2025/03/05 by Petrovich, Federico, Rossignoli, R.
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2503.03887
We determine the necessary and sufficient conditions which ensure that an N=2m-particle fermionic or bosonic state has the form |Ψ⟩∝(A†)m|0⟩, where A†=\tfrac12∑i,jAijci†cj† is a general pair creation operator. These conditions can be cast as an eigenvalue equation for a modified two-body density matrix, and enable an exact reconstruction of the operator A^†, providing as well a measure of the proximity of a given state to an exact pair condensate. Through a covariance-based formalism, it is also shown that such states are fully characterized by a set of L "conserved" one-body operators which have |Ψ⟩ as exact eigenstate, with L determined just by the single particle space dimension involved. The whole set of two-body Hamiltonians having |Ψ⟩ as exact eigenstate is in this way determined, while a general subset having |Ψ⟩ as nondegenerate ground state is also identified. Extension to states ∝ f(A^†)|0⟩ with f an arbitrary function is also discussed.