Gap solitons in superfluid boson-fermion mixtures

Sadhan K. Adhikari and Boris A. Malomed

Phys. Rev. A 76, 043626 – Published 26 October 2007

Abstract

Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two band gaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intragap and intergap solitons, with the chemical potentials of the boson and fermion components falling in the same or different band gaps, respectively. Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.

Received 16 July 2007

DOI:https://doi.org/10.1103/PhysRevA.76.043626

Authors & Affiliations

Sadhan K. Adhikari^*

Instituto de Física Teórica, UNESP—São Paulo State University, 01.405-900 São Paulo, São Paulo, Brazil

Boris A. Malomed^†

Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel

^*adhikari@ift.unesp.br; http://www.ift.unesp.br/users/adhikari
^†malomed@eng.tau.ac.il; http://www.eng.tau.ac.il/ malomed/

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Vol. 76, Iss. 4 — October 2007

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Images

Figure 1
(Color online) The effective nonlinearity coefficients, $g_{B} N_{B}$ for bosons (a) and $g_{F} N_{F}^{2 ∕ 3}$ for fermions (b) versus the chemical potentials of the boson and fermion components, $μ_{B}$ and $μ_{F}$ , respectively, for families of the fundamental compact gap solitons in the first and second band gaps of periodic potential $ϵ cos (2 x)$ (numerical results are presented in this and other figures for $ϵ = 5$ ). As indicated in the figure, continuous curves and chains of symbols display, respectively, results obtained from the numerical solution (“num”) and variational approximation (“var”). Shaded vertical areas represent Bloch bands which separate the gaps.Reuse & Permissions
Figure 2
(Color online) Profiles of the probability density, ${| ϕ_{B, F} (x) |}^{2}$ [subject to normalization $\int_{\infty}^{\infty} {| ϕ_{B, F} (x) |}^{2} = 1$ ] in the boson (“bos”) and fermion (“fer”) components of the fundamental gap solitons, in four different cases with (a) both components of the soliton having their chemical potentials, $μ_{B}$ and $μ_{F}$ , in the second band gap, (b) $μ_{B}$ and $μ_{F}$ in the first and second gaps, respectively; (c) vice versa to (b); (d) both components of the first band gap. In terms of Ref. [30], the two-component gap solitons in panels (a) and (d) are of the intragap type, while the ones in (b) and (c) are intergap solitons. The thin dotted lines, here and in other figures, represent the OL potential, $\propto - cos (2 x)$ .Reuse & Permissions
Figure 3
(Color online) Same as in Fig. 2 with (a) intraspecies attraction among bosonic atoms corresponding to a negative $g_{B}$ and (b) interspecies attraction between bosons and fermions corresponding to a negative $g_{B F}$ . In (a) the bosonic GS is in the first band gap and fermionic GS is in the second band gap, in (b) vice versa to (a).Reuse & Permissions
Figure 4
(Color online) Profiles labeled I, II, III [normalized according to $\int_{\infty}^{\infty} {| ϕ_{B, F} (x) |}^{2} = 1$ ] represent the bosonic (a) and fermionic (b) components of three distinct stable nonfundamental gap solitons, extended over several lattice cells, for the same parameters (except for $μ_{B, F}$ ) as in Fig. 2a. The corresponding values of the chemical potentials are indicated in the panels.Reuse & Permissions
Figure 5
(Color online) The evolution of the boson (a) and fermion (b) components of the nonfundamental gap soliton, labeled III in Fig. 4, with $μ_{B} = - 0.80$ and $μ_{F} = - 0.60$ . A rather strong perturbation was applied to the soliton at $t = 10$ , in the form of $ϕ_{B, F} (x) \to 1.1 ϕ_{B, F} (x)$ . The perturbed soliton remains stable as long as the simulation was running.Reuse & Permissions
Figure 6
(Color online) The same stability test as shown in Fig. 5 for the fundamental soliton from Fig. 2a.Reuse & Permissions

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