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

Salasnich, Luca; Malomed, Boris A.; Toigo, Flavio

doi:10.1103/physreva.81.045603

Cited by 33 publications

(13 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In nonlinear optics, the SBB was predicted for continuous-wave (spatially uniform) states [6], and for solitons [7,10], in the models of dual-core fibers and Bragg gratings. The SBB was also analyzed for matter-wave solitons in the BEC loaded into double-channel potential traps [11]- [14].…”

Section: Introduction and The Modelmentioning

confidence: 99%

Symmetric and asymmetric localized modes in linear lattices with an embedded pair ofχ(2)-nonlinear sites

Brazhnyi

Malomed

2012

Phys. Rev. A

View full text Add to dashboard Cite

We construct families of symmetric, antisymmetric, and asymmetric solitary modes in onedimensional bichromatic lattices with the second-harmonic-generating (χ (2) ) nonlinearity concentrated at a pair of sites placed at distance l. The lattice can be built as an array of optical waveguides. Solutions are obtained in an implicit analytical form, which is made explicit in the case of adjacent nonlinear sites, l = 1. The stability is analyzed through the computation of eigenvalues for small perturbations, and verified by direct simulations. In the cascading limit, which corresponds to large mismatch q, the system becomes tantamount to the recently studied single-component lattice with two embedded sites carrying the cubic nonlinearity. The modes undergo qualitative changes with the variation of q. In particular, at l ≥ 2, the symmetry-breaking bifurcation (SBB), which creates asymmetric states from symmetric ones, is supercritical and subcritical for small and large values of q, respectively, while the bifurcation is always supercritical at l = 1. In the experiment, the corresponding change of the phase transition between the second and first kinds may be implemented by varying the mismatch, via the wavelength of the input beam. The existence threshold (minimum total power) for the symmetric modes vanishes exactly at q = 0, which suggests a possibility to create the solitary mode using low-power beams. The stability of solution families also changes with q.

show abstract

Section: Introduction and The Modelmentioning

confidence: 99%

Symmetric and asymmetric localized modes in linear lattices with an embedded pair ofχ(2)-nonlinear sites

Brazhnyi

Malomed

2012

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Subsequently, the SBB was studied for gap solitons in dual-core fiber Bragg gratings with the * brazhnyy@gmail.com † malomed@post.tau.ac.il same Kerr (cubic) nonlinearity as in the ordinary fibers [11]. In another physical setting which also features the cubic nonlinearity, the SBB was predicted for matter-wave solitons in the self-attractive BEC loaded into a dual-trough potential trap [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous symmetry breaking in Schrödinger lattices with two nonlinear sites

Brazhnyi

Malomed

2011

Phys. Rev. A

View full text Add to dashboard Cite

We introduce discrete systems in the form of straight (infinite) and ring-shaped chains, with two symmetrically placed nonlinear sites. The systems can be implemented in nonlinear optics (as waveguiding arrays) and Bose-Einstein condensates (by means of an optical lattice). A full set of exact analytical solutions for symmetric, asymmetric, and antisymmetric localized modes is found, and their stability is investigated in a numerical form. The symmetry-breaking bifurcation, through which the asymmetric modes emerge from the symmetric ones, is found to be of the subcritical type. It is transformed into a supercritical bifurcation if the nonlinearity is localized in relatively broad domains around two central sites, and also in the ring of a small size, i.e., in effectively nonlocal settings. The family of antisymmetric modes does not undergo bifurcations and features both stable and unstable portions. The evolution of unstable localized modes is investigated by means of direct simulations. In particular, unstable asymmetric states, which exist in the case of the subcritical bifurcation, give rise to breathers oscillating between the nonlinear sites, thus restoring an effective dynamical symmetry between them.

show abstract

“…A specific example is the SBB for gap solitons in dual-core fiber Bragg gratings [12]. Later, manifestations of the SBB for matter-wave solitons held in dual-trough potential traps (including solitons of the gap type, supported by a periodic optical-lattice potential) were explored too [13][14][15][16]. The difference of the dual-trough configuration from the usual double well is the presence of an additional free direction, transverse to that in which the double-well potential acts (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Symmetric and asymmetric solitons trapped inH-shaped potentials

2011

View full text Add to dashboard Cite

We report results of numerical and analytical studies of the spontaneous symmetry breaking in solitons, both two-and one-dimensional (2D and 1D), which are trapped in H-shaped potential profiles built of two parallel potential troughs linked by a narrow rung in the transverse direction. This system can be implemented in self-attractive Bose-Einstein condensates (BECs), as well as in a nonlinear bulk optical waveguide. We demonstrate that the introduction of the transverse link changes the character of the symmetry-breaking bifurcation (SBB) in the system from subcritical to supercritical. (In terms of the corresponding phase transition, it is a change between the first and second kinds.) A noteworthy feature of the SBB in this setting is a nonmonotonous dependence of the soliton's norm at the bifurcation point on the strength of the transverse link. In the full 2D system, the results are obtained in a numerical form. An exact analytical solution is found for the bifurcation in the 1D version of the model, with the transverse rung modeled by the local linear coupling between the parallel troughs with the δ-functional longitudinal profile. By replacing the δ function by its finite-width Gaussian counterpart, similar results are obtained by means of the variational approximation (VA). The VA is also applied to the 1D system with a mixed linear and nonlinear transverse localized coupling. Comparison of the results produced by the different varieties of the system clearly reveals basic features of its the symmetry-breaking transition.

show abstract

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

Cited by 33 publications

References 41 publications

Symmetric and asymmetric localized modes in linear lattices with an embedded pair ofχ(2)-nonlinear sites

Symmetric and asymmetric localized modes in linear lattices with an embedded pair ofχ(2)-nonlinear sites

Spontaneous symmetry breaking in Schrödinger lattices with two nonlinear sites

Symmetric and asymmetric solitons trapped inH-shaped potentials

Contact Info

Product

Resources

About