Properties of Bose-Einstein condensates with altermagnetism

We investigate a weakly interacting two-component Bose–Einstein condensate in the miscible regime in the presence of \emph{altermagnetism}, i.e., a collinear and globally compensated magnetic order that breaks spin-rotation symmetry while maintaining zero net magnetization. Within Bogoliubov theory, we derive the quasiparticle spectrum and coherence factors and show that altermagnetic order generically induces an angular dependence of the low-energy excitations. As a result, the sound velocity, momentum-resolved magnetization in the quantum depletion, and density–spin response functions acquire anisotropic components. We show that these anisotropic contributions vanish after angular averaging, consistent with the defining feature of altermagnetism: nontrivial local spin polarization without a global magnetization. Finally, we evaluate the Lee–Huang–Yang correction to the ground-state energy in the altermagnetic phase. Our results should be testable with ultracold-atom experiments in the foreseeable future.

💡 Research Summary

In this work the authors develop a comprehensive Bogoliubov‑theory description of a weakly interacting two‑component Bose–Einstein condensate (BEC) subject to altermagnetism, a recently identified magnetic order that is globally compensated (zero net magnetization) yet breaks spin‑rotation symmetry through a momentum‑dependent dₓ²‑y²‑type spin splitting. The single‑particle Hamiltonian acquires an anisotropic term Jₖ = λ(kₓ²‑kᵧ²)/2m, where the dimensionless parameter λ (0 ≤ λ ≤ 1) controls the strength of the altermagnetic coupling. This term can be absorbed into an effective mass tensor with masses m₊ = m(1 + λ) and m₋ = m(1 ‑ λ), leading to direction‑dependent dispersions ε↑(k) and ε↓(k).

The interaction sector is treated with contact potentials g_{σσ′} that are renormalized by the usual three‑dimensional s‑wave scattering lengths a_{σσ′}. In the miscible regime the mean‑field solution assumes both spin components condense at zero momentum with densities n↑ = n↓ = n/2. The resulting chemical potentials are μ↑ = g̃↑↑ n↑ + g̃↑↓ n↓ and μ↓ = g̃↑↓ n↑ + g̃↓↓ n↓, where the tilded couplings incorporate the effective mass scale m₀ = γ₀ m (γ₀ =