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A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is π and close to it, where is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung-rung correlation function and the spin-spin and charge-charge static structure factors.

We obtain the spectral functions of a two-velocities Tomonaga-Luttinger liquid at T 0K in terms of the Appell hypergeometric functions F1 and F2. In the case of SU(N) spin symmetry, the spectral functions can be expressed with the Gauss hypergeometric functions. We discuss the singularities and thresholds of the spectral functions for both the SU(N) invariant case and the general case.

We theoretically investigate the droplets formation in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar interaction becomes sufficiently attractive compared to the contact one, we show how a solitonic-like density profile evolves into a liquid-like droplet on increasing the number of particles in the trap. The incipient gas-liquid transition is also signalled by a steep increase of the breathing mode and a change in sign of the chemical potential. Upon a sudden release of the trap, varying the number of trapped atoms and the scattering length, the numerical solution of a time-dependent generalized Gross-Pitaevskii equation shows either an evaporation of the cloud, the formation of a single self-bound droplet or a fragmentation in multiple droplets.These results can be probed with lanthanides atoms and help in characterizing the effect of the dipolar interaction in a quasi-one-dimensional geometry.

We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational approximation to a gas of dipolar bosons in the single mode approximation and obtain its ground state energy per unit length. This allows for the calculation of the Tomonaga-Luttinger exponent as a function of density and the determination of the structure factor at small momenta. Moreover, in the case of attractive dipolar interaction, an instability is predicted at a critical density, which could be accessed in lanthanide atoms.

Probing the radial collective oscillation of a trapped quantum system is an accurate experimental tool to investigate interactions and dimensionality effects. We consider a fully polarized quasi-one dimensional dipolar quantum gas of bosonic dysprosium atoms in a parabolic trap at zero temperature. We model the dipolar gas with an effective quasi-one dimensional Hamiltonian in the single-mode approximation, and derive the equation of state using a variational approximation based on the Lieb-Liniger gas Bethe Ansatz wavefunction or perturbation theory. We calculate the breathing mode frequencies while varying polarization angles by a sum-rule approach, and find them in good agreement with recent experimental findings.

We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for the case of three components.

We consider a two leg bosonic ladder in a \\(U(1)\\) gauge field with both interleg hopping and interleg repulsion. As a function of the flux, the interleg interaction converts the commensurate-incommensurate transition from the Meissner to a Vortex phase, into an Ising-type of transition towards a density wave phase. A disorder point is also found after which the correlation functions develop a damped sinusoid behavior signaling a melting of the vortex phase. We discuss the differences on the phase diagram for attractive and repulsive interleg interaction. In particular, we show how repulsion favors the Meissner phase at low-flux and a phase with a second incommensuration in the correlation functions for intermediate flux, leading to a richer phase diagram than in the case of interleg attraction. The effect of the temperature on the chiral current is also discussed.

A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semi-metal through a semi-Dirac phase towards a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.

We consider a two-leg boson ladder in an artificial U(1) gauge field and show that, in the presence of interleg attractive interaction, the flux induced Vortex state can be melted by dislocations. For increasing flux, instead of the Meissner to Vortex transition in the commensurate-incommensurate universality class, first an Ising transition from the Meissner state to a charge density wave takes place, then, at higher flux, the melted Vortex phase is established via a disorder point where incommensuration develops in the rung current correlation function and in momentum distribution.Finally, the quasi-long range ordered Vortex phase is recovered for sufficiently small interaction. Our predictions for the observables, such as the spin current and the static structure factor, could be tested in current experiments with cold atoms in bosonic ladders.

Atomtronics deals with matter-wave circuits of ultra-cold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed, in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, we survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. We review some of the latest progresses achieved in matter-wave circuits design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done both at the level of equilibrium and non-equilibrium situations. Numerous relevant problems in mesoscopic physics, like persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. We summarize some of the atomtronics quantum devices and sensors. Finally, we discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.