arXiv subjects

L. Salasnich

Publications and source records attributed to L. Salasnich.

At least 91 records · Page 5Linked to original sources

arXiv2010

Dimensional reduction of a binary Bose-Einstein condensate in mixed dimensions

We present effective reduced equations for the study of a binary Bose-Einstein condensate (BEC), where the confining potentials of the two BEC components have distinct asymmetry so that the components belong to different space dimensions as in a recent experiment [G. Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)]. Starting from a binary three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a Lagrangian variational approach we derive a binary effective nonlinear Schroedinger equation with components in different reduced dimensions, e. g., the first component in one dimension and the second in two dimensions as appropriate to represent a cigar-shaped BEC coupled to a disk-shaped BEC. We demonstrate that the effective reduced binary equation, which depend on the geometry of the system, is quite reliable when compared with the binary 3D GPE and can be efficiently used to perform numerical simulation and analytical calculation for the investigation of static and dynamic properties of a binary BEC in mixed dimensions.

cond-mat.quant-gas↗

arXiv2010

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the order parameter of the Fermi superfluid, which is derived from the respective density functional in the unitarity limit (a similar model applies to the BCS regime too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP is impossible, as it requires an attractive self-interaction, while the intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we demonstrate that the symmetry breaking is possible in the mixture with attraction between fermions and bosons, like 40K and 87Rb. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, N_F and N_B, and by phase diagrams in the (N_F,N_B) plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relation between N_F and N_B, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.

cond-mat.quant-gas↗

arXiv2010

Competition between symmetry breaking and onset of collapse in weakly coupled atomic condensates

We analyze the symmetry breaking of matter-wave solitons in a pair of cigar-shaped traps coupled by tunneling of atoms. The model is based on a system of linearly coupled nonpolynomial Schrödinger equations (NPSEs). Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in coupled cubic equations, in the present model the SSB competes with the onset of collapse in this system. Stability regions of symmetric and asymmetric solitons, as well as the collapse region, are identified in the parameter space of the system.

cond-mat.quant-gas↗

arXiv2010

Quantum-tunneling dynamics of a spin-polarized Fermi gas in a double-well potential

We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system is made of non-interacting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions in interaction with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to the one observed in absence of BEC but with the Rabi frequencies of fermionic excited states explicitly depending on the number of bosons and on the boson-fermion interaction strength. From this, the possibility to control quantum fermionic dynamics by means of Feshbach resonances is suggested.

cond-mat.quant-gas↗

arXiv2009

Collapse of triaxial bright solitons in atomic Bose-Einstein condensates

We study triaxial bright solitons made of attractive Bose-condensed atoms characterized by the absence of confinement in the longitudinal axial direction but trapped by an anisotropic harmonic potential in the transverse plane. By numerically solving the three-dimensional Gross-Pitaevskii equation we investigate the effect of the transverse trap anisotropy on the critical interaction strength above which there is the collapse of the condensate. The comparison with previous predictions [Phys. Rev. A {\bf 66}, 043619 (2002)] shows significant differences for large anisotropies.

cond-mat.quant-gas↗

arXiv2009

Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation

The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrödinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce "model 1" (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. "Model 2", that was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction of the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2 -- in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

nlin.PS↗

arXiv2009

Surface Effects in the Unitary Fermi Gas

We study the extended Thomas-Fermi (ETF) density functional of the superfluid unitary Fermi gas. This functional includes a gradient term which is essential to describe accurately the surface effects of the system, in particular with a small number of atoms, where the Thomas-Fermi (local density) approximation fails. We find that our ETF functional gives density profiles which are in good agreement with recent Monte Carlo results and also with a more sophisticated superfluid density functional based on Bogoliubov-de Gennes equations. In addition, by using extended hydrodynamics equations of superfluids, we calculate the frequencies of collective surface oscillations of the unitary Fermi gas, showing that quadrupole and octupole modes strongly depend on the number of trapped atoms.

cond-mat.quant-gas↗

arXiv2009

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation we study different aspects of the localization of a non-interacting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a non-interacting BEC. We also simulate the non-linear dynamics when a harmonically trapped BEC is suddenly released into a quasi-periodic potential, {as done experimentally in a laser speckle potential [Billy et al., Nature 453, 891 (2008)]$ We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.

cond-mat.quant-gas↗

arXiv2008

Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity

In the case of tight transverse confinement (cigar-shaped trap) the three-dimensional (3D) nonlinear Schrödinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length $|a|\to \infty$), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion number $N$ the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a two-dimensional form is also performed for a tight axial confinement (disk-shaped trap). The resultant effective 2D nonpolynomial equation also produces results in agreement with the original 3D equation and has simple power-law nonlinearity for small and large $N$. For both cigar- and disk-shaped superfluids our nonpolynomial Schrödinger equations are quite attractive for phenomenological application.

