arXiv subjects

A. Trombettoni

Publications and source records attributed to A. Trombettoni.

At least 55 records · Page 3Linked to original sources

arXiv2013

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

cond-mat.quant-gas↗

arXiv2013

Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models

We consider two weakly coupled Richardson models to study the formation of a relative phase and the Josephson dynamics between two mesoscopic attractively interacting fermionic systems: our results apply to superconducting properties of coupled ultrasmall metallic grains and to Cooper-pairing superfluidity in neutral systems with a finite number of fermions. We discuss how a definite relative phase between the two systems emerges and how it can be conveniently extracted from the many-body wavefunction: we find that a definite relative phase difference emerges even for very small numbers of pairs ~10. The Josephson dynamics and the current-phase characteristics are then investigated, showing that the critical current has a maximum at the BCS-BEC crossover. For the considered initial conditions a two-state model gives a good description of the dynamics and of the current-phase characteristics.

cond-mat.mes-hall↗

arXiv2010

Phase Structure and Compactness

In order to study the influence of compactness on low-energy properties, we compare the phase structures of the compact and non-compact two-dimensional multi-frequency sine-Gordon models. It is shown that the high-energy scaling of the compact and non-compact models coincides, but their low-energy behaviors differ. The critical frequency $β^2 = 8π$ at which the sine-Gordon model undergoes a topological phase transition is found to be unaffected by the compactness of the field since it is determined by high-energy scaling laws. However, the compact two-frequency sine-Gordon model has first and second order phase transitions determined by the low-energy scaling: we show that these are absent in the non-compact model.

hep-th↗

arXiv2010

Local Correlations in the Super Tonks-Girardeau Gas

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite temperature we obtain that the three-body correlator has a weak dependence on the temperature up to the degeneracy temperature. We also find that for temperatures larger than the degeneracy temperature the values of the three-body correlator for the super Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar even for relatively small couplings.

cond-mat.quant-gas↗

arXiv2010

1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model

The repulsive Lieb-Liniger model can be obtained as the non-relativistic limit of the Sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian and operators) can be put in correspondence with those of the former. We use this mapping, together with the Thermodynamical Bethe Ansatz equations and the exact form factors of the Sinh-Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb-Liniger model both at zero and finite temperature. The computation of one-point correlators is thoroughly detailed and, when possible, compared with known results in the literature.

cond-mat.stat-mech↗

arXiv2010

(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions.

hep-th↗

arXiv2010

Expectation Values in the Lieb-Liniger Bose Gas

Taking advantage of an exact mapping between a relativistic integrable model and the Lieb-Liniger model we present a novel method to compute expectation values in the Lieb-Liniger Bose gas both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.

cond-mat.stat-mech↗

arXiv2009

Comparison of renormalization group schemes for sine-Gordon type models

The scheme-dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoric models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising type phase transition of the massive sine-Gordon model. For the latter case the Maxwell construction represents a strong constraint on the RG flow which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.

hep-th↗

arXiv2009

Soliton Dynamics in Linearly Coupled Discrete Nonlinear Schrödinger Equations

We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use a unitary transformation to remove the linear coupling terms, and show that the existing soliton solutions oscillate from one species to the other. When the nonlinear coupling strengths are different, the soliton dynamics is numerically investigated and the findings are compared to the results of an effective two-mode model. The case of two linearly coupled Ablowitz-Ladik equations is also investigated.

nlin.PS↗

arXiv2009

Ultracold Bosons with 3-Body Attractive Interactions in an Optical Lattice

We study the effect of an optical lattice (OL) on the ground-state properties of one-dimensional ultracold bosons with three-body attraction and two-body repulsion, which are described by a cubic-quintic Gross-Pitaevskii equation with a periodic potential. Without the OL and with a vanishing two-body interaction term, soliton solutions of the Townes type are possible only at a critical value of the three-body interaction strength, at which an infinite degeneracy of the ground-state occurs; a repulsive two-body interaction makes such localized solutions unstable. We show that the OL opens a stability window around the critical point when the strength of the periodic potential is above a critical threshold. We also consider the effect of an external parabolic trap, studying how the stability of the solitons depends on matching between minima of the periodic potential and the minimum of the parabolic trap.

