  Let X be a smooth projective curve over an algebraically closed field of
characteristic >2. Let Bun_{Mp_2} be the stack of metaplectic bundles on X of
rank 2. In this paper we study the derived category of genuine l-adic sheaves
on Bun_{Mp_2} in the framework of the quantum geometric Langlands. We describe
the corresponding Whittaker category, develop the theory of geometric
Eisenstein series and calculate the most non-degenerate Fourier coefficients of
these Eisenstein series. The existing constructions of automorphic sheaves for
GL_n are based on using Whittaker sheaves. Our calculations lead to a
conjectural characterization of the Whittaker sheaf for Mp_2, though its
existence is not clear. We also formulate a conjectural relation between the
quantum Langlands functors and the theta-lifting functors for the dual pair
(Mp_2, PGL_2).
