Splitting of doubly quantized vortices in dilute Bose-Einstein condensates

Abstract

We investigate the dynamics of doubly charged vortices generated in dilute Bose-Einstein condensates by using the topological phase imprinting technique. We find splitting times of such vortices and show that thermal atoms are responsible for their decay.In their recent Letter [1], Huhtamäki et al. theoretically investigated the splitting of a topologically imprinted doubly charged vortex into two singly charged vortices as occurring in a dilute atomic Bose-Einstein condensate. They compare the results of simulation with recent experiment [2] and show that the combination of gravitational sag and the time dependence of the trapping potential alone are enough to explain the observed splitting times. Based on such an outcome the authors of Ref. [1] claim that, contrary to previous theoretical results [3], the thermal excitations are not relevant in modeling the experiment of Ref. [2]. We are going to show in this Brief Report that, indeed, the opposite is true. In fact, a number of thermal (uncondensed) atoms appears in the system while disturbing the gas. They continue to appear after the perturbation is over and until the doubly quantized vortex breaks into two singly quantized vortices. The overall number of uncondensed atoms remains approximately on the level of 20%, which is already at the edge of experimental detection capabilities. However, the uncondensed atoms do not form the broad cloud allowing the identification by fitting to a bimodal distribution -they are rather located in the core of the vortex and therefore are harder to detect. Perhaps, the signatures of the presence of thermal atoms in vortices cores are already visible in experiment in a way that after splitting the cores of two singly charged vortices get darker in comparison with the core of initially imprinted doubly quantized vortex (see Fig. 2 in Ref. [2]).To investigate the thermal excitations in a Bose gas we use the classical fields approximation [4] -an approach that treats both condensed and thermal atoms at the same footing until the detection time when the splitting into the condensate and the thermal cloud occurs. Technically, such a decomposition requires calculation of time and space average of a one-particle density matrix built of the classical field evolving according to the GrossPitaevskii equation [4].Therefore, we have repeated the calculations of Ref. Fig. 1 clearly shows that the uncondensed atoms appear in the system during the evolution. Although initially all atoms are in the condensate (i.e., the condensate fraction equals 1 as in Fig. 1(e)), already after 6 ms distinguishable fraction of uncondensed atoms is produced. This is not surprising since the process of imprinting the vortex is accompanied by a sudden squeeze of the condensate in the radial direction and a kick of it in the vertical direction [2]. The thermal atoms continue to appear after the imprinting is over and until the doubly quantized vortex splits into two singly charged vortices (production of thermal atoms while the system was initially at zero ...

Free expansion of a Bose–Einstein condensate in the presence of a thermal cloud

“…The physically important (averaged along y direction) one-particle density matrix is given bȳ ρ(x, z, x , z ; t) = dy Ψ(x, y, z, t) Ψ * (x , y, z , t) (3) and the splitting procedure requires the diagonalization of (3). This kind of averaging was already used to investigate a decay of multiply charged vortices [6]. The splitting procedure is then summarized as:…”

Singular and regular vortices on top of a background pulled to the center

“…The latter condition excludes m = 1, hence the above-mentioned drift instability in ruled out. Further, usual dark vortices with l ≥ 2 tend to be unstable against spontaneous splitting into a set of l unitary eddies, as demonstrated in detail in various settings [46,[50][51][52][53][54] (see also Fig. 12 below).…”

“…Detailed analysis of this conjecture should be a subject of a separate work. Another essential point of the analysis is instability of double dark vortices, with l = 2, against splitting into unitary ones, which occurs in many models supporting dark vortex modes [46,[50][51][52][53][54]. In this case too, the HO trapping potential should be kept in Eq.…”

Spin distillation cooling of ultracold Bose gases

“…Then a new cycle is begun starting with the remaining atoms in . Condensate fractions of the clouds are estimated by the spatial averaging technique 34 , 60 . In this case, the cloud is averaged over the z coordinate to construct an approximate one-body density matrix .…”