  Bilayer quantum Hall states have been shown to be described by a BCS-paired
state of composite fermions. However, finding a qualitatively accurate model
state valid across all values of the bilayer separation is challenging. Here,
we introduce two variational wavefunctions, each with a single variational
parameter, which can be thought of as a proxy for the BCS order parameter.
Studying systems of up to 9+9 electrons in a spherical geometry using Monte
Carlo methods, we show that the ground state can be accurately described by
these single-parameter variational states. In addition, for the first time we
provide a numerically exact wavefunction for the Halperin-111 state in terms of
composite fermions.
