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.
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) 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 case with dissipation, shedding a new light on the understanding of quantum vortex and dynamical instabilities in multicomponent superfluids.
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
(1,1) 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
(1,0) vortex and a $(0,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)$ vortex. Second, the
(2,1) vortex exhibits a two-step decay process in which its initial splitting into a
(2,0) vortex and a
(0,1) vortex is followed by the off-axis splitting of the
(2,0) vortex into two
(1,0) 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
(1,0) 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.
We explore instabilities in binary superfluids with a nonvanishing relative superflow, particularly focusing on counterflow and coflow instabilities. We extend recent results on the thermodynamic origin of finite superflow instabilities in single-component superfluids to binary systems and derive a criterion for the onset of instability through a hydrodynamic analysis, which applies to interacting many-body systems at finite temperature. We find that the onset of these instabilities is signaled by the determinant of the Hessian of the thermal free energy diverging and changing sign. We verify this hydrodynamic prediction in a holographic binary superfluid modeled with gauge/gravity duality, which naturally incorporates strong coupling, finite temperature, and dissipation. We also compare to results obtained using the Gross-Pitaevskii equation for weakly interacting Bose-Einstein condensates and find that the same criterion continues to apply at zero temperature, where it reduces to evaluating derivatives of the supercurrents with respect to the superfluid velocities. We observe that the critical velocities of these instabilities follow a general scaling law related to the interaction strength between superfluid components. Finally, the nonlinear stages of the instabilities are studied by full time evolution using gauge/gravity duality, where vortex annihilation leads to a decrease of superfluid velocity back to a value where the binary superfluid phase is stable.
Understanding the interface dynamics in nonequilibrium quantum systems remains a challenge. We study the interface dynamics of strongly coupled immiscible binary superfluids by using holographic duality. The full nonlinear evolution of the binary superfluids with a relative velocity shows rich nonlinear patterns toward quantum turbulence, which is reminiscent of the quantum Kelvin-Helmholtz instability. The wave number of the fastest growing modes
k0 extracted from the interface pattern yields a nonmonotonic dependence of the relative velocity, independent of the temperature and interaction. The value of
k0 first increases with the velocity difference and then decreases, which stands in sharp contrast to the results of mean-field theory described by the Gross-Pitaevskii equation and is confirmed by using the linear analyses on top of the stationary configuration. We uncover that the critical velocity associated with the maximum corresponds to the case when the mean separation of vortices generated by interface instabilities becomes comparable to the vortex size, which could be a universal physical mechanism at strongly interacting superfluids and is directly testable in laboratory experiments.
Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
Abstract Utilizing the dissipative Gross–Pitaevskii equation, we investigated the splitting dynamics of triply quantized vortices at finite temperature. Through linear perturbation analysis, we determined the excitation modes of these vortices across various dissipation parameters. We identified three unstable modes with p = 2-, 3- and 4-fold rotational symmetries, revealing a significant dynamic transition of the most unstable mode. That is, as the dissipation parameter increases the most unstable mode transitions from the p = 2 mode to the p = 3 mode. Throughout the entire range of dissipation parameters, the p = 4 unstable mode is never the dominant mode. Subsequently, we performed nonlinear numerical simulations of the vortex splitting process. Under random perturbations we confirmed the dynamical transition, and under specific perturbations we confirmed the instability of the p = 4 mode. Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.