arXiv subjects

Francesco Lorenzi

Publications and source records attributed to Francesco Lorenzi.

10 recordsLinked to original sources

arXiv2026

Dimensional reduction for optical beams with thermal nonlocal nonlinearity

Nonlocal optical nonlinearities arising from the thermorefractive effect provide a long-range material response determined by heat diffusion and absorption. In graded-index media, this nonlocality fundamentally alters modal interactions, yet its accurate modeling remains computationally demanding when starting from the full spatial nonlinear Schrödinger equation. In this work, inspired by the nonpolynomial Schrödinger equation (NPSE) framework, we extend the dimensional reduction techniques to incorporate thermally mediated nonlocal nonlinearities. By coupling the optical field to an equation for the temperature-induced refractive index change, and employing a variational ansatz based on Laguerre--Gauss modes of the annular kind, of arbitrary azimuthal order, we derive explicit analytic expressions for the variational equations. The resulting effective model captures the dependence of the nonlinear interaction on mode order and degree of nonlocality, providing a tractable reduced description of the dynamics in thermal nonlocal media.

nlin.PS↗

arXiv2026

Bosonic Josephson junction dynamics: interplay between quantum and thermal fluctuations

We investigate the superfluid dynamics of a Josephson junction beyond the mean-field description, incorporating the role of thermal fluctuations as well as quantum fluctuations. Using a formalism that accounts for the fluctuations in a homogeneous gas, and under the assumption that the transport of the non-condensed component is negligible, we derive a corrected equation of motion within the two-site approximation. The resulting corrections for the typical dynamical quantities, like the Josephson frequency, the strength of macroscopic quantum self-trapping, and the threshold for spontaneous symmetry breaking, allow us to predict the effects of both types of fluctuations and assess their relative importance in different regimes in a semianalytical fashion. For all the dynamical quantities, the quantum fluctuations are shown to play an opposite role with respect to the thermal fluctuations. Josephson frequency is decreased by thermal fluctuations and both the critical strenghts of macroscopic quantum self trapping and spontaneous symmetry breaking are increased. We assess the experimentally accessible regimes by calculating the relevant parameters of recent experimental realizations of Bosonic Josephson junction and show that the expected regime is dominated by quantum fluctuations.

cond-mat.quant-gas↗

arXiv2026

Variational treatment of the electromagnetic field in an optical cavity with a moving mirror

Optical cavities with moving mirrors provide a versatile platform for exploring radiation-matter interactions and optically mediated mechanical effects, whose control has wide technological implications. However, capturing the coupled dynamics of the electromagnetic field and of the mirror within a consistent theoretical framework remains challenging. We analyze the problem of the coupling between classical electromagnetic fields in a cavity and a movable mirror, considering both nonrelativistic and relativistic regimes of motion. Starting from the equations of motion for a mirror subject to a generic external potential, we provide a variational formulation of the mirror-radiation interaction. Within this framework, a single-mode variational approximation is introduced, which captures the essential dynamical features of the coupled system. In the special case of a mirror undergoing free motion, the variational method yields an exact solution. This unified treatment highlights the connection between different dynamical regimes and provides a basis for analyzing applications ranging from precision interferometry to relativistic radiation-pressure effects.

physics.optics↗

arXiv2025

Experimental Observation of Single- and Multisite Matter-Wave Solitons in an Optical Accordion Lattice

We report the experimental observation of discrete bright matter-wave solitons with attractive interaction in an optical lattice. Using an accordion lattice with adjustable spacing, we prepare a Bose-Einstein condensate of cesium atoms across a defined number of lattice sites. By quenching the interaction strength and the trapping potential, we generate both single-site and multisite solitons. Our results reveal the existence and characteristics of these solitons across a range of lattice depths and spacings. We identify stable regions of the solitons based on interaction strength and lattice properties, and compare these findings with theoretical predictions. The experimental results qualitatively agree with a Gaussian variational model and match quantitatively with numerical simulations of the three-dimensional Gross-Pitaevskii equation extended with a quintic term to account for the loss of atoms. Our results provide insights into the quench dynamics and collapse mechanisms, paving the way for further studies of transport and dynamical properties of matter-wave solitons in lattices.

cond-mat.quant-gas↗

arXiv2025

Optical Cavity in Relativistic Regime for Laser Propulsion

Laser propulsion has been proposed for relativistic interstellar flights, but it faces the significant challenge of requiring extremely powerful laser radiation due to the inherently low momentum transfer between the beam and the sail. The photon-recycling technique enhances thrust by transferring momentum through multiple reflections within a cavity setup, formed by the lightsail and a ground-based mirror in a laser system array. In this work, a delay differential model is developed to describe the evolution of the beam and thrust, incorporating both the Doppler effect and the round-trip time delay experienced by each beam component. With optimized multilayer reflectors, the thrust performance gain is shown to be significant for interstellar flight, though limited by diffraction and the necessity of removing harmful redshifted radiation that could overheat the lightsail. By balancing thrust performance with thermal stability, we derive a simple condition for determining the spectral requirements of the mirrors. Given a selected laser wavelength, this condition fully specifies the necessary properties of the cavity mirrors, enabling the same system to effectively support a range of launch protocols.

