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.
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.
In this work, we study the linear stability of superfluid phases of matter irrespective of the nature of microscopic degrees of freedom and the strength of interactions between them. Famously, assuming invariance under Galilean boosts and a phonon-roton single-particle dispersion relation, Landau predicted superfluid helium 4 would become unstable for large enough superfluid velocities. Here, we demonstrate that such instabilities generically follow from a change of sign of one of the eigenvalues of the matrix of second derivatives of the free energy. Our only assumption is the existence of static thermodynamic equilibrium, irrespective of any invariance under boosts or microscopic statistics. Turning on dissipation, we show that a linear dynamical instability also develops, leading to exponential growth in time of perturbations around equilibrium. Specializing to Galilean superfluids and assuming the existence of bosonic quasiparticles, our criterion reproduces Landau's critical velocity for Bose-Einstein condensates. Our criterion also reduces to the well-known maximal supercurrent in weakly coupled superconductors described either by Landau-Ginzburg or Bardeen-Cooper-Schrieffer theory. Further, it correctly reproduces the onset of the instability in relativistic, strongly coupled superfluids without quasiparticles at zero as well as finite temperature, which we construct using gauge/gravity duality. As a less trivial application of our criterion, we show that in dirty superfluids the instability manifests itself first in the thermal diffusion mode instead of the superfluid sound mode. Our work provides a simple, comprehensive, and unified description of the large superflow instability of superfluids and superconductors at any temperature independent of the microscopic details of the system and the strength of interactions.
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the upper half complex frequency plane, thereby signalling a dynamical instability. At the same time, however, this instability is also thermodynamic, as its onset is controlled by one of the second derivatives of the free energy changing sign. We carry out our analysis in two main setups: the "probe limit", where the fluctuations of the temperature and the normal fluid's velocity are frozen, and a complete approach, which includes them. In both cases we test our results with the help of gauge-gravity duality, finding good agreement between the hydrodynamic modes of the boundary theory and the quasinormal modes of the gravity theory. Our criterion for the onset of the instability, which is formulated in a model-independent way, applies to interacting systems irrespective of the strength of interactions, does not rely on boost invariance and does not assume any specific quantum statistics. As a final check, we also show that it yields the Landau critical velocity for Galilean superfluids with Bose-Einstein quasiparticles.
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.
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.
We study theoretically the instability of countersuperflow, i.e., two counterpropagating miscible superflows, in uniform two-component Bose-Einstein condensates. Countersuperflow instability causes mutual friction between the superfluids, causing a momentum exchange between the two condensates, when the relative velocity of the counterflow exceeds a critical value. The momentum exchange leads to nucleation of vortex rings from characteristic density patterns due to the nonlinear development of the instability. Expansion of the vortex rings drastically accelerates the momentum exchange, leading to a highly nonlinear regime caused by intervortex interaction and vortex reconnection between the rings. For a sufficiently large interaction between the two components, rapid expansion of the vortex rings causes isotropic turbulence and the global relative motion of the two condensates relaxes. The maximum vortex line density in the turbulence is proportional to the square of the relative velocity.
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.