase. We discuss the use of noise correlation measurements to experimentally probe these phases.Comment: 8 pages, 6 figure

Dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap

We derive a set of dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap across a Feshbach resonance. Our derivation is based on a variational ansatz, which generalizes the crossover wavefunction to the inhomogeneous case, and the assumption that the order parameter is slowly varying over the size of the Cooper pairs. The equations reduce to a generalized time-dependent Gross-Pitaevskii equation on the BEC side of the resonance. We discuss an iterative method to solve these mean-field equations, and present the solution for a harmonic trap as an illustrating example to self-consistently verify the approximations made in our derivation.Comment: replaced with the published versio

Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: For the particular example of a linear ramp we examine the transient regime of prethermalization [M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime the momentum distribution resembles a zero temperature Fermi liquid as the energy inserted by the ramp remains located in high energy modes. Thus ultracold fermions prove robust to heating which simplifies the observation of nonequilibrium BCS dynamics in optical lattices.Comment: 27 pages, 8 figures Second version with small modifications in section

Optical Self Energy in Graphene due to Correlations

In highly correlated systems one can define an optical self energy in analogy to its quasiparticle (QP) self energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta ($k$) of the charge carriers, the structure in the optical self energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for $k$ equal to or near the Fermi momentum $k_F$. Consequently plasmaronic structures which are associated with momenta near the Dirac point at $k=0$ are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self energies around $k_F$ of the lower Dirac cone associated with the occupied states.Comment: 30 pages, 10 figure

System size scaling of topological defect creation in a second-order dynamical quantum phase transition

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for large N, we find that the net defect number variance in convex volumina scales like the surface area of the sample for short-range correlations. This behaviour follows generally from spatial and internal symmetries. Conversely, if spatial isotropy is broken, e.g., by a lattice, and in addition long-range periodic correlations develop in the broken-symmetry phase, we get the rather counterintuitive result that the scaling strongly depends on the dimension being even or odd: For even dimensions, the net defect number variance scales like the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.Comment: 20 pages of IOP style, 6 figures; as published in New Journal of Physic