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We study the entanglement in various fully-gapped complex paired states offermions in two dimensions, focusing on the entanglement spectrum (ES), andusing the BCS form of the ground state wavefunction on a cylinder. Certainforms of the pairing functions allow a simple and explicit exact solution forthe ES. In the weak-pairing phase of l-wave paired spinless fermions (l odd),the universal low-lying part of the ES consists of |l| chiral Majorana fermionmodes [or 2|l| (l even) for spin-singlet states]. For |l|>1, thepseudo-energies of the modes are split in general, but for all l there is azero--pseudo-energy mode at zero wavevector if the number of modes is odd. ThisES agrees with the perturbed conformal field theory of the edge excitations.For more general BCS states, we show how the entanglement gap diverges as amodel pairing function is approached.

Entanglement spectra of complex paired superfluids