Bogoliubov–de Gennes soliton dynamics in unconventional Fermi superfluids

Abstract

Exact self-consistent soliton dynamics based on the Bogoliubov-de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an S U(d)-symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the d = 2 systems, which describe the mixture of singlet s-wave and triplet p-wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, s-p mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and N-flavor generalization are discussed.

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

“…More generally, multiple twisted kinks with arbitrary phase and positions [75,76] can be further constructed systematically due to the integrable structure behind the model known as the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy for the nonlinear Schrödinger equation [77][78][79]. Recent developments include time-dependent soliton scatterings [80,81], multi-component condensates [82][83][84], a ring geometry [85], and an interval with a Casimir force [86].…”

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

“…It agrees with equation ( 9) modulo a gauge transformation. The relevant gauge transformation can be inferred from equation (30) and the periodicity conditions in n. It is easy to verify that…”

“…coupled Dirac equations. This was done in two different physics settings, first in the context of the multi-component BdG equation for exotic superconductors [30,31] and later for solving the NJL 2 model with flavor and color [32,33]. Since this requires only a mild generalization of the formalism, it may be interesting to repeat the present investigation for the multi-component case and hopefully end up with an integrable matrix generalization of affine Toda field theory.…”

Collective Modes of a Soliton Train in a Fermi Superfluid

“…Moreover, cold-atom experiments can now engineer matter-wave solitons in atomic superfluids, and directly observe their motion [13-18, 26, 27]. Understanding the behavior of these collective objects is vital to the larger problem of forming a cohesive theory of nonequilibrium dynamics [28]. In particular, the next generation of Fermi gas experiments will be creating clouds with many of these nonlinear defects [27].…”