Dynamics of pair correlations in the attractive Lieb-Liniger gas

We investigate the dynamics of a 1D Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and exact numerical simulations. After the quench the system is found to be predominantly in an excited gas-like state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter component leads to a rather pronounced oscillation of the local density-density correlation with a frequency corresponding to the binding energy of the pair, making two-particle bound states observable in an experiment. Contributions from bound states with larger particle numbers are found to be negligible.Comment: 4 pages, 4 figure

Fermionisation dynamics of a strongly interacting 1D Bose gas after an interaction quench

We study the dynamics of a one-dimensional Bose gas after a sudden change of the interaction strength from zero to a finite value using the numerical time-evolving block decimation (TEBD) algorithm. It is shown that despite the integrability of the system, local quantities such as the two-particle correlation $g^{(2)}(x,x)$ attain steady state values in a short characteristic time inversely proportional to the Tonks parameter $\gamma$ and the square of the density. The asymptotic values are very close to those of a finite temperature grand canonical ensemble with a local temperature corresponding to initial energy and density. Non-local density-density correlations on the other hand approach a steady state on a much larger time scale determined by the finite propagation velocity of oscillatory correlation waves.Comment: 11 pages, 5 figures, extende

Discretized vs. continuous models of p-wave interacting fermions in 1D

We present a general mapping between continuous and lattice models of Bose- and Fermi-gases in one dimension, interacting via local two-body interactions. For s-wave interacting bosons we arrive at the Bose-Hubbard model in the weakly interacting, low density regime. The dual problem of p-wave interacting fermions is mapped to the spin-1/2 XXZ model close to the critical point in the highly polarized regime. The mappings are shown to be optimal in the sense that they produce the least error possible for a given discretization length. As an application we examine the ground state of a interacting Fermi gas in a harmonic trap, calculating numerically real-space and momentum-space distributions as well as two-particle correlations. In the analytically known limits the convergence of the results of the lattice model to the continuous one is shown.Comment: 7 pages, 5 figure

Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs

Repulsively bound pairs of particles in a lattice governed by the Bose-Hubbard model can form stable incompressible clusters of dimers corresponding to finite-size n=2 Mott insulators. Here we study the dynamics of hole defects in such clusters corresponding to unpaired particles which can resonantly tunnel out of the cluster into the lattice vacuum. Due to bosonic statistics, the unpaired particles have different effective mass inside and outside the cluster, and "evaporation" of hole defects from the cluster boundaries is possible only when their quasi-momenta are within a certain transmission range. We show that quasi-thermalization of hole defects occurs in the presence of catalyzing particle defects which thereby purify the Mott insulating clusters. We study the dynamics of one-dimensional system using analytical techniques and numerically exact t-DMRG simulations. We derive an effective strong-interaction model that enables simulations of the system dynamics for much longer times. We also discuss a more general case of two bosonic species which reduces to the fermionic Hubbard model in the strong interaction limit.Comment: 12 pages, 10 figures, minor update

Steady-state crystallization of Rydberg excitations in an optically driven lattice gas

We study resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential which suppresses simultaneous excitation of neighboring atoms. Considering two- and three-level excitation schemes, we analyze the dynamics and stationary state of the continuously-driven, dissipative many-body system employing time-dependent density-matrix renormalization group (t-DMRG) simulations. We show that two-level atoms can exhibit only nearest neighbor correlations, while three-level atoms under dark-state resonant driving can develop finite-range crystalline order of Rydberg excitations. We present an approximate rate equation model whose analytic solution yields qualitative understanding of the numerical results.Comment: 5 pages,3 figure

Particle number conservation in quantum many-body simulations with matrix product operators

Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in simulation where the dynamically evolving entities are matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that in this case often the entanglement imposed by the global constraint of fixed particle number is the limiting factor.Comment: minor changes, 18 pages, 5 figure

Early Visual Cultures and Panofsky’s Perspektive als ‘symbolische Form’

This paper investigates the historical dimension of perspectival representations. It aims to provide a heterogeneous though comparative picture of culturally unrelated visual con- ceptualizations of pictorial spaces, written with a view toward explaining how the multiple modes of perspective were introduced in antiquity. Point of departure for this critical approach is Erwin Panofsky’s essay Die Perspektive als ‘symbolische Form’ , published in 1927. His essay analyses the pictorial visualization of space and spatiality in different historical contexts, examining their cultural codification in terms of the heuristic category of ‘sym- bolic form’. However, ‘perspective’, which is commonly understood as synonymous with ‘linear perspective’, deserves a new discussion in the context of diverse visual cultures: A ‘naturalisation’ of the gaze as it is suggested by pictorial spaces which function mimetically is primarily associated with the early modern period in Western art. Instead of merely re- reading Panofsky’s canonical text, this paper presents an interdisciplinary re-viewing of a selection of the pictorial examples chosen by Panofsky, commenting upon their perspec- tive(s) from different vantage points