cond-mat.other↗

arXiv2008

DC Josephson Effect with Fermi gases in the Bose-Einstein regime

We show that the DC Josephson effect with ultracold fermionic gases in the BEC regime of composite molecules can be described by a nonlinear Schrodinger equation (NLSE). By comparing our results with Bogoliubov-de Gennes calculations [Phys. Rev. Lett. 99, 040401 (2007)] we find that our superfluid NLSE, which generalizes the Gross-Pitaevskii equation taking into account the correct equation of state, is reliable in the BEC regime of the BCS-BEC crossover up to the limit of very large (positive) scattering length. We also predict that the Josephson current displays relevant beyond mean-field effects.

cond-mat.other↗

arXiv2008

DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance

We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the BEC side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.

cond-mat.other↗

arXiv2008

Dynamics of kicked matter-wave solitons in an optical lattice

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in a optical lattice. The resulting soliton's dynamics is studied within the framework of the time-dependent nonpolynomial Schrodinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.

cond-mat.other↗

arXiv2008

Effects of Axial Vorticity in Elongated Mixtures of Bose-Einstein Condensates

We consider a meniscus between rotating and nonrotating species in the Bose-Einstein condensate (BEC) with repulsive inter-atomic interactions, confined to a pipe-shaped trap. In this setting, we derive a system of coupled one-dimensional (1D) nonpolynomial Schrodinger equations (NPSEs) for two mean-field wave functions. Using these equations, we analyze the phase separation/mixing in the pipe with periodic axial boundary conditions, i.e. in a toroidal configuration. We find that the onset of the mixing, in the form of suction, i.e., filling the empty core in the vortical component by its nonrotating counterpart, crucially depends on the vorticity of the first component, and on the strengths of the inter-atomic interactions.

cond-mat.other↗

arXiv2008

Macroscopic Periodic Tunneling of Fermi Atoms in the BCS-BEC Crossover

We study the macroscopic quantum tunneling of two weakly-linked superfluids made of interacting fermionic atoms. We derive atomic Josephson junction equations and find that zero-mode and pi-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of ^40K atoms, we calculate these oscillation frequencies in the crossover from the Bardeen-Cooper-Schrieffer state of weakly-bound Cooper pairs to the Bose-Einstein Condensate of strongly-bound molecular dimers.

cond-mat.stat-mech↗

arXiv2007

Bose-Einstein condensates under a spatially-modulated transverse confinement

We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form (using both the effective NPSE and the full 3D Gross-Pitaevskii equation) and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.

cond-mat.other↗

arXiv2007

Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices

Within the framework of the mean-field description, we investigate atomic Bose-Einstein condensates (BECs), with attraction between atoms, under the action of strong transverse confinement and periodic (optical-lattice, OL) axial potential. Using a combination of the variational approximation (VA), one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE), and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation (GPE), we show that the ground state of the condensate is a soliton belonging to the semi-infinite bandgap of the periodic potential. The soliton may be confined to a single cell of the lattice, or extend to several cells, depending on the effective self-attraction strength, $g$ (which is proportional to the number of atoms bound in the soliton), and depth of the potential, $V_{0}$, the increase of $V_{0}$ leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton's shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, $g=g_{c}$, which gradually decreases with the increase of the depth of the periodic potential, $V_{0}$; under typical experimental conditions, the corresponding maximum number of $^{7}$Li atoms in the soliton, $N_{\max}$, ranges between $8,000$ and $4,000$. Examples of stable multi-peaked solitons are also found in the first finite bandgap of the lattice spectrum. The respective critical value $g_{c}$ again slowly decreases with the increase of $V_{0}$, corresponding to $N_{\max }\simeq 5,000$.

cond-mat.other↗

arXiv2007

Self-induced density modulations in the free expansion of Bose-Einstein condensates

We simulate numerically the free expansion of a repulsive Bose-Einstein condensate with an initially Gaussian density profile. We find a self-similar expansion only for weak inter-atomic repulsion. In contrast, for strong repulsion we observe the spontaneous formation of a shock wave at the surface followed by a significant depletion inside the cloud. In the expansion, contrary to the case of a classical viscous gas, the quantum fluid can generate radial rarefaction density waves with several minima and maxima. These intriguing nonlinear effects, never observed yet in free-expansion experiments with ultra-cold alkali-metal atoms, can be detected with the available setups.

cond-mat.other↗

arXiv2006

Thermodynamics of Solitonic Matter Waves in a Toroidal Trap

We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.

cond-mat.other↗