Radially symmetric nonlinear states of harmonically trapped Bose-Einstein condensates

Abstract

Dated: To appear in Phys. Rev. A)Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with nr = 0, 1 and 2 radial nodes respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge m, i.e., vorticity. It is found that for repulsive interatomic interactions only the ground state is linearly stable throughout the parameter range examined. Furthermore, this is true for topological charges m = 0 or m = 1; solutions with higher topological charge can be unstable even in that case. All higher excited states are found to be unstable in a wide parametric regime. However, for the focusing/attractive case the ground state with nr = 0 and m = 0 can only be stable for a sufficiently low number of atoms. Once again, excited states are found to be generically unstable. For unstable profiles, the dynamical evolution of the corresponding branches is also followed to monitor the temporal development of the instability.

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity

“…In the absence of external potential, the Townes profile [52,53] marks the limit between directly collapsing waves and those dispersing to infinity. The harmonic potential changes the picture, permitting stable stationary solutions [54]. We have not found any set of initial conditions yielding the sought structure of delayed collapses and below threshold solutions remain regular for all times.…”

Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates

“…Subsequent detailed studies of their stability [41,42] illustrated that they are unstable for all values of the chemical potential from the linear limit onwards, progressively becoming more unstable as µ is increased. The initial instability is towards a quadrupolar mode leading to 4 vortices, while subsequently hexapolar (leading to 6 vortices), octapolar (leading to 8 vortices) etc.…”

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates

“…4 symmetry-breaking bifurcations giving rise to a new triangular form of solutions (denoted as TS). An additional remarkable feature is that while such ring dark solitons were proposed in both atomic condensates [29][30][31] and in cGL gain/loss systems (as radial Nozaki-Bekki holes) in both contexts they were found to be unstable and thus break up into more prototypical coherent structures, including vortices and spiral waves, respectively. We now turn to a more detailed examination of their properties including the existence and stability domains, also highlighting similarities and importantly differences from the above atomic case, including the generically gray nature of such excitations in our polariton setting.…”

“…In addition to these more standard states, we will also consider states that, to the best of our knowledge, have not been previously presented in the context of polariton condensates, although they have been discussed for atomic condensates 28 . A principal example of this form is the so-called ring dark soliton (RDS) which, remarkably, although never stable in the context of atomic BECs [29][30][31] , can in fact be shown to be stable in suitable (gain) parametric regimes here. This is, effectively, a potentially stable radial form of a Nozaki-Bekki hole 32 that was previously explored in cGL contexts 33 , yet was not found to be stable in these settings; instead, it was found there to potentially initiate a form of spiral wave turbulence.…”