Thermally induced instability of a doubly quantized vortex in a Bose–Einstein condensate

Abstract

We study the instability of a doubly quantized vortex topologically imprinted on 23 Na condensate, as reported in recent experiment [Phys. Rev. Lett. 93, 160406 (2004)]. We have performed numerical simulations using three-dimensional Gross-Pitaevskii equation with classical thermal noise. Splitting of a doubly quantized vortex turns out to be a process that is very sensitive to the presence of thermal atoms. We observe that even very small thermal fluctuations, corresponding to 10 to 15% of thermal atoms, cause the decay of doubly quantized vortex into two singly quantized vortices in tens of milliseconds. As in the experiment, the lifetime of doubly quantized vortex is a monotonic function of the interaction strength. [4]. The quantization of the circulation is a manifestation of the existence of a macroscopic wave function. Direct 2π-change of the phase of the condensate wave function when going around the vortex core was experimentally demonstrated by using the interferometric technique [5]. The quantized vortex can not just disappear, it can leave the condensate or annihilate with a vortex having the opposite circulation. There exists another route for vortices that have multiple topological charge, they can also split into several vortices having smaller charges decreasing in such a way the energy of the system.In recent experiments [6,7] doubly quantized vortices have been imprinted in Bose-Einstein condensate of 23 Na atoms. A novel approach allowing to create vortices with multiple topological charge was implemented [8]. In this new method, as opposed to dynamical phaseimprinting techniques like rotating the atomic cloud in an anisotropic trap or stirring the condensate with the help of a laser beam, vortices are generated by adiabatically reversing the magnetic bias field along the trap axis. This topological phase imprinting technique leads to vortices displaying winding numbers 2 or 4 depending on the hyperfine state the sodium condensate was prepared in (|1, −1 > and |2, +2 >, respectively) [6]. In Ref.[7] the authors investigate the evolution of doubly quantized vortices by using a tomographic imaging method [9]. They observe the decay of doubly quantized vortex into singly quantized vortices and suggest the possible explanation of this splitting as being a result of dynamical instability, however, not specifying the character of the perturbation seeding the instability.Existing theoretical explanation of decay of doubly quantized vortices involves the analysis of stability of the vortex at zero temperature in terms of eigenmode spectrum of the Bogoliubov equations in two-and threedimensional geometry as well as the numerical solution of the Gross-Pitaevskii equation in slightly anisotropic trap [10]. Two-dimensional Bogoliubov eigenvalue spectrum shows complex frequencies for certain values of the interaction strength [10,11]. In fact, quasiperiodic behavior is found -the stability windows are followed by the instability regions. Neither the anisotropy of the trap nor the phenomenologically introd...

Splitting Times of Doubly Quantized Vortices in Dilute Bose-Einstein Condensates

“…This effect is also visible in the recent theoretical study of Ref. [8], but it is not clearly observable in the experimental results [7]. The splitting time attains its minimum at an z 3, which is in good agreement with the Bogoliubov eigenvalue spectrum analysis accomplished in Refs.…”

“…Contrary to previous theoretical results presented in Ref. [8], we find that the gravitational and the time-dependent trapping potentials together break the rotational symmetry and initiate the splitting process strongly enough to alone yield splitting times in good agreement with experiments. Thus the effect of thermal excitations is not relevant in modeling the experiments.…”

Constructing a classical field for a Bose-Einstein condensate in an arbitrary trapping potential: Quadrupole oscillations at nonzero temperatures

“…This approach was used to investigate the thermodynamics of an interacting gas [16,17], as well as dynamical processes like the photoassociation of molecules [18], the dissipative dynamics of a vortex [19], the superfluidity in ring-shaped traps [20], and the thermalization in spinor condensates [21]. The classical field approximation was also tested at a quantitative level when, for example, the Bogoliubov-Popov quasiparticle energy spectrum in a uniform Bose gas was obtained [17] or when the process of splitting of doubly quantized vortices in dilute Bose-Einstein condensates [22] was studied.…”

Core sizes and dynamical instabilities of giant vortices in dilute Bose-Einstein condensates

“…States with a multiquantum vortex are in general dynamically unstable: the state may annihilate due to a slight perturbation even in the absence of dissipation. Dynamical stability of multiquantum vortices has been investigated theoretically [21][22][23][24][25], and splitting of multiquantum vortices into single-quantum ones has been studied both experimentally and theoretically [26][27][28][29][30][31][32]. In addition, dynamical stability of coreless vortices [33,34] and vortex clusters [35][36][37][38][39][40] has been investigated.…”