  In a magnetic field superconductors (SC) with small orbital effect exhibit
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase above the Pauli limiting
field. It is characterized by Cooper pairs with finite center of mass momentum
and is stabilized by the gain in Zeeman energy of depaired electrons in the
imbalanced Fermi gas. The ground state is a coherent superposition of paired
and depaired states. This concept, although central to the FFLO state lacks a
direct experimental confirmation. We propose that STM quasiparticle
interference (QPI) can give a direct momentum space image of the depaired
states in the FFLO wave function. For a proof of principle we investigate a 2D
single orbital tight binding model with a SC s-wave order parameter. Using the
equilibrium values of pair momentum and SC gap we calculate the spectral
function of quasiparticles and associated QPI spectrum as function of magnetic
field. We show that the characteristic depaired Fermi surface parts appear as a
fingerprint in the QPI spectrum of the FFLO phase and we demonstrate its
evolution with field strength. Its observation in STM experiments would
constitute a direct proof for FFLO ground state wave function.
