We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.

In our paper we analyzed nonlocally coupled bosons in ladder lattices, or equivalently two-component bosons in onedimensional ͑1D͒ lattices. We showed that due to the direct Mott-insulator ͑MI͒ to pair-superfluid ͑PSF͒ transition, the MI lobes become severely distorted, leading to a counterintuitive behavior of the MI spatial regions in harmonic traps.In our paper, we characterized the possible phases, i.e., MI, PSF, and a phase of two superfluids ͑2SF͒, by employing as order parameters ͗b i,␣ ͘ and ͗b i,1 b i,2 ͘, where b i,␣ denotes the annihilation operator for the rung i and the wire ␣ =1,2. These order parameters characterize indeed the phases in the grand-canonical ensemble, since for PSF ͗b i,1 b i,2 ͘ 0 and ͗b i,␣ ͘ = 0, for 2SF both are nonzero, and for MI all are zero. Although our matrix-product-state ͑MPS͒ calculations conserve in principle the number of particles ͑and hence work in the canonical ensemble͒, a slight numerical inaccuracy in our simulations allowed for the violation of the number conservation. This effectively allowed for the identification of the MI, PSF, and 2SF phases. However, more accurate simulations do conserve the number of particles, and hence ͗b i,1 b i,2 ͘ = ͗b i,␣ ͘ = 0 in any case. Consequently, we have to rely in number conserving order parameters for the phases. In particular we employ the correlationsWe have calculated these correlation functions as a function of the site distance ⌬. For the MI phase both correlations decay exponentially with ⌬, for the PSF G 1 decays exponentially and G 2 polynomically, whereas for 2SF both decay polynomically. By fitting the correlation functions using exponential functions or power laws ͑see Fig. 1͒, we have identified for different values of the chemical potential and the tunneling rate J the different regions ͑see Fig. 2͒, which coincide almost exactly with those in our paper.

We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, in excellent agreement with our numerical calculations for one-dimensional (1D) systems. Thus, our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized by using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.

We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2)⊗SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-1/2 gases.

We study the transport properties of an ultracold gas of Bose-Einstein condensate that is coupled from a magnetic trap into a one-dimensional waveguide. Our theoretical approach to tackle this problem is based on the truncated Wigner method for which we assume the system to consist of two semi-infinite non-interacting leads and a finite interacting scattering region with two constrictions modelling an atomic quantum dot. The transmission is computed in the steady-state regime and we find a good agreement between truncated Wigner and Matrix-Product State calculations. We also identify clear signatures of inelastic resonant scattering by analyzing the distribution of energy in the transmitted atomic matter wave beam.

We analyze the Mott-insulator phases of dipolar bosonic gases placed in neighboring but unconnected 1D traps. Whereas for short-range interactions the 1D systems are independent, the non-local dipole-dipole interaction induces a direct Mott-insulator to pair-superfluid transition which significantly modifies the boundaries of the lowest Mott-insulator phases. The lowest boundary of the lowest Mott regions becomes progressively constant as a function of the hopping rate, eventually inverting its slope, leading to a re-entrant configuration which is retained in 2D. We discuss the consequences of this effect on the spatial Mott-insulator plateaux in experiments with additional harmonic confinement, showing that anti-intuitively the plateaux may become wider for increasing hopping. Our results are also applicable to non-dipolar boson-boson mixtures. U 0 J U 0 −|U'| J

We construct, using simple geometrical arguments, a Wigner function defined on a discrete phase space of arbitrary integer Hilbert-space dimension that is free of redundancies. "Ghost images" plaguing other Wigner functions for discrete phase spaces are thus revealed as artifacts. It allows to devise a corresponding phase-space propagator in an unambiguous manner. We apply our definitions to eigenstates and propagator of the quantum baker map. Scars on unstable periodic points of the corresponding classical map become visible with unprecedented resolution.

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