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Register a new userIs a doubly quantized vortex dynamically unstable in uniform superfluids?
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We revisit the fundamental problem of the splitting instability of a doubly quantized vortex in uniform single-component superfluids at zero temperature. We analyze the system-size dependence of the excitation frequency of a doubly quantized vortex through large-scale simulations of the Bogoliubov--de Gennes equation, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.
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The splitting instability of a doubly-quantized vortex in the BEC-BCS crossover of a superfluid Fermi gas is investigated by means of a low-energy effective field theory. Our linear stability analysis and non-equilibrium numerical simulations reveal that the character of the instability drastically changes across the crossover. In the BEC-limit, the splitting of the vortex into two singly-quantized vortices occurs through the emission of phonons, while such an emission is completely absent in the BCS-limit. In the crossover-regime, the instability and phonon emission are enhanced, and the lifetime of a doubly-quantized vortex becomes minimal. The emitted phonon is amplified due to the rotational superradiance and can be observed as a spiraling pattern in the superfluid. We also investigate the influence of temperature, population imbalance, and three-dimensional effects.
We study the dynamics of a doubly quantized vortex (DQV), created by releasing a ring-shaped Bose-Einstein condensate with quantized circulation into harmonic potential traps. It is shown that a DQV can be generated and exists stably in the middle of the ring-shaped condensate with the initial circulation $s = 2$ after released into the rotationally symmetric trap potential. For an asymmetric trap with a small degree of anisotropy the DQV initially splits into two singly quantized vortices and revives again but eventually evolves into two unit vortices due to the dynamic instability. For the degree of anisotropy above a critical value, the DQV is extremely unstably and decays rapidly into two singlet vortices. The geometry-dependent lifetime of the DQV and vortex-induced excitations are also discussed intensively.
We propose to induce topological defects in particle-hole symmetric superfluids, with the prime example of the BCS state of ultracold atoms and detect their time evolution and decay. We demonstrate that the time evolution is qualitatively distinct for particle-hole symmetric superfluids, and point out that the dynamics of topological defects is strongly modified in particle-hole symmetric fluids. We obtain results for different charges and compare them with the standard Gross-Pitaevskii prediction for Bose-Einstein condensates. We highlight the observable signatures of the particle-hole symmetry in the dynamics of decaying solitons and subsequent vortices.
Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one dimensional spuerfluids, such as Bose-Einstein condensates, involves the dynamics of dark solitons and, therefore, the description of a statistical ensemble of dark-solitons, i.e. soliton gases, is necessary. In this work, we propose a phase-space (kinetic) description of dark-soliton gases, introducing a kinetic equation that is formally similar to the Vlasov equation in plasma physics. We show that the proposed kinetic theory can capture the dynamical features of soliton gases and show that it sustains an acoustic mode, a fact that we corroborate with the help of direct numerical simulations. Our findings motivate the investigation of the microscopic structure of out-of-equilibrium and turbulent regimes in low-dimensional superfluids.
The domain-area distribution in the phase transition dynamics of ${rm Z}_2$ symmetry breaking is studied theoretically and numerically for segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Due to the dynamic scaling law of the phase ordering kinetics, the domain-area distribution is described by a universal function of the domain area, rescaled by the mean distance between domain walls. The scaling theory for general coarsening dynamics in two dimensions hypothesizes that the distribution during the coarsening dynamics has a hierarchy with the two scaling regimes, the microscopic and macroscopic regimes with distinct power-law exponents. The power law in the macroscopic regime, where the domain size is larger than the mean distance, is universally represented with the Fishers exponent of the percolation theory in two dimensions. On the other hand, the power-law exponent in the microscopic regime is sensitive to the microscopic dynamics of the system. This conjecture is confirmed by large-scale numerical simulations of the coupled Gross--Pitaevskii equation for binary condensates. In the numerical experiments of the superfluid system, the exponent in the microscopic regime anomalously reaches to its theoretical upper limit of the general scaling theory. The anomaly comes from the quantum-fluid effect in the presence of circular vortex sheets, described by the hydrodynamic approximation neglecting the fluid compressibility. It is also found that the distribution of superfluid circulation along vortex sheets obeys a dynamic scaling law with different power-law exponents in the two regimes. An analogy to quantum turbulence on the hierarchy of vorticity distribution and the applicability to chiral superfluid $^3$He in a slab are also discussed.
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