cond-mat.stat-mech↗

arXiv2008

Critical temperature of non-interacting Bose gases on disordered lattices

For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential.

cond-mat.stat-mech↗

arXiv2008

Quantum measuring processes for trapped ultracold bosonic gases

The standard experimental techniques usually adopted in the study of the behaviour of ultracold atoms in optical lattices involve extracting the atom density profile from absorption images of the atomic sample after trap release. Quantum mechanically this procedure is described by a generalized measure (POVM); interference patterns found in absorption images suggest a generalized measure based on fixed-phase, coherent-like states. We show that this leads to an average atomic density which differs from the usually adopted one, obtained as the expectation value of the atom density operator in the many-body state.

quant-ph↗

arXiv2008

Rabi switch of condensate wavefunctions in a multicomponent Bose gas

Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wavefunction of one component to the other. This "Rabi switch" can be generated in a binary BEC mixture by an electromagnetic field between the two components, typically two hyperfine states. When the wavefunction to be transfered is - at a given time - a stationary state of the multicomponent Hamiltonian, then, after a time delay (depending on the Rabi frequency), it is possible to have the same wavefunction on the other condensate. The Rabi switch can be used to transfer also moving bright matter-wave solitons, as well as vortices and vortex lattices in two-dimensional condensates. The efficiency of the proposed switch is shown to be 100% when inter-species and intra-species interaction strengths are equal. The deviations from equal interaction strengths are analyzed within a two-mode model and the dependence of the efficiency on the interaction strengths and on the presence of external potentials is examined in both 1D and 2D settings.

cond-mat.other↗

arXiv2008

Optical Lattices: Theory

This chapter presents an overview of the properties of a Bose-Einstein condensate (BEC) trapped in a periodic potential. This system has attracted a wide interest in the last years, and a few excellent reviews of the field have already appeared in the literature (see, for instance, [1-3] and references therein). For this reason, and because of the huge amount of published results, we do not pretend here to be comprehensive, but we will be content to provide a flavor of the richness of this subject, together with some useful references. On the other hand, there are good reasons for our effort. Probably, the most significant is that BEC in periodic potentials is a truly interdisciplinary problem, with obvious connections with electrons in crystal lattices, polarons and photons in optical fibers. Moreover, the BEC experimentalists have reached such a high level of accuracy to create in the lab, so to speak, paradigmatic Hamiltonians, which were first introduced as idealized theoretical models to study, among others, dynamical instabilities or quantum phase transitions.

cond-mat.stat-mech↗

arXiv2008

One-Dimensional Bose Gases with N-Body Attractive Interactions

We study the ground state properties of a one-dimensional Bose gas with N-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schroedinger equation, we compute the chemical potential and the ground state energy. For N=3, a localized soliton wave-function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parameterized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of N-body attractive contact interactions in higher dimensions is presented.

cond-mat.stat-mech↗

arXiv2007

Spatially Inhomogeneous Superconducting and Bosonic Networks With Emergent Complex Behaviors

The spontaneous emergence of enhanced responses and local orders are properties often associated with complex matter where nonlinearities and spatial inhomogeneities dominate. We discuss these phenomena in quantum devices realized with superconducting Josephson junction networks and cold atoms in optical lattices. We evidence how the pertinent engineering of the network's shape induces the enhancement of the zero-voltage Josephson critical currents in superconducting arrays as well as the emergence of spatially localized condensates for cold atoms in inhomogeneous optical lattices.

cond-mat.supr-con↗

arXiv2007

Soliton Propagation in Chains with Simple Nonlocal Defects

We study the propagation of solitons on complex chains built by inserting finite graphs at two sites of an unbranched chain. We compare numerical findings with the results of an analytical linear approximation scheme describing the interaction of large-fast solitons with non-local topological defects on a chain. We show that the transmission properties of the solitons strongly depend on the structure of the inserted graph, giving a tool to control the soliton propagation through the choice of pertinent graphs to be attached to the chain.

nlin.PS↗

arXiv2006

BEC in a star-comb graph

We investigate the properties of free bosons hopping on a star-comb network, discussing the single-particle spectrum and the main thermodynamic equilibrium properties: Bose-Einstein critical temperature, fraction of condensate, and spatial boson distribution. We find an enhancement of the critical temperature with respect to other inhomogeneous networks.

cond-mat.stat-mech↗