  We theoretically analyze the observations reported in a four-path quantum
interference experiment via multiple beam Ramsey interference [Phys. Rev. Lett.
86, 559 (2001)]. In this experiment, a selective scattering of photons from
just one interfering path causes decoherence. However, contrary to
expectations, there is an increase in the contrast of the interference pattern,
demonstrating that path selective decoherence can not only lead to a decrease,
but under certain conditions, to an increase of the fringe contrast. Here we
explain this seemingly counter-intuitive effect based on a model for a
multi-path interference, with four to six slits, in the presence of
decoherence. The effect of the environment is modeled via a coupling to a bath
of harmonic oscillators. When decoherence is introduced in one of the multiple
paths, an enhancement in fringe contrast is seen under certain conditions. A
similar effect is shown to appear if instead of path-selective decoherence, a
selective path detector is introduced. Our analysis points to the fact that
while traditional fringe visibility captures the wave nature in the two-path
case, it can fail in multi-path situations. We explain the enhancement of
fringe visibility and also show that quantum coherence based on the l1 norm of
coherence, in contrast to traditional visibility, remains a good quantifier of
wave nature, even in such situations. The enhancement of fringe contrast in the
presence of environmental decoherence underscores the limitations of
traditional visibility as a good measure for wave nature in quantifying
complementarity and also makes it an unlikely candidate for quantifying
decoherence. Our analysis could lead to better insight in ways to quantify
decoherence in multi-path interference, and in studies that seek to exploit
quantum superpositions and quantum coherence for quantum information
applications.
