Two-dimensional Bright Solitons Research Articles

Two-dimensional bright soliton in exciton-polariton condensate

In non-conservative nonlinear systems, the basic physical mechanics of soliton generation is that the kinetic energy and nonlinear terms of the system, as well as the gain and dissipation terms reach a double dynamic balance. How to generate stable free high-dimensional solitons in such a system is currently a challenging topic in soliton theory. In this article, we propose a theoretical scheme for realizing two-dimensional free bright solitons in exciton-polariton Bose-Einstein condensates, which proposes a physical mechanism for generating stable two-dimensional free space bright solitons through time periodic modulation interactions and a dual balance between gain and dissipation. In this end, firstly, we obtain the dynamic equations of two-dimensional bright soliton parameters through the Lagrange variational method, and obtain its dynamically stable parameter space. Secondly, the evolution of the generalized dissipative Gross-Pitaveskii equation is numerically simulated to verify the stability of two-dimensional bright solitons. Finally, we add Gaussian noise to simulate a real experimental environment and find that two-dimensional bright solitons are also stable within the observable time range of the experiment. Our experimental scheme opens the door to the study of bright solitons in high-dimensional free space in non-conservative systems.

Stability and Controllability of Various Spatial Solitons in Exciton–Polariton Condensates by a Composite Pumping

We investigate the stability and controllability of one-dimensional bright and dark solitons, and two-dimensional bright solitons and vortices with the charges m = 1 and 2, respectively, in a nonresonantly incoherent pumped exciton–polariton condensates. A composite pumping, consisting of the constant part and the Bessel-type spatially modulating part, is introduced to balance the gain and loss. We demonstrate that the pumping can not only stabilize all these solitons but also modulate the profiles of these solitons. We also find that all these solitons obtained in this study are different from the ones in the previous studies. Our work may pave a way to modulate these solitons in the nonresonantly pumped exciton–polariton system.

One- and two-dimensional bright solitons in inhomogeneous defocusing nonlinearities with an antisymmetric periodic gain and loss

We address that various branches of bright solitons exist in a spatially inhomogeneous defocusing nonlinearity with an imprinted antisymmetric periodic gain–loss profile. The spectra of such systems with a purely imaginary potential never become complex and thus the parity-time symmetry is unbreakable. The mergence between pairs of soliton branches occurs at a critical gain–loss strength, above which no soliton solutions can be found. Intriguingly, which pair of soliton branches will merge together can be changed by varying the modulation frequency of gain and loss. Most branches of one-dimensional solitons are stable in wide parameter regions. We also provide the first example of two-dimensional bright solitons with unbreakable parity-time symmetry.

Two-dimensional bright solitons in dipolar Bose-Einstein condensates with tilted dipoles

The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate-plane. The tilting angle constitutes an additional tuning parameter, which help us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon-instability in a homogeneous 2D condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach, involving the tuning of tilting angle.

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

We demonstrate the existence of one and two-dimensional bright solitons in the Bose-Einstein condensate with repulsive dipole-dipole interactions induced by a combination of dc and ac polarizing fields, oriented perpendicular to the plane in which the BEC is trapped, assuming that the strength of the fields grows in the radial ($r$) direction faster than $r^{3}$. Stable tightly confined 1D and 2D fundamental solitons, twisted solitons in 1D, and solitary vortices in 2D are found in a numerical form. The fundamental solitons remain robust under the action of an expulsive potential, which is induced by the interaction of the dipoles with the polarizing field. The confinement and scaling properties of the soliton families are explained analytically. The Thomas-Fermi approximation is elaborated for fundamental solitons. The mobility of the fundamental solitons is limited to the central area. Stable 1D even and odd solitons are also found in the setting with a double-well modulation function, along with a regime of Josephson oscillations.

Interaction forces among two-dimensional bright solitons and many-soliton molecules

We consider two-dimensional bright matter-wave solitons in two-dimensional Bose-Einstein condensates. From the asymptotic form of their wave function, we derive an analytic expression for the force of interaction between solitons in the large separation limit, which turns out to decay with solitons separation Δ as F(Δ)∝exp(-Δ)/√Δ. Simulating the dynamics of two solitons using the relevant Gross-Pitaevskii equation, we obtain the force of the interaction for the full range of Δ, which turns out to be of molecular type. We show that many-soliton molecules can exist as a result of such a molecular-type of interaction. These include string-shaped, ring-shaped, or regular-lattice-shaped soliton molecules. By calculating their binding energy, we investigate the stability of these structures. Contrary to one-dimensional soliton molecules, which have no binding energy, two-dimensional molecules of a lattice of solitons with alternating phases are robust and have a negative binding energy. Lattices of size larger than 2 × 2 solitons have many discrete equilibrium values of the separation between two neighboring solitons.

Phonon Instability with Respect to Soliton Formation in Two-Dimensional Dipolar Bose-Einstein Condensates

The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar Bose-Einstein condensates, which is followed by collapse in 3D geometries. We show that in 2D, the nature of the post-instability dynamics is fundamentally different, due to the stabilization of 2D solitons. As a result, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic trap, the post-instability dynamics is characterized by a transient pattern formation followed by the creation of stable 2D solitons. This dynamics should be observable in ongoing experiments, allowing for the creation of stable 2D solitons for the first time ever in quantum gases.

Two-dimensional nonlocal multisolitons

We study the bound states of two-dimensional bright solitons in nonlocal nonlinear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady bound state of coherent nonrotating and rotating solitary structures (azimuthons) can exist above some threshold power. A dipolar nonrotating multisoliton occurs to be stable within the finite range of the beam power. Azimuthons turn out to be stable if the beam power exceeds some threshold value. The bound states of three or four nonrotating solitons appear to be unstable.

Internal oscillations of solitons in two-dimensional NLS equation with nonlocal nonlinearity

We develop asymptotic theory to find small eigenfrequencies of two-dimensional bright solitons in the nonlinear Schrödinger equation with weak nonlocality.