Elementary Excitations of Bose-Condensed, Spin-Aligned Atomic Hydrogen

Ground-state properties and elementary excitations of superfluid spin-aligned atomic H are studied using methods adapted from the theory of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The ground state is a $k=0\mathrm{}$ condensate of the $\left|\downarrow \right(\mathrm{electron}), \uparrow (\mathrm{proton})〉$ hyperfine state with a small admixture of $|\uparrow \downarrow 〉$ due to the hyperfine interaction. Excitations can also be labeled approximately by their hyperfine states. ${\varphi }_{\downarrow \uparrow }\mathrm{}\left(k\right)\mathrm{}$ excitations are phononlike. ${\varphi }_{\downarrow \uparrow }\mathrm{}\left(k\right)\mathrm{}$ and ${\varphi }_{\uparrow \downarrow }\mathrm{}\left(k\right)\mathrm{}$ are free-particle-like with energy gaps, and ${\varphi }_{\uparrow \downarrow }\mathrm{}\left(k\right)\mathrm{}$ excitations resemble spin waves.