Supplementary material for “Coherent Backscattering in Fock Space: a Signature of Quantum Many-Body Interference in Interacting Bosonic Systems”

The semiclassical propagator cannot be directly obtained in Fock state representation, since the Fock states form a discrete basis rather than a continuous one as required by the path integral formalism. To solve this problem, we first derive a semiclassical propagator in quadrature representation and then project the result on Fock states. The quadrature eigenstates |q 〉 ≡ |q1, . . . , qL 〉 and |p 〉 ≡ |p1, . . . , pL 〉 are defined as the eigenstates of linear hermitian combinations of the creation and annihilation operators associated with the single-particle orbitals χα (α = 1, . . . , L), i.e., b ( âα + â † α ) |q 〉 = qα |q 〉 (1) −ib ( âα − â†α ) |p 〉 = pα |p 〉, (2) with an arbitrary but fixed scale b. These quadrature eigenstates obey the resolutions of unity