arXiv subjects

Patrizia Vignolo

Publications and source records attributed to Patrizia Vignolo.

At least 37 records · Page 2Linked to original sources

arXiv2018

Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature

The universal Tan relations connect a variety of microscopic features of many-body quantum systems with two-body contact interactions to a single quantity, called the contact. The latter has become pivotal in the description of quantum gases.We provide a complete characterization of the Tan contact of the harmonically trapped Lieb-Liniger gas for arbitrary interactions and temperature.Combining thermal Bethe ansatz, local-density approximation, and exact quantum Monte Carlo calculations,we show that the contact is a universal function of only two scaling parameters, and determine the scaling function.We find that the temperature dependence of the contact, or equivalently the interaction dependence of the entropy, displays a maximum. The presence of this maximum provides an unequivocal signature of the crossover to the fermionized regime and it is accessible in current experiments.

cond-mat.quant-gas↗

arXiv2018

Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many

We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and DMRG calculations are more pronounced when the interaction energy is maximal (i.e. at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe Ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local-density, to obtain N-boson contact and ground state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy.

cond-mat.quant-gas↗

arXiv2018

Tan's contact in a cigar-shaped dilute Bose gas

We compute the Tan's contact of a weakly interacting Bose gas at zero temperature in a cigar-shaped configuration. Using an effective one-dimensional Gross-Pitaeskii equation and Bogoliubov theory, we derive an analytical formula that interpolates between the three-dimensional and the one-dimensional mean-field regimes. In the strictly one-dimensional limit, we compare our results with Lieb-Liniger theory. Our study can be a guide for actual experiments interested in the study of Tan's contact in the dimensional crossover.

cond-mat.quant-gas↗

arXiv2017

Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations

We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb-Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan's contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture.

cond-mat.quant-gas↗

arXiv2017

Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions

We study Tan's contact, i.e. the coefficient of the high-momentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion. Our results are relevant for ongoing experiments with ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2016

High-momentum tails as magnetic structure probes for strongly-correlated $SU(κ)$ fermionic mixtures in one-dimensional traps

A universal $k^{-4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. {\bf 10}, 198 (2014)], realizing a gas with tunable $SU(κ)$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $κ$ components of the gas and the Young tableaux for the $S_N$ permutation symmetry group identifying the magnetic structure of the ground-state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach in the limit of infinite interactions, we show that the contact increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref.~[Nat. Phys. {\bf 10}, 198 (2014)].

cond-mat.quant-gas↗

arXiv2016

Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides

We consider a mixture of one-dimensional strongly interacting Fermi gases up to six components, subjected to a longitudinal harmonic confinement. In the limit of infinitely strong repulsions we provide an exact solution which generalizes the one for the two-component mixture. We show that an imbalanced mixture under harmonic confinement displays partial spatial separation among the components, with a structure which depends on the relative population of the various components. Furthermore, we provide a symmetry characterization of the ground and excited states of the mixture introducing and evaluating a suitable operator, namely the conjugacy class sum. We show that, even under external confinement, the gas has a definite symmetry which corresponds to the most symmetric one compatible with the imbalance among the components. This generalizes the predictions of the Lieb-Mattis theorem for a fermionic mixture with more than two components.

cond-mat.quant-gas↗

arXiv2015

Enhancing quantum coherence with short-range correlated disorder

We introduce a two-dimensional short-range correlated disorder that is the natural generalization of the well-known one-dimensional dual random dimer model [Phys. Rev. Lett 65, 88 (1990)]. We demonstrate that, as in one dimension, this model induces a localization-delocalization transition in the single-particle spectrum. Moreover we show that the effect of such a disorder on a weakly-interacting boson gas is to enhance the condensate spatial homogeneity and delocalisation, and to increase the condensate fraction around an effective resonance of the two-dimensional dual dimers. This study proves that short-range correlations of a disordered potential can enhance the quantum coherence of a weakly-interacting many-body system.

cond-mat.quant-gas↗

arXiv2014

Energy landscape in two-dimensional Penrose-tiled quasicrystal

Since their spectacular experimental realisation in the early 80's, quasicrystals have been the subject of very active research, whose domains extend far beyond the scope of solid state physics. In optics, for instance, photonic quasicrystals have attracted strong interest for their specific behaviour, induced by the particular spectral properties, in light transport, plasmonic and laser action. Very recently, one of the most salient spectral feature of quasicrystals, namely the gap labelling, has been observed for a polariton gas confined in a one dimensional quasi-periodic cavity. This experimental result confirms a theory which is now very complete in dimension one. In dimension greater than one, the theory is very far from being complete. Furthermore, some intriguing phenomena, like the existence of self-similar eigenmodes can occur. All this makes two dimensional experimental realisations and numerical simulations pertinent and attractive. Here, we report on measurements and energy-scaling analysis of the gap labelling and the spatial intensity distribution of the eigenstates for a microwave Penrose-tiled quasicrystal. Far from being restricted to the microwave system under consideration, our results apply to a more general class of systems.

