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arXiv:1808.08223 · Physical Review A

Splitting of singly and doubly quantized composite vortices in two-component Bose-Einstein condensates

Pekko Kuopanportti, Soumik Bandyopadhyay, Arko Roy, D. Angom

Published Sep 20, 2019• 33 citations
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Abstract

We study numerically the dynamical instabilities and splitting of singly and doubly quantized composite vortices in two-component Bose-Einstein condensates harmonically confined to quasi two dimensions. In this system, the vortices become pointlike composite defects that can be classified in terms of an integer pair $({\ensuremath{\kappa}}_{1},\phantom{\rule{0.16em}{0ex}}{\ensuremath{\kappa}}_{2})$ of phase winding numbers. Our simulations based on zero-temperature mean-field theory reveal several vortex splitting behaviors that stem from the multicomponent nature of the system and do not have direct counterparts in single-component condensates. By calculating the Bogoliubov excitations of stationary axisymmetric composite vortices, we find nonreal excitation frequencies (i.e., dynamical instabilities) for the singly quantized $(1,\phantom{\rule{0.16em}{0ex}}1)$ and $(1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1)$ vortices and for all variants of doubly quantized vortices, which we define by the condition ${max}_{j=1,2}|{\ensuremath{\kappa}}_{j}|=2$. While the short-time predictions of the linear Bogoliubov analysis are confirmed by direct time integration of the Gross-Pitaevskii equations of motion, the time integration also reveals intricate long-time decay behavior not captured by the linearized dynamics. First, the $(1,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)$ vortex is found to be unstable against splitting into a $(1,\phantom{\rule{0.16em}{0ex}}0)$ vortex and a $(0,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)$ vortex. Second, the $(2,\phantom{\rule{0.16em}{0ex}}1)$ vortex exhibits a two-step decay process in which its initial splitting into a $(2,\phantom{\rule{0.16em}{0ex}}0)$ vortex and a $(0,\phantom{\rule{0.16em}{0ex}}1)$ vortex is followed by the off-axis splitting of the $(2,\phantom{\rule{0.16em}{0ex}}0)$ vortex into two $(1,\phantom{\rule{0.16em}{0ex}}0)$ vortices. Third, the $(2,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}2)$ vortex is observed to split into a $(\ensuremath{-}1,\phantom{\rule{0.16em}{0ex}}1)$ vortex, three $(1,\phantom{\rule{0.16em}{0ex}}0)$ vortices, and three $(0,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1)$ vortices. Each of these splitting processes is the dominant decay mechanism of the respective stationary composite vortex for a wide range of intercomponent interaction strengths and relative populations of the two condensate components and should be amenable to experimental detection. Our results contribute to a better understanding of vortex physics, hydrodynamic instabilities, and two-dimensional quantum turbulence in multicomponent superfluids.

