Lower bound for the population of hyperfine component $μ=0$ particles in the ground state of spin-1 condensates

An analytical expression for the lower bound of the average number of hyperfine component $μ=0$ particles in the ground state of spin-1 condensates (denoted as $\overset{\_\_}{ρ_{0}}$) under a magnetic field has been derived. In the derivation the total magnetization $M$ is kept rigorously conserved. Numerical examples are given to show the applicability of the analytical expression. It was found that, in a broad domain of parameters specified in the paper, the lower bound is very close to the actual $\overset{\_\_}{ρ_{0}}$. Thereby, in this domain, $\overset{\_\_}{% ρ_{0}}$ can be directly evaluated simply by using the analytical expression.

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