  We show theoretically that it is possible to create and manipulate a pair of
bound states in continuum in ultracold atoms by two lasers in the presence of a
magnetically tunable Feshbach resonance. These bound states are formed due to
coherent superposition of two electronically excited molecular bound states and
a quasi-bound state in ground-state potential. These superposition states are
decoupled from the continuum of two-atom collisional states. Hence, in the
absence of other damping processes they are non-decaying. We analyze in detail
the physical conditions that can lead to the formation of such states in cold
collisions between atoms, and discuss the possible experimental signatures of
such states. An extremely narrow and asymmetric shape with a distinct minimum
of photoassociative absorption spectrum or scattering cross section as a
function of collision energy will indicate the occurrence of a bound state in
continuum (BIC). We prove that the minimum will occur at an energy at which the
BIC is formed. We discuss how a BIC will be useful for efficient creation of
Feshbach molecules and manipulation of cold collisions. Experimental
realizations of BIC will pave the way for a new kind of bound-bound
spectroscopy in ultracold atoms.
