Dissipation-induced Ring Dark Solitons And Vortex Pairs In BEC

Ring Dark Solitons is a variant of solitons,a nonlinear effect originally proposed and experimentally realized in the field of nonlinear optics and later introduced in BoseEinstein condensates(BEC).Compared with rectilinear dark solitons,ring dark solitons are more stable and have richer dynamical properties,thus attracting much attention from physicists.In quasi-two-dimensional confined BECs,the RDSs behave as a ringshaped density defect,and there are phase jumps in the ring.Unlike one-dimensional systems,in two-dimensional and above,the transverse binding frequency is weak and the transverse modes are excited,leading to the serpentine instability of the solitons.As a result,ring dark solitons tend to decay into more stable vortex or vortex ring structures.Thus,how to generate a more stable and longer-lived ring dark soliton has become a matter of great interest in this field.Experimentally,ring dark solitons are often excited in BECs by phase imprinting.Theoretically,the common idea is to form ring dark solitons by constructing clever potential wells(e.g,cylindrical unrestricted deep potential wells,resonant double potential wells,toroidal potential wells,etc.)so that the BEC interferes with itself during the diffusion.In our work,we theoretically propose a new method for inducing ring dark soliton production by introducing a local dissipative potential.The ring dark soliton production with different dissipation parameters and the ring dark soliton production after quenching are also explored.We discuss quasi-two-dimensional dissipative BEC systems imprisoned in a resonant potential well,and the mean-field theory is used to study the evolution of the system by numerically simulating the Gross-Pitaevskii equation containing the dissipative term.We note that the dissipative potential is capable of generating density defects in the system while causing phase variations.In this system,we describe the local dissipation by a toroidal Gaussian imaginary potential,which causes the formation of a ring density defect in the system,while the phase in this ring region jumps,which means that a ring dark soliton is formed in this region,i.e,we obtain a ring dark soliton generated by dissipation induction.We then investigated the effect of different values of the dissipative strength on the induced ring dark soliton production by adjusting the height of the ring Gaussian potential.We find that when the dissipation strength is very small(γ = 0.001),no ring dark solitons are excited and the system evolves very similarly to the dissipation-free system.When the dissipation is slightly stronger(γ = 0.015),the ring dark soliton formed in the system is not stable and evolves for some time with a broadening of the soliton and its splitting into two concentric ring dark solitons,which is suppressed when the dissipation is stronger.At stronger dissipation(γ = 15,γ = 1500),the ring dark solitons are very stable.In addition,the dissipation-induced ring dark soliton generation is accompanied by acoustic oscillations in the system,and the increase of the dissipation strength contributes to the excitation of oscillatory waves.Increasing the dissipation width(i.e,dissipation range)suppresses the excitation of oscillatory waves.The larger the width of dissipation,the wider the density defect.After the sudden withdrawal of dissipation(i.e,quenching),the density defect splits into a series of concentric ring dark solitons because it loses the maintenance of the dissipation potential.The larger the width of the density defect,the larger the number of ring dark solitons formed after cleavage,and interestingly,the width of the ring dark solitons formed by these different density defects are all the same.Our work provides a feasible idea for the experimental generation of ring dark solitons.The dissipative potential can be achieved by an electron beam,and the removal of atoms from the BEC by the electron beam can produce density defects,and the width of the density defects can be adjusted to give single or multiple ring dark solitons after the withdrawal of the electron beam.