arXiv subjects

Patrizia Vignolo

Publications and source records attributed to Patrizia Vignolo.

At least 19 recordsLinked to original sources

arXiv2026

Exact statistical transmutation of quantum mixtures on a ring

One-dimensional strongly repulsive quantum mixtures exhibit non-trivial exchange statistics arising from the interplay between orbital and spin degrees of freedom. Using an exact solution, we demonstrate that in the single-impurity limit the wavefunction of Fermi-Fermi and Bose-Bose mixtures on a ring threaded by an artificial gauge field display exact anyonic statistics under exchange of the impurity with the majority particles. The resulting fractional exchange phase is fixed by the angular momentum sector selected through the applied flux. We find that the impurity momentum distribution coincide exactly with the anyonic one, independently of the bosonic or fermionic nature of the mixture, with the large-momentum tails encoding a direct signature of the anyonic statistical angle. Finally, we devise a quench protocol for reversible dynamical anyonization. Our results provide a path for realizing and manipulating anyonized states with ultracold atoms.

cond-mat.quant-gas↗

arXiv2026

Emergence of magnetic excitations in one-dimensional quantum mixtures under confinement

We obtain an exact solution for the spectral function for one-dimensional Bose-Bose and Fermi- Fermi mixtures with strong repulsive interactions, valid in arbitrary confining potentials and at all frequency scales. For the case of harmonic confinement we show that, on top of the ladder structure of the density excitations imposed by the external confinement, spin excitations emerge as sideband peaks, with dispersion related to the one of ferromagnetic or antiferromagnetic spin chains and a width fundamentally larger for fermionic mixtures than for bosonic ones, as determined by the different symmetry of spin excited states. The observation of spin excitation branches can provide a univocal probe of interaction-induced magnetism in ultracold atoms.

cond-mat.quant-gas↗

arXiv2025

Exact Solution for Two $\delta$-Interacting Bosons on a Ring in the Presence of a $\delta$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States

In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a $\delta$-function barrier. Only half of the Hilbert space--namely, the two-body states that are odd under point inversion about the position of the barrier--is accessible to this method. The other half is presumably non-integrable. We consider benchmarking the recently proposed $1/g$ expansion about the hard-core boson point [A. G. Volosniev, D. V. Fedorov, A. S. Jensen, M. Valiente, N. T. Zinner, Nature Communications 5, 5300 (2014)] as one application of our results. Additionally, we find that when the $\delta$-barrier is converted to a $\delta$-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its non-interacting counterpart while its eigenstates display features of a strongly interacting system. We discuss this phenomenon in the "Summary and Future Research" section of our paper.

math-ph↗

arXiv2025

Interaction induced Anderson transition in a kicked one dimensional Bose gas

We investigate the Lieb-Liniger model of one-dimensional bosons subjected to periodic kicks. In both the non-interacting and strongly interacting limits, the system undergoes dynamical localization, leading to energy saturation at long times. However, for finite interactions, we reveal an interaction-driven transition from an insulating to a metallic phase at a critical kicking strength, provided the number of particles is three or more. Using the Bethe Ansatz solution of the Lieb-Liniger gas, we establish a formal correspondence between its dynamical evolution and an Anderson model in $N$ spatial dimensions, where $N$ is the number of particles. This theoretical prediction is supported by extensive numerical simulations for three particles, complemented by finite-time scaling analysis, demonstrating that this transition belongs to the orthogonal Anderson universality class.

cond-mat.quant-gas↗

arXiv2025

Shortcut to spin dynamics for quantum mixtures

The study of the long-time dynamics of quantum systems can be a real challenge, especially in systems like ultracold gases, where the required timescales may be longer than the lifetime of the system itself. In this work, we show that it is possible to access the long-time dynamics of a strongly repulsive atomic gas mixture in shorter times. The shortcut-to-dynamics protocol that we propose does not modify the fate of the observables, but effectively jumps ahead in time without changing the system's inherent evolution. Just like the next-chapter button in a movie player that allows to quickly reach the part of the movie one wants to watch, it is a leap into the future.

cond-mat.quant-gas↗

arXiv2024

Dynamical probing of high-order spin coherence in one-dimensional mixtures

We investigate the dynamics of one-dimensional SU(2) ultracold fermions near the Tonks-Girardeau limit, confined in a box potential. The system is driven out of equilibrium by initially preparing the two spin components in a fully separated configuration, and its evolution is described by the Hamiltonian in the presence of strong repulsive interactions. Building on the results in [arXiv:2302.02828, Phys$.$Rev. A, 107, L061301 (2023)], we extend the analysis to out-of-equilibrium dynamics, uncovering the emergence of time-dependent oscillating high-momentum tails in the momentum distribution. These oscillations, due to the finite size of the system, are governed by a nonlocal, high-order spin coherence term, whose amplitude and phase evolve over time. We show that this term initially grows as time to the power N/2 and subsequently follows the spin-mixing dynamics of the system. Notably, when the spin components are fully mixed, the amplitude of this border-to-border spin coherence reaches its maximum value.