physics.optics↗

arXiv2025

Low-energy atomic scattering: s-wave relation between the interaction potential and the phase shift

We investigate the on-shell approximation in the context of s-wave scattering for ultracold two-body collisions. Our analysis systematically covers spatial dimensions D=1,2,3 , with the aim of identifying the regimes in which the approximation remains valid when applied to commonly used model interaction potentials. Specifically, we focus on the square well and delta shell potentials, both of which admit analytical solutions for the s-wave scattering problem in all dimensions considered. By employing the exact analytical expressions for the s-wave scattering phase shift, we perform a direct comparison between the exact on-shell matrix element of the interaction potential and their corresponding approximations across a range of collision momenta. Particular attention is given to the low-energy regime. Our findings indicate that, although the on-shell approximation generally improves with increasing momentum, its accuracy also improves for weaker potentials. Remarkably, in the limit of weak interactions, we demonstrate that the on-shell approximation becomes exact at leading order. In this regime, the approximation offers a controlled means of deriving the low-momentum expansion of the potential and may serve as a useful tool in constructing effective interactions for quantum field theories.

cond-mat.quant-gas↗

arXiv2025

Variational approach to multimode nonlinear optical fibers

We analyze the spatiotemporal solitary waves of a graded-index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schrödinger equation approach, we derive an effective one-dimensional Lagrangian associated with the Laguerre-Gauss modes with a generic radial mode number p and azimuthal index m. We show that the form of the equations of motion for any Laguerre-Gauss mode is particularly simple, and we derive the critical power for the collapse for every mode. By solving the nonpolynomial Schrödinger equation, we provide a comparison of the stationary mode profiles in the radial and temporal coordinates.

nlin.PS↗

arXiv2024

Only-phase Popov action: thermodynamic derivation and superconducting electrodynamics

We provide a thermodynamic derivation of the only-phase Popov action functional, which is often adopted to study the low-energy effective hydrodynamics of a generic nonrelativistic superfluid. It is shown that the crucial assumption is the use of the saddle point approximation after neglecting the quantum-pressure term. As an application, we analyze charged superfluid (superconductors) coupled to the electromagnetic field at zero temperature. Our only-phase and minimally-coupled theory predicts the decay of the electrostatic field inside a superconductor with a characteristic length much smaller than the London penetration depth of the static magnetic field. This result is confirmed also by a relativistic only-phase Popov action we obtain from the Klein-Gordon Lagrangian.

cond-mat.quant-gas↗

arXiv2024

Atomic soliton transmission and induced collapse in scattering from a narrow barrier

We report systematic numerical simulations of the collision of a bright matter-wave soliton made of Bose-condensed alkali-metal atoms through a narrow potential barrier by using the three-dimensional Gross-Pitaevskii equation. In this way, we determine how the transmission coefficient depends on the soliton impact velocity and the barrier height. Quite remarkably, we also obtain the regions of parameters where there is the collapse of the bright soliton induced by the collision. We compare these three-dimensional results with the ones obtained by three different one-dimensional nonlinear Schrödinger equations. We find that a specifically modified nonpolynomial Schrödinger equation is able to accurately assess the transmission coefficient even in a region in which the usual nonpolynomial Schrödinger equation does collapse. In particular, this simplified but very effective one-dimensional model takes into account the transverse width dynamics of the soliton with an ordinary differential equation coupled to the partial differential equation of the axial wave function of the Bose-Einstein condensate.

cond-mat.quant-gas↗

arXiv2024

Quantum fluctuations in atomic Josephson junctions: the role of dimensionality

We investigate the role of quantum fluctuations in the dynamics of a bosonic Josephson junction in $D$ spatial dimensions, by using beyond mean-field Gaussian corrections. We derive some key dynamical properties in a systematic way for $D=3, 2, 1$. In particular, we compute the Josephson frequency in the regime of low population imbalance. We also obtain the critical strength of the macroscopic quantum self-trapping. Our results show that quantum corrections increase the Josephson frequency in spatial dimensions $D=2$ and $D=3$, but they decrease it in the $D=1$ case. The critical strength of macroscopic quantum self-trapping is instead reduced by quantum fluctuations in $D=2$ and $D=3$ cases, while it is enhanced in the $D=1$ configuration. We show that the difference between the cases of D = 2 and D = 3 on one side, and D = 1 on the other, can be related to the qualitatively different dependence of the interaction strength on the scattering length in the different dimensions.

cond-mat.quant-gas↗