New Journal of Physics Complementarity in variable strength quantum non-demolition measurements

doi:10.1088/1367-2630/11/9/093012 Abstract. Using a linear optic quantum gate we perform a variable strength quantum non-demolition measurement, to elucidate the role of which-path knowledge in a complementarity experiment. Specifically, we demonstrate that the entanglement created by the measurement interaction prevents an exhaustive description in terms of complementary wave-like and particle-like behaviour of a single photon in an interferometer. Complementarity is one of the most distinct features of quantum mechanical systems [1]. A quantum object is unable to exhibit both perfect particle-like and wave-like behaviour in the same experiment. Put differently, any knowledge about the localization of the object prevents us from observing perfect quantum interference: this has been extensively tested in a variety of physical systems, including photons [2]–[4], atoms [5]–[7], molecules [8, 9] and electrons [10, 11]. A clear example is provided by the Mach–Zender interferometer. Here, light is split by a partially reflective mirror into two arms, then recombined on a second half-relfective mirror. The transmittivity of the first beam splitter gives us a priori knowledge about the likely path taken by the photon; this information prevents perfect interference between the two paths, except when the beam splitter is symmetric. In the general case, the which-path 4 Author to whom any correspondence should be addressed