Complementarity via error-free measurement in a two-path interferometer

Abstract

We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information I path are derived: their complementary relation V + I path ≤ 1 are found, and the condition for the equality is also presented.

Wave-particle duality in asymmetric beam interference

“…We define the distinguishability of two paths, D Q , as the maximum probability with which the two paths can be unambiguously distinguished. To get distinguishability, we first use (7) to rewrite (11) as |ψ(t) c 1 |ψ 1 (t) |d 1 + c 2 |ψ 2 (t) |d 2 c 1 α|ψ 1 (t) |q 1 + c 2 γ|ψ 2 (t) |q 2 +(c 1 β|ψ 1 (t) + c 2 δ|ψ 2 (t) )|q 3 (16) where |ψ 1 (t) , |ψ 2 (t) represent the wave-packets appearing in (11). From (16) one can see that the unambiguous path discrimination fails when one gets the state |q 3 while measuring the operator A.…”

“…We define the distinguishability of two paths, D Q , as the maximum probability with which the two paths can be unambiguously distinguished. To get distinguishability, we first use (7) to rewrite (11) as…”

“…where |ψ 1 (t) , |ψ 2 (t) represent the wave-packets appearing in (11). From ( 16) one can see that the unambiguous path discrimination fails when one gets the state |q 3 while measuring the operator A.…”

“…This asymmetric case has not been probed in as much detail as the symmetic case [5]. There have been other studies on asymmetric two-path interference [10,11], but none provides a tight duality relation for this case. The aim of this paper is obtain a general duality relation which also holds for asymmetric two-slit interference experiments.…”

Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter

“…The complementary relationship between the fringe visibility and the distinguishability has been obtained in the standard MZI [5]. Later, the complementary relationship in a general MZI with an asymmetric beam splitter (BS) has also attracted great attention [24][25][26]. The asymmetry of the BS1 is equivalent to changing the initial state of the input particles.…”