DOI
10.1103/physreva.100.033615

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We study numerically the dynamical instabilities and splitting of singly and doubly quantized composite vortices in two-component Bose-Einstein condensates harmonically confined to quasi two dimensions. In this system, the vortices become pointlike composite defects that can be classified in terms of an integer pair (\ensuremathκ1,\ensuremathκ2)({\ensuremath{\kappa}}_{1},\phantom{\rule{0.16em}{0ex}}{\ensuremath{\kappa}}_{2})(\ensuremathκ1​,\ensuremathκ2​) of phase winding numbers. Our simulations based on zero-temperature mean-field theory reveal several vortex splitting behaviors that stem from the multicomponent nature of the system and do not have direct counterparts in single-component condensates. By calculating the Bogoliubov excitations of stationary axisymmetric composite vortices, we find nonreal excitation frequencies (i.e., dynamical instabilities) for the singly quantized (1,1)(1,\phantom{\rule{0.16em}{0ex}}1)(1,1) and (1,\ensuremath−1)(1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1)(1,\ensuremath−1) vortices and for all variants of doubly quantized vortices, which we define by the condition maxj=1,2∣\ensuremathκj∣=2{max}_{j=1,2}|{\ensuremath{\kappa}}_{j}|=2maxj=1,2​∣\ensuremathκj​∣=2. While the short-time predictions of the linear Bogoliubov analysis are confirmed by direct time integration of the Gross-Pitaevskii equations of motion, the time integration also reveals intricate long-time decay behavior not captured by the linearized dynamics. First, the (1,\ifmmode±\else\textpm\fi1)(1,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)(1,\ifmmode±\else\textpm\fi1) vortex is found to be unstable against splitting into a (1,0)(1,\phantom{\rule{0.16em}{0ex}}0)(1,0) vortex and a (0,\ifmmode±\else\textpm\fi1)(0,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)(0,\ifmmode±\else\textpm\fi1) vortex. Second, the (2,1)(2,\phantom{\rule{0.16em}{0ex}}1)(2,1) vortex exhibits a two-step decay process in which its initial splitting into a (2,0)(2,\phantom{\rule{0.16em}{0ex}}0)(2,0) vortex and a (0,1)(0,\phantom{\rule{0.16em}{0ex}}1)(0,1) vortex is followed by the off-axis splitting of the (2,0)(2,\phantom{\rule{0.16em}{0ex}}0)(2,0) vortex into two (1,0)(1,\phantom{\rule{0.16em}{0ex}}0)(1,0) vortices. Third, the (2,\ensuremath−2)(2,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}2)(2,\ensuremath−2) vortex is observed to split into a (\ensuremath−1,1)(\ensuremath{-}1,\phantom{\rule{0.16em}{0ex}}1)(\ensuremath−1,1) vortex, three (1,0)(1,\phantom{\rule{0.16em}{0ex}}0)(1,0) vortices, and three (0,\ensuremath−1)(0,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1)(0,\ensuremath−1) vortices. Each of these splitting processes is the dominant decay mechanism of the respective stationary composite vortex for a wide range of intercomponent interaction strengths and relative populations of the two condensate components and should be amenable to experimental detection. Our results contribute to a better understanding of vortex physics, hydrodynamic instabilities, and two-dimensional quantum turbulence in multicomponent superfluids.
The stability properties and splitting dynamics of multiply quantized vortices are the subject of interest in both theoretical and experimental investigations. Going beyond the regime of validity of Gross-Pitaevskii equation (GPE), we study the composite vortices in miscible strongly interacting binary superfluids by employing a holographic model that naturally incorporate finite temperature and dissipation. The composite vortices is classified in terms of an integer pair (S1,S2)(S_1, S_2)(S1​,S2​) of phase winding numbers and can share the same vortex core, while either co-rotating or counter-rotating, leading to very diverse vortex structures. We uncover different dynamical behaviors compared to results from GPE that is valid in weak coupling limit and zero temperature. In particular, we show that the occurrence of dynamic instabilities and the instability strength are sensitive to the temperature. We identify several temperature dependent dynamical transitions in (1,1)(1,1)(1,1), (2,±1)(2,\pm 1)(2,±1) and (2,2)(2,2)(2,2) vortices. The splitting behaviors associated with different multipolarities are demonstrated by solving the full-time evolution for slightly perturbed composite vortices. We find that the final states of all composite vortices are generally singly quantized vortices, and no additional long living vortex is formed due to strong dissipation. Our results highlight the important role of temperature and the distinction between dynamics of composite vortices in weakly interacting superfluids without dissipation and strongly interacting case with dissipation, shedding a new light on the understanding of quantum vortex and dynamical instabilities in multicomponent superfluids.
The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23Na{}^{23}\mathrm{Na}23Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards division into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al., Phys. Rev. Lett. 89, 190403 (2002)].
A bstract The stability properties and splitting dynamics of multiply quantized vortices are the subject of interest in both theoretical and experimental investigations. Going beyond the regime of validity of Gross-Pitaevskii equation (GPE), we study the composite vortices in miscible strongly interacting binary superfluids by employing a holographic model that naturally incorporates finite temperature and dissipation. The composite vortices are classified in terms of an integer pair ( S 1 , S 2 ) of phase winding numbers and can share the same vortex core, while either co-rotating or counter-rotating, leading to very diverse vortex structures. We uncover different dynamical behaviors compared to results from GPE that is valid in weak coupling limit and zero temperature. In particular, we show that the occurrence of dynamic instabilities and the instability strength are sensitive to the temperature. We identify several temperature dependent dynamical transitions in (1, 1), (2 , ±1) and (2, 2) vortices. The splitting behaviors associated with different multipolarities are demonstrated by solving the full-time evolution for slightly perturbed composite vortices. We find that the final states of all composite vortices are generally singly quantized vortices, and no additional long living vortex is formed due to strong dissipation. Our results highlight the important role of temperature and the distinction between dynamics of composite vortices in weakly interacting superfluids without dissipation and strongly interacting superfluids with dissipation, shedding new light on the understanding of quantum vortex and dynamical instabilities in multicomponent superfluids.
We study the nonlinear dynamics of the splitting of a doubly quantized vortex in a trapped Bose-Einstein condensate. The dynamics is studied in detail by solving the Gross-Pitaevskii equation. The main dynamical features are explained in terms of a nonlinear three-level system, to which we find an analytical solution. This result is compared to linear Bogoliubov analysis and to the full numerical time evolution. It is concluded that the time scale for the splitting is mainly determined by the instability of the linearized system, and nonlinear effects contribute logarithmically.
The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].
Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.