cond-mat.mes-hall↗

arXiv2014

Brillouin zone labelling for quasicrystals

We propose a scheme to determine the energy-band dispersion of quasicrystals which does not require any periodic approximation and which directly provides the correct structure of the extended Brillouin zones. In the gap labelling viewpoint, this allow to transpose the measure of the integrated density-of-states to the measure of the effective Brillouin-zone areas that are uniquely determined by the position of the Bragg peaks. Moreover we show that the Bragg vectors can be determined by the stability analysis of the law of recurrence used to generate the quasicrystal. Our analysis of the gap labelling in the quasi-momentum space opens the way to an experimental proof of the gap labelling itself within the framework of an optics experiment, polaritons, or with ultracold atoms.

cond-mat.soft↗

arXiv2014

Probing quantum transport by engineering correlations in a speckle potential

We develop a procedure to modify the correlations of a speckle potential. This procedure, that is suitable for spatial light modulator devices, allows one to increase the localization efficiency of the speckle in a narrow energy region whose position can be easily tuned. This peculiar energy-dependent localization behavior is explored by pulling the potential through a cigar-shaped Bose-Einstein condensate. We show that the percentage of dragged atoms as a function of the pulling velocity depends on the potential correlations below a threshold of the disorder strength. Above this threshold, interference effects are no longer clearly observable during the condensate drag.

cond-mat.quant-gas↗

arXiv2012

Localization of an inhomogeneous Bose-Einstein condensate in a moving random potential

We study the dynamics of a harmonically trapped quasi-one-dimensional Bose-Einstein condensate subjected to a moving disorder potential of finite extent. We show that, due to the inhomogeneity of the sample, only a percentage of the atoms is localized at supersonic velocities of a random potential. We find that this percentage can be sensitively increased by introducing suitable correlations in the disorder potential such as those provided by random dimers.

cond-mat.quant-gas↗

arXiv2012

Universal contact for a Tonks-Girardeau gas at finite temperature

We determine the finite-temperature momentum distribution of a strongly interacting 1D Bose gas in the Tonks-Girardeau (impenetrable-boson) limit under harmonic confinement, and explore its universal properties associated to the scale invariance of the model. We show that, at difference from the unitary Fermi gas in three dimensions, the weight of its large-momentum tails -- given by the Tan's contact -- increase with temperature, and calculate the high-temperature universal second contact coefficient using a virial expansion.

cond-mat.quant-gas↗

arXiv2011

Anderson localization in optical lattices with speckle disorder

We study the localization properties of non-interacting waves propagating in a speckle-like potential superposed on a one-dimensional lattice. Using a decimation/renormalization procedure, we estimate the localization length for a tight-binding Hamiltonian where site-energies are square-sinc-correlated random variables. By decreasing the width of the correlation function, the disorder patterns approaches a $δ$-correlated disorder, and the localization length becomes almost energy-independent in the strong disorder limit. We show that this regime can be reached for a size of the speckle grains of the order of (lower than) four lattice steps.

cond-mat.dis-nn↗

arXiv2011

Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping we find the solution for the whole set of ground-state wavefunctions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system we propose an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical simulations.

cond-mat.quant-gas↗

arXiv2011

Shortcuts to adiabaticity for trapped ultracold gases

We study, experimentally and theoretically, the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose-Einstein condensate which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the atomic sample goes through strongly out-of-equilibrium states while the external confinement is modified until the system reaches the desired stationary state. The scheme is theoretically based on the invariants of motion and scaling equations techniques and can be generalized to decompression trajectories including an arbitrary deformation of the trap. It is also directly applicable to arbitrary initial non-equilibrium states.

cond-mat.quant-gas↗

arXiv2011

Fast optimal transition between two equilibrium states

We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of Rubidium 87 atoms held in a harmonic magnetic trap, in the presence of gravity. We are able to decompress the trap by a factor of 15 within 35 ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of 37 on the transition time.

cond-mat.quant-gas↗

arXiv2010

Shortcut to adiabaticity for an interacting Bose-Einstein condensate

We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles.

cond-mat.quant-gas↗