  The Jaynes-Cummings Model (JCM) is a fundamental model and building block for
light-matter interactions, quantum information and quantum computation. We
analytically analyze the topological feature manifested by the JCM in the
presence of non-Hermiticity which may be effectively induced by dissipation and
decay rates. Indeed, the eigenstates of the JCM are topologically characterized
by spin windings in two-dimensional plane. The non-Hermiticity tilts the spin
winding plane and induces out-of-plane component, while the topological feature
is maintained. In particular, besides the invariant spin texture nodes, we find
a non-Hermiticity-induced reversal transition of the tilting angle and spin
winding direction with a fractional phase gain at gap closing, a partially
level-independent reversal transition without gap closing, and a completely
level-independent super invariant point with untilted angle and also without
gap closing. Our result demonstrates that the topological feature is robust
against non-Hermiticity, which would be favorable in practical applications. On
the other hand, one may conversely make use of the disadvantageous dissipation
and decay rates to reverse the spin winding direction, which might add a
control way for topological manipulation of quantum systems in light-matter
interactions.
