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arXiv:2506.12688 · Journal of Computational Physics

Computing the Bogoliubov-de Gennes excitations of two-component Bose-Einstein condensates

Manting Xie, Yong Zhang

Published Feb 26, 2026• 0 citations
arXivHTMLPDF
DOI
10.1016/j.jcp.2026.114813

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arXiv:0810.3088•Physical Review A•Apr 15, 2009•13 citations
Abstract We report the effects of anisotropy in the confining potential on two component Bose–Einstein condensates (TBECs) through the properties of the low energy quasiparticle excitations. Starting from generalized Gross–Pitaevskii equation, we obtain the Bogoliubov–de Gennes equation for TBECs using the Hartree–Fock–Bogoliubov theory. Based on this theory, we present the influence of radial anisotropy on TBECs in the immiscible or the phase-separated domain. In particular, the TBECs of 85 Rb– 87 Rb and 133 Cs– 87 Rb TBECs are chosen as specific examples of the two possible interface geometries, shell-structured and side by side, in the immiscible domain. We also show that the dispersion relation for the TBEC shell-structured interface has two branches, and anisotropy modifies the energy scale and structure of the two branches.
We construct quantum field theory in an analog curved spacetime in Bose-Einstein condensates based on the Bogoliubov--de Gennes equations by exactly relating quantum particles in curved spacetime with Bogoliubov quasiparticle excitations in Bose-Einstein condensates. Here, we derive a simple formula relating the two, which can be used to calculate the particle creation spectrum by solving the time-dependent Bogoliubov--de Gennes equations. Using our formulation, we numerically investigate particle creation in an analog expanding universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate. We obtain its spectrum, which follows the thermal Maxwell-Boltzmann distribution, the temperature of which is experimentally attainable. Our derivation of the analogy is useful for general Bose-Einstein condensates and not limited to homogeneous ones, and our simulation is an example of particle creations by solving the Bogoliubov--de Gennes equation in an inhomogeneous condensate.