  The remarkable properties and potential applications of Majorana fermions
have led to considerable efforts in recent years to realize topological matters
that host these excitations. For a number-conserving system, there have been a
few proposals, using either coupled-chain models or multi-component system with
spin-orbit coupling, to create number fluctuation of fermion pairs in achieving
Majorana fermion. In this work, we show that Majorana edge states can occur in
a spinless Fermi gas in 1D lattices with tunable $p$-wave interaction. This is
facilitated by the conversion between a pair of (open-channel) fermions and a
(close-channel) boson, thereby allowing the number fluctuation of fermion pairs
in a single chain. This scheme requires neither spin-orbit coupling nor
multi-chain setup and can be implemented easily. Using the
density-matrix-renormalization-group method, we have identified the Majorana
phase in a wide range of parameter regime as well as its associated phase
transitions. The topological nature of the Majorana phase manifests itself in a
strong edge-edge correlation in an open chain that is robust against disorder,
as well as in a non-trivial winding number in the bulk generated by using
twisted boundary condition. It is also shown that the Majorana phase in this
system can be stable against atom losses due to few-body collisions on the same
site, and can be easily identified from the fermion momentum distribution.
These results pave the way for probing the intriguing Majorana physics in a
simple and stable cold atoms system.
