Non-loose Legendrian spheres with trivial contact homology DGA

Loose Legendrian n-submanifolds, n>1, were introduced by Murphy and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are in fact actually Legendrian isotopic. Legendrian contact homology is a Floer theoretic invariant that associates a differential graded algebra (DGA) to a Legendrian submanifold. The DGA of a loose Legendrian submanifold is trivial. We show that the converse is not true by constructing non-loose Legendrian n-spheres in standard contact (2n+1)-space, n > 1, with trivial DGA.