  The oscillation of Majorana modes with near zero energy plays a very
important role for ascertaining Majorana fermions. The edge states, which also
have almost-zero-energy in one-dimensional Su-Schrieffer-Heeger chain (SSHc),
have been extensively studied for their topologically protected properties when
the on-sites have dissipations induced by independent environments. We here
show that common environments shared by each pair of the nearest neighbour
sites in the SSHc can result in dissipative couplings between sites, and thus
change topologically trivial phase to nontrivial one. The Majorana-like
oscillation for the finite-size hybridizations of two non-Hermitian edge states
with complex localization lengths can be induced by the dissipative coupling.
The controllable topology parameter of the SSHc plays the role of the magnetic
field in the nanowire for controlling Majorana oscillation. The measurement for
the oscillation is proposed. Our study provides a new way to manipulate edge
states and is experimentally feasible within current technology of
superconducting quantum circuits.
