Symmetry Breaking Of Solitons Research Articles

Spontaneous symmetry breaking and ghost states in two-dimensional fractional nonlinear media with non-Hermitian potential

The interaction of fractional diffraction and parity-time ({{{{{mathcal{PT}}}}}}) symmetric would bring some unique properties to certain physical system. Here we report a spontaneous symmetry breaking (SSB) phenomenon and ghost states of solitons supported by the two-dimensional (2D) fractional nonlinear Schrödinger (FNLS) equation with focusing and defocusing Kerr media under 2D non-Hermitian {{{{{mathcal{PT}}}}}}-symmetric potential. The continuous asymmetric soliton bifurcates out in a SSB way. For the focusing regime, as the power exceeds a critical value, the asymmetric soliton bifurcates from fundamental symmetric solitons, and when it turns to the defocusing regime, the symmetry breaking phenomenon is found in the branch of the first excited state. The symmetric solitons (including fundamental one and first excited state) are destabilized at this point. Intriguingly, the branches of asymmetry solitons are existing with complex conjugate propagation constants (alias ghost states), which is solely in fractional media. Moreover, we investigate the dependence of fractional Lévy index (α) on the symmetry breaking of solitons in detail. And the stabilities of fundamental symmetric soliton, asymmetric solitons, as well as the first excited states are explored. Moreover, The management of optical field propagation is achieved by modulation of the external potential. Meanwhile, we find the stable excitations of solitons via adiabatic excitations of system parameters. These results will provide some theoretical basis for the study of SSB phenomena and related physical experiments in the 2D fractional media with {{{{{mathcal{PT}}}}}}-symmetric potentials.

Spontaneous symmetry breaking and ghost states supported by the fractional PT-symmetric saturable nonlinear Schrödinger equation.

We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole and tripole solitons (i.e., first and second excited states) are also studied numerically. Moreover, we analyze the influences of fractional Lévy index ( α) and saturable nonlinear parameters (S) on the symmetry breaking of solitons in detail. The stability of fundamental symmetric soliton, asymmetric, dipole, and tripole solitons is explored via the linear stability analysis and direct propagations. Moreover, we explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons. Meanwhile, we find the stable excitations from the fractional diffraction with saturation nonlinearity to integer-order diffraction with Kerr nonlinearity via the adiabatic excitations of parameters. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related physical experiments in the fractional media with PT-symmetric potentials.

Symmetry breaking of solitons in the PT-symmetric nonlinear Schrödinger equation with the cubic-quintic competing saturable nonlinearity.

The symmetry breaking of solitons in the nonlinear Schrödinger equation with cubic-quintic competing nonlinearity and parity-time symmetric potential is studied. At first, a new asymmetric branch separates from the fundamental symmetric soliton at the first power critical point, and then, the asymmetric branch passes through the branch of the fundamental symmetric soliton and finally merges into the branch of the fundamental symmetric soliton at the second power critical point, while the power of the soliton increases. This leads to the symmetry breaking and double-loop bifurcation of fundamental symmetric solitons. From the power-propagation constant curves of solitons, symmetric fundamental and tripole solitons, asymmetric solitons can also exist. The stability of symmetric fundamental solitons, asymmetric solitons, and symmetric tripole solitons is discussed by the linear stability analysis and direct simulation. Results indicate that symmetric fundamental solitons and symmetric tripole solitons tend to be stable with the increase in the soliton power. Asymmetric solitons are unstable in both high and low power regions. Moreover, with the increase in saturable nonlinearity, the stability region of fundamental symmetric solitons and symmetric tripole solitons becomes wider.

Symmetry breaking of solitons in two-dimensional complex potentials.

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schrödinger equation with a two-dimensional complex potential. This symmetry breaking is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, it is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenvalues and thus exhibit nonreciprocal nonlinear evolutions under random-noise perturbations.

Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials.

Symmetry breaking of solitons in a class of one-dimensional parity-time (PT) symmetric complex potentials with cubic nonlinearity is reported. In generic PT-symmetric potentials, such symmetry breaking is forbidden. However, in a special class of PT-symmetric potentials V(x)=g(2)(x)+αg(x)+ig'(x), where g(x) is a real and even function and α a real constant, symmetry breaking of solitons can occur. That is, a branch of non-PT-symmetric solitons can bifurcate out from the base branch of PT-symmetric solitons when the base branch's power reaches a certain threshold. At the bifurcation point, the base branch changes stability, and the bifurcated branch can be stable.

Symmetry breaking of solitons in two-component Gross-Pitaevskii equations

We revisit the problem of the spontaneous symmetry breaking (SSB) of solitons in two-component linearly coupled nonlinear systems, adding the nonlinear interaction between the components. With this feature, the system may be realized in new physical settings, in terms of optics and the Bose-Einstein condensate (BEC). SSB bifurcation points are found analytically, for both symmetric and antisymmetric solitons (the symmetry between the two components is meant here). Asymmetric solitons, generated by the bifurcations, are described by means of the variational approximation (VA) and numerical methods, demonstrating good accuracy of the variational results. In the space of the self-phase-modulation (SPM) parameter and soliton's norm, a border separating stable symmetric and asymmetric solitons is identified. The nonlinear coupling may change the character of the SSB bifurcation, from subcritical to supercritical. Collisions between moving asymmetric and symmetric solitons are investigated too. Antisymmetric solitons are destabilized by a supercritical bifurcation, which gives rise to self-confined modes featuring Josephson oscillations, instead of stationary states with broken antisymmetry. An additional instability against delocalized perturbations is also found for the antisymmetric solitons.