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arXiv:2401.09189 · Physical review. D/Physical review. D.

Interface dynamics of strongly interacting binary superfluids

Yu-Ping An, Li Li, Chuan-Yin Xia, Hua-Bi Zeng

Published May 29, 2024• 10 citations
arXivHTMLPDF

Abstract

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 ${k}_{0}$ extracted from the interface pattern yields a nonmonotonic dependence of the relative velocity, independent of the temperature and interaction. The value of ${k}_{0}$ 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.

DOI
10.1103/physrevd.109.106022

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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{k}_{0}k0​ extracted from the interface pattern yields a nonmonotonic dependence of the relative velocity, independent of the temperature and interaction. The value of k0{k}_{0}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 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.
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.
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 theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number WeWeWe, clarifying the microscopic aspects unique to the quantum fluid system. For We≲1We \lesssim 1We≲1, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to WeWeWe. When We≳1We \gtrsim 1We≳1 in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.
We investigate the Kelvin-Helmholtz instability of counter-rotating annular Fermi superfluids using time-dependent superfluid density functional theory. When the two initially separated superflows merge, a necklace of quantized vortices forms at their interface and subsequently becomes unstable. We extract mode-resolved instability growth rates and study their dependence on relative flow velocity, interaction strength, and temperature across the strongly interacting unitary regime and the weakly attractive BCS regime. In the unitary gas and moderate BCS regimes, the growth rates remain qualitatively consistent with the point-vortex model, though systematically at or above its predictions, with no significant dependence on interaction strength or temperature up to approximately 0.3Tc0.3 T_c0.3Tc​. Deeper in the BCS regime, the dynamics change qualitatively: boundary-generated antivortices proliferate faster than the Kelvin-Helmholtz instability itself, destroying the initial vortex necklace before the instability can fully develop. These results provide a microscopic benchmark for Kelvin-Helmholtz dynamics in fermionic superfluids and help constrain possible explanations of the existing experiment-theory discrepancy.
The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.