Interference fringes controlled by noninterfering photons

Abstract

We observe spatial fringes in the interference of two beams, which are controlled by a third beam through the phenomenon of induced coherence without induced emission. We show that the interference pattern depends on the alignment of this beam in an analogous way as fringes created in a traditional division-of-amplitude interferometer depend on the relative alignment of the two interfering beams. We demonstrate that the pattern is characterized by an equivalent wavelength, which corresponds to a combination of the wavelengths of the involved physical light beams.The relationship between path-information and interference is fundamental to quantum physics [1] and has been studied in various contexts [2][3][4]. A particularly remarkable manifestation of this relationship is the phenomenon of induced coherence without induced emission [5,6]. This phenomenon was used for fundamental tests of complementarity [7-9] and led to applications in imaging [10,11], metrology [12], spectrum shaping [13], and spectroscopy [14,15]. If two spatially separated nonlinear crystals produce photon pairs (signal and idler) by spontaneous parametric down-conversion (SPDC) [16,17], the emitted signal beams in general do not interfere, even if the two pump beams are mutually coherent. This is due to the fact that the idler beams carry information which source a down-converted pair originated from. By aligning the idler beams emitted by the two crystals, this information can be suppressed. If the path lengths are chosen accordingly, then lowest-order interference is observed between the two signal beams. It has been shown that path distinguishability can be introduced through a time delay between the two idler beams [18] or by attenuating the idler beam from one source using a partially transmissive filter. In the latter case, the resulting visibility was quantitatively connected to the transmission coefficient [5,6].Here, we analyze a situation, in which distinguishability is introduced in a different way. This is done by marginally misaligning the idler beams, either by tilting or by defocusing one with respect to the other. One could conjecture that this has the analogous effect of merely a reduced visibility. However, our experiment shows that because the misalignment can be described by a transverse phase gradient, it results in the observation of spatial interference fringes. This interference pattern leads to a reduction of visibility when intensities are obtained by integrating over a transverse section of the beam.We demonstrate analogies and differences between these fringes created by induced coherence and those cre- * Electronic address: armin.hochrainer@univie.ac.at † Electronic address: anton.zeilinger@univie.ac.at ated in traditional interferometry by division of amplitude, i.e. by interfering two beams, which are derived from a single beam by splitting it on a semi-reflecting surface. In a standard division-of-amplitude interferometer (e.g. a Michelson interferometer), a fringe pattern is observed, when one of the two interf...

Perspectives for Applications of Quantum Imaging

“…It is depicted in Figure . Additional lenses implement the imaging system, where the plane of the first nonlinear crystal (NL1) is imaged onto the plane of the second nonlinear crystal (NL2) with the object in the Fourier plane . The object plane itself is imaged onto the electron multiplying charge‐coupled device (EMCCD) camera.…”

“…EMCCDs are commonly used in quantum imaging experiments, too. Examples are subshot‐noise correlation measurements and imaging, entanglement detection by Einstein–Podolsky–Rosen experiments, and quantum imaging with undetected photons …”

Entanglement, coherence, and redistribution of quantum resources in double spontaneous down-conversion processes

“…II C, namely eliminating one, and respectively two, modes from the three-mode matrix (26). Finally, notice that all reduced single-mode states are thermal.…”

“…In this case, we see that the symplectic eigenvalues ν ± and ν coincide to very good approximation and we ignore contributions of the order O(δ / ). We can therefore obtain the elements of the covariance matrix σ of the final state (26) which, to lowest order, reduce to α = ν cosh(2 r ab ),…”

“…The field is developing fast, with several experimental platforms being used recently to generate tripartite states with high efficiency: cascaded parametric down-conversion setups employing two [17,18] or three separate crystals [19], nonlinear waveguides [20], quantum dots [21], and hybrid systems comprising a Rb-85 hot atom cell and a nonlinear waveguide [22]. The applications include, for example, quantum imaging [23], interferometry [24][25][26], and quantum computing using networks and cluster states [27][28][29][30][31]. The results presented here are device-independent; therefore, they can be tested on any of these experimental platforms.…”