Piero Naldesi, Juan Polo, Peter D. Drummond, Vanja Dunjko, Luigi Amico, Anna Minguzzi, Maxim Olshanii
SciPost Phys. 15, 187 (2023) ·
published 8 November 2023

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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 matterwave 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 centerofmass 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 DMRGbased analysis of the dynamics of the appropriate manybody system, we find that the interferometric fringes persist even when the centerofmass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms.
P. Naldesi, J. Polo, V. Dunjko, H. Perrin, M. Olshanii, L. Amico, A. Minguzzi
SciPost Phys. 12, 138 (2022) ·
published 22 April 2022

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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 quantummanybody feature, we demonstrate that angular momentum fractionalization occurs and that such effect manifests on time of flight measurements. As a consequence, the matterwave current in our system can react to very small changes of rotation or other artificial gauge fields. We work out a protocol to entangle such quantum solitonic currents, allowing to operate rotation sensors and gyroscopes to Heisenberglimited sensitivity. Therefore, we demonstrate that the specific coherence and entanglement properties of the system can induce an enhancement of sensitivity to an external rotation.
SciPost Phys. 12, 092 (2022) ·
published 14 March 2022

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We address the origins of the quasiperiodic breathing observed in [Phys. Rev.\ X vol. 9, 021035 (2019)] in diskshaped harmonically trapped twodimensional Bose condensates, where the quasiperiod $T_{\text{quasibreathing}}\sim$~$2T/7$ and $T$ is the period of the harmonic trap. We show that, due to an unexplained coincidence, the first instance of the collapse of the hydrodynamic description, at $t^{*} = \arctan(\sqrt{2})/(2\pi) T \approx T/7$, emerges as a `skillful impostor' of the quasibreathing halfperiod $T_{\text{quasibreathing}}/2$. At the time $t^{*}$, the velocity field almost vanishes, supporting the requisite timereversal invariance. We find that this phenomenon persists for scaleinvariant gases in all spatial dimensions, being exact in one dimension and, likely, approximate in all others. In $\bm{d}$ dimensions, the quasibreathing halfperiod assumes the form $T_{\text{quasibreathing}}/2 \equiv t^{*} = \arctan(\sqrt{d})/(2\pi) T$. Remaining unresolved is the origin of the period$2T$ breathing, reported in the same experiment.
Dmitry Yampolsky, N. L. Harshman, Vanja Dunjko, Zaijong Hwang, Maxim Olshanii
SciPost Phys. 12, 035 (2022) ·
published 24 January 2022

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We consider a toy model for emergence of chaos in a quantum manybody shortrangeinteracting system: two onedimensional hardcore 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 verbatim 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 statesthe quantum analogues of the classical KAM tori.
M. Olshanii, D. Deshommes, J. Torrents, M. Gonchenko, V. Dunjko, G. E. Astrakharchik
SciPost Phys. 10, 114 (2021) ·
published 26 May 2021

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The recently proposed map [arXiv:2011.01415] between the hydrodynamic equations governing the twodimensional triangular coldbosonic breathers [Phys. Rev. X 9, 021035 (2019)] and the highdensity zerotemperature triangular freefermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial ($t=0$) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times $t<0$. A similar singularity appears at $t = T/4$, where $T$ is the period of the harmonic trap, with the FermiBose map becoming invalid at $t > T/4$. Here, we first mapusing the scale invariance of the problemthe trapped motion to an untrapped one. Then we show that in the new representation, the solution [arXiv:2011.01415] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating onedimensional shock wave of a class proposed by Damski in [Phys.~Rev.~A 69, 043610 (2004)]. There, for a broad class of initial conditions, the onedimensional hydrodynamic equations can be mapped to the inviscid Burgers' equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the $t=0$ singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [Ballistic Research Laboratory Report No. 423 (1943)]. At $t=T/8$, our interpretation ceases to exist: at this instance, all three effectively onedimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D1D correspondence between the solution of [arXiv:2011.01415] and the DamskiChandrasekhar shock wave becomes invalid.
Prof. Dunjko: "We thank the referee for this ..."
in Submissions  report on The origin of the period$2T/7$ quasibreathing in diskshaped GrossPitaevskii breathers