arXiv:cond-mat/0607169 · Laser Physics Letters

Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture

Sadhan K. Adhikari

Published Jul 11, 2006• 10 citations

Abstract

Employing a time-dependent mean-field-hydrodynamic model we study the generation of black solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical solutions. The black soliton is found to be the first stationary vibrational excitation of the system and is considered to be a nonlinear continuation of the vibrational excitation of the harmonic oscillator state. We illustrate the stationary nature of the black soliton, by studying different perturbations on it after its formation.

DOI: 10.1002/lapl.200610050

Related papers

Fermionic bright soliton in a boson-fermion mixture

Sadhan K. Adhikari

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a quasi-one-dimensional cigar-shaped geometry. Due to a strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be bright fermionic solitons in the case of repulsive boson-fermion interactions. However, we demonstrate that stable bright fermionic solitons can be formed for a sufficiently attractive boson-fermion interaction in a boson-fermion mixture. We also consider the formation of fermionic solitons in the presence of a periodic axial optical-lattice potential. These solitons can be formed and studied in the laboratory with present technology.

arXiv:cond-mat/0509257Physical Review ANov 10, 200578 citations

Formation of bright solitons and soliton trains in a fermion–fermion mixture by modulational instability

Sadhan K. Adhikari

We employ a time-dependent mean-field-hydrodynamic model to study the generation of bright solitons in a degenerate fermion–fermion mixture in a cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

arXiv:cond-mat/0702337Journal of Physics A Mathematical and TheoreticalFeb 28, 200715 citations

Free expansion of fermionic dark solitons in a boson–fermion mixture

Sadhan K Adhikari

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate Fermi gas mixed with a Bose–Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a 'notch' in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.

arXiv:cond-mat/0509215Journal of Physics B Atomic Molecular and Optical PhysicsSep 19, 200521 citations

Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates

Georgios Theocharis, A. Weller, J. P. Ronzheimer +4 more

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.

arXiv:0909.2122Physical Review AJun 3, 2010128 citations

Sound wave propagation in strongly elongated fermion clouds at finite collisionality

P. Capuzzi, Patrizia Vignolo, F. Federici +1 more

We evaluate the transition from zero-sound to first-sound behaviour with increasing collisionality in the propagation of density waves through an ultracold gaseous mixture of fermionic atoms in the normal state confined inside a cigar-shaped harmonic trap. We study for this purpose the evolution of the one-body distribution functions associated with a density perturbation generated in the central region of the cloud, as obtained by numerical solution of the Vlasov–Landau equations. We examine a variety of trap anisotropies and of repulsive or attractive interaction strengths between the components of the mixture. The speed of propagation of the density disturbance is found to decrease in both cases as the magnitude of the coupling strength is increased. The results are compared with the values of the speed of zero sound and of first sound, as obtained analytically from the limit of vanishing collisionality and from linearized hydrodynamics. The main effects of the quasi-one-dimensional confinement are the stabilization of zero-sound excitations in the attractive regime before collapse and the lowering of the hydrodynamic sound velocity by a factor relative to three-dimensional behaviour.

arXiv:cond-mat/0511578Journal of Physics B Atomic Molecular and Optical PhysicsMay 2, 20067 citations

BOSE-EINSTEIN CONDENSATION (BEC): Part III. Dark solitons

Celso Hernández-Tenorio, J. Alcántara, L. E. Morales +4 more

The dynamics of dark solitons is studied within the framework of the mathematical model of nonlinear Schrodinger equation (NSE) with an external harmonic potential. A comparative analysis of the solution of no stationary problems is performed for a linear harmonic oscillator and the NSE model with a harmonic potential for different signs of the self-action potential. It is shown that the main specific feature of the dynamics of dark NSE solitons in a parabolic trap is the formation of solitons with dynamically changing form factors producing the periodic variation in the modulation depth (the degree of blackness) of dark solitons. The oscillation period of the dark solitons does not coincide with the oscillation period of a linear quantum-mechanical oscillator, which is caused by the periodic transformation of the black solitons to the gray one and vice versa.

Jan 1, 20060 citations