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We introduce a new variational wavefunction for a quantum Hall bilayer attotal filling $\nu = 1$, which is based on $s$-wave BCS pairing betweencomposite-fermion electrons in one layer and composite-fermion holes in theother. We compute the overlap of the optimized trial function with the groundstate from exact diagonalization calculations of up to 14 electrons in aspherical geometry, and we find excellent agreement over the entire range ofvalues of the ratio between the layer separation and the magnetic length. Thetrial wavefunction naturally allows for charge imbalance between the layers andprovides important insights into how the physics at large interlayerseparations crosses over to that at small separations in a fashion analogous tothe BEC-BCS crossover.

$s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu=1$