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We discuss an interferometric scheme employing interference of bright solitons formed as specific bound states of attracting bosons on a lattice. We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, it was assumed that the scattering is perfectly elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption: By employing a combination of Bethe ansatz and DMRG-based analysis of the dynamics of the appropriate many-body system, we find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms. 

We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by two equal mass particles.To that system, we apply a quantum generalization of Chirikov's criterion for the onset of chaos, i.e. the criterion of overlapping resonances.There, classical nonlinear resonances translate almost automatically to the quantum language. Quantum mechanics intervenes at a later stage: the resonances occupying less than one Hamiltonian eigenstate are excluded from the chaos criterion. Resonances appear as contiguous patches of low purity unperturbed eigenstates, separated by the groups of undestroyed states-the quantum analogues of the classical KAM tori. 

We study a gas of attracting bosons confined in a ring shape potential pierced by an artificial magnetic field. Because of attractive interactions, quantum analogs of bright solitons are formed. As a genuine quantum-many-body feature, we demonstrate that angular momentum fractionalization occurs and that such an effect manifests on time of flight measurements.As a consequence, the matter-wave current in our system can react to very small changes of rotation or other artificial gauge fields. We worked out a protocol to entangle such quantum solitonic currents, allowing us to operate rotation sensors and gyroscopes to Heisenberg-limited sensitivity.Therefore, we demonstrate that the specific coherence and entanglement properties of the system can induce an enhancement of sensitivity to an external rotation. 

The recently proposed map [5] between the hydrodynamic equationsgoverning the two-dimensional triangular cold-bosonic breathers [1] andthe high-density zero-temperature triangular free-fermionic clouds, bothtrapped harmonically, perfectly explains the former phenomenon butleaves uninterpreted the nature of the initial(t=0)singularity. This singularity is a density discontinuity that leads, inthe bosonic case, to an infinite force at the cloud edge. The map itselfbecomes invalid at times t<0 t < 0 .A similar singularity appears at t = T/4 t = T / 4 ,where Tis the period of the harmonic trap, with the Fermi-Bose map becominginvalid at t > T/4 t > T / 4 . Here, we first map—using the scale invariance of the problem—thetrapped motion to an untrapped one. Then we show that in the newrepresentation, the solution [5] becomes, along a ray in the directionnormal to one of the three edges of the initial cloud, a freelypropagating one-dimensional shock wave of a class proposed by Damski in[7]. There, for a broad class of initial conditions, the one-dimensionalhydrodynamic equations can be mapped to the inviscid Burgers’ equation,which is equivalent to a nonlinear transport equation. Morespecifically, under the Damski map, thet=0singularity of the original problem becomes, verbatim, the initialcondition for the wave catastrophe solution found by Chandrasekhar in1943 [9]. At t=T/8 t = T / 8 ,our interpretation ceases to exist: at this instance, all threeeffectively one-dimensional shock waves emanating from each of the threesides of the initial triangle collide at the origin, and the 2D-1Dcorrespondence between the solution of [5] and the Damski-Chandrasekharshock wave becomes invalid.