Decoherence and visibility enhancement in multipath interference

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, lead to an increase of the fringe contrast. Here we explain this seemingly counterintuitive effect based on a model for a multipath 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 multipath situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the $l_1$ 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 multipath interference and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.

Figure 1

Schematic diagram of an $n$-slit interference experiment, with a quantum path detector. The interfering quanton is affected by interaction with an environment only in one path which has an additional phase of $\pi$.

Figure 2

Variation in visibility with respect to one-path knowledge ($1-\beta$) for (a) three-path, (b) four-path, (c) five-path, and (d) six-path interference.

Figure 3

Variation in coherence with respect to one-path knowledge ($1-\beta$) for (a) three-path, (b) four-path, (c) five-path, and (d) six-path interference.

Figure 4

Plots of $\rho (x,x,t)/\rho (0,0,0)$ at the screen, for four-path interference, showing how decoherence progressively affects interference. The following parameters used are adapted from the interference experiment on ultracold neon atoms [2]: $m=3.349\times {10}^{-26}\text{Kg},T=2.5\text{mK},\lambda =0.018\mu \text{m},\ell =6\mu \text{m},L=37\text{mm}$. The dashed blue plots are $t/{\tau }_d=0$ while the red plots are for (a) $t/{\tau }_d=1/12$, (b) $t/{\tau }_d=1/4$, (c) $t/{\tau }_d=1/2,$ and (d) $t/{\tau }_d=2$ where ${\tau }_d=12{\hslash }^2/D{\ell }^2$. We can observe that with increase in time the there is an enhancement of the visibility.

Figure 5

Variation of visibility (in red filled circles) and coherence (in blue empty circles) with respect to scaled time $t/{\tau }_d$ for (a) three-path, (b) four-path, (c) five-path, and (d) six-path interference.