Domain-area distribution anomaly in segregating multicomponent superfluids

Abstract

The domain-area distribution in the phase transition dynamics of ${\mathrm{Z}}_2$ 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 Fisher's 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.

9 pages, 5 figures

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• Coarsening and percolation in the kinetic $2d$ Ising model with spin exchange updates and the voter model
• Spin-Current Instability at a Magnetic Domain Wall in a Ferromagnetic Superfluid: a Generation Mechanism of Eccentric Fractional Skyrmions
• Thermal suppression of demixing dynamics in a binary condensate
• Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalance
• Excitations and phase ordering of the spin-stripe phase of a binary dipolar condensate
• On internal structure of smaller domains in domain coarsening dynamics of spontaneous Z_2-symmetry breaking in two dimensions
• Dynamic scaling of vorticity in phase-separating superfluid mixtures