cond-mat.quant-gas↗

arXiv2024

Symmetry oscillations in strongly interacting one-dimensional mixtures

Multicomponent quantum mixtures in one dimension can be characterized by their symmetry under particle exchange. For a strongly interacting Bose-Bose mixture, we show that the time evolution of the momentum distribution from an initially symmetry-mixed state is quasiconstant for a SU(2) symmetry conserving Hamiltonian, while it displays large oscillations in time for the symmetry-breaking case where inter- and intraspecies interactions are different. Using the property that the momentum distribution operator at strong interactions commutes with the class-sum operator, the latter acting as a symmetry witness, we show that the momentum distribution oscillations correspond to symmetry oscillations, with a mechanism analogous to neutrino flavor oscillations.

cond-mat.quant-gas↗

arXiv2024

Necklace Ansatz for strongly repulsive spin mixtures on a ring

We propose an alternative to the Bethe Ansatz method for strongly-interacting fermionic (or bosonic) mixtures on a ring. Starting from the knowledge of the solution for single-component non-interacting fermions (or strongly-interacting bosons), we explicitly impose periodic condition on the amplitudes of the spin configurations. This reduces drastically the number of independent complex amplitudes that we determine by constrained diagonalization of an effective Hamiltonian. This procedure allows us to obtain a complete basis for the exact low-energy many-body solutions for mixtures with a large number of particles, both for $SU(\kappa)$ and symmetry-breaking systems.

cond-mat.quant-gas↗

arXiv2024

Spin-charge separation in the quantum boomerang effect

We study the localization dynamics of a SU(2) fermionic wavepacket launched in a (pseudo)random potential. We show that in the limit of strong inter-component repulsions, the total wavepacket exhibits a boomerang-like dynamics, returning near its initial position as expected for non-interacting particles, while separately each spin-component does not. This spin-charge separation effect occurs both in the infinite repulsive limit and at finite interactions. At infinite interactions, the system is integrable and thermalization cannot occur: the two spin-components push each other during the dynamics and their centers of mass stop further from each other than their initial position. At finite interactions, integrability is broken, the two spin-components oscillate and mix, with their center-of-mass positions converging very slowly to the center of mass of the whole system. This is a signature that the final localized state is a fully spin-mixed thermalized state.

cond-mat.quant-gas↗

arXiv2023

High-momentum oscillating tails of strongly interacting 1D gases in a box

We study the momentum distribution of strongly interacting one-dimensional mixtures of particles at zero temperature in a box potential. We find that the magnitude of the $1/k^4$ tail of the momentum distribution is not only due to short-distance correlations, but also to the presence of the rigid walls, breaking the Tan's relation relating this quantity to the adiabatic derivative of the energy with respect to the inverse of the interaction strength. The additional contribution is a finite-size effect that includes a $k$-independent and an oscillating part. This latter, surprisingly, encodes information on long-range spin correlations.

cond-mat.quant-gas↗

arXiv2022

Persistent currents in a strongly interacting multicomponent Bose gas on a ring

We consider a two-component Bose-Bose mixture at strong repulsive interactions in a tightly confining, one-dimensional ring trap and subjected to an artificial gauge field. By employing the Bethe Ansatz exact solution for the many-body wavefunction, we obtain the ground state energy and the persistent currents. For each value of the applied flux, we then determine the symmetry of the state under particles exchange. We find that the ground-state energy and the persistent currents display a reduced periodicity with respect to the case of non-interacting particles, corresponding to reaching states with fractional angular momentum per particle. We relate this effect to the change of symmetry of the ground state under the effect of the artificial gauge field. Our results generalize the ones previously reported for fermionic mixtures with both attractive and repulsive interactions and highlight the role of symmetry in this effect

cond-mat.quant-gas↗

arXiv2022

Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions

We study the equilibrium properties of a one-dimensional mixture of two Tonks-Girardeau gases on a ring geometry in the limit of strongly-repulsive inter-species interactions. We derive the exact many-body wavefunction and compare it to the $SU(2)$ solution where intra- and inter-species interactions are also diverging but equal. We focus on the role of the $SU(2)$-symmetry breaking on the behaviour of the large- and short-distance correlations by studying the zero-momentum occupation number and the Tan's contact from the asymptotic behavior of the momentum distribution. Although the symmetry is only weakly broken, it has important consequences on spin correlations in the system as the reduction by a factor of two of the zero-momentum occupation number with respect to the $SU(2)$ case in the thermodynamic limit and the decrease of the Tan's contact.

cond-mat.quant-gas↗

arXiv2022

Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas

We study the spin-mixing dynamics of a one-dimensional strongly repulsive Fermi gas under harmonic confinement. By employing a mapping onto an inhomogeneous isotropic Heisenberg model and the symmetries under particle exchange, we follow the dynamics till very long times. Starting from an initial spin-separated state, we observe superdiffusion, spin-dipolar large amplitude oscillations and thermalization. We report a universal scaling of the oscillations with particle number N^1/4, implying a slow-down of the motion and the decrease of the zero-temperature spin drag coefficient as the particle number grows.

cond-mat.quant-gas↗

arXiv2022

Observation of the Quantum Boomerang Effect

A particle in an Anderson-localized system, if launched in any direction, should on average return to its starting point and stay there. Despite the central role played by Anderson localization in the modern understanding of condensed matter, this "quantum boomerang" effect, an essential feature of the localized state, was only recently theoretically predicted and has not previously been observed. We report the experimental observation of the quantum boomerang effect. Using a degenerate gas and a phase-shifted pair of optical lattices, we probe the role of time reversal symmetry breaking, Floquet gauge, and initial state symmetry in supporting or disrupting the boomerang effect. Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears. Measured dynamics are in agreement with analytical and numerical predictions. These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.

cond-mat.quant-gas↗

arXiv2022

Strongly interacting trapped one-dimensional quantum gases: an exact solution

Quantum correlations can be used as a resource for quantum computing, eg for quantum state manipulation, and for quantum sensing, eg for creating non-classical states which allow to achieve the quantum advantage regime. This review collects the predictions coming from a family of exact solutions which allows to describe the many-body wavefunction of strongly correlated quantum fluids confined by a tight waveguide and subjected to any form of longitudinal confinement. It directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved. The exact solution applies to bosons, fermions and mixtures. It allows to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillations regime yielding the collective modes of the system and the large quench regime where the system parameters are changed considerably. The solution can be extended to describe finite-temperature conditions, spin and magnetization effects. The review illustrates the idea of the solution, presents the key theoretical achievements and the main experiments on strongly correlated one-dimensional quantum gases.

cond-mat.quant-gas↗

arXiv2020

Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momenta, which is an important fingerprint of long range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with non zero momentum is exponential. The distribution of the quasi-condensate is however quasi Gaussian. Experimental relevance of our findings for recent cold atoms experiments are discussed.

cond-mat.quant-gas↗

arXiv2020

Density wave propagation in a two-dimensional random dimer potential: from a single to a bipartite square lattice

We study the propagation of a density perturbation in a weakly interacting boson gas confined on a lattice and in the presence of square dimerized impurities. Such a two-dimensional random-dimer model (2D-DRDM), previously introduced in [Capuzzi et al., Phys. Rev. A 92, 053622 (2015)], is the disorder transition from a single square lattice, where impurities are absent, to a bipartite square lattice, where the number of impurities is maximum and coincides with half the number of lattice sites. We show that disorder correlations can play a crucial role in the dynamics for a broad range of parameters by allowing density fluctuations to propagate in the 2D-DRDM lattice, even in the limit of strong disorder. In such a regime, the propagation speed depends on the percentage of impurities, interpolating between the speed in a single monoperiodic lattice and that in a bipartite one.

cond-mat.quant-gas↗

arXiv2019

Localisation and transport in bidimensional random models with separable Hamiltonians

We consider two bidimensional random models characterised by the following features: a) their Hamiltonians are separable in polar coordinates and b) the random part of the potential depends either on the angular coordinate or on the radial one, but not on both. The disorder correspondingly localises the angular or the radial part of the eigenfunctions. We analyse the analogies and the differences which exist between the selected 2D models and their 1D counterparts. We show how the analogies allow one to use correlated disorder to design a localisation length with pre-defined energy dependence and to produce directional localisation of the wavefunctions in models with angular disorder. We also discuss the importance of finite-size and resonance effects in shaping the eigenfunctions of the model with angular disorder; for the model with disorder associated to the radial variable we show under what conditions the localisation length coincides with the expression valid in the 1D case.

cond-mat.dis-nn↗