SUMMARYIndistinguishable quantum states interfere, but the mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Quantum interference imaging can outperform classical imaging or even have entirely new features.Here, we introduce and experimentally demonstrate a quantum imaging concept that relies on the indistinguishability of the possible sources of a photon that remains undetected. Our experiment uses pair creation in two separate down-conversion crystals. While the photons passing through the object are never detected, we obtain images exclusively with the sister photons that do not interact with the object. Therefore the object to be imaged can be either opaque or invisible to the detected photons. Moreover, our technique allows the probe wavelength to be chosen in a range for which suitable sources and/or detectors are unavailable. Our experiment is a prototype in quantum information where knowledge can be extracted by and about a photon that is never detected.2

A novel quantum imaging technique has recently been demonstrated in an experiment, where the photon used for illuminating an object is not detected; the image is obtained by interfering two beams, none of which ever interacts with the object. Here we present a detailed theoretical analysis of the experiment. We show that the object information is present only in the interference term and not in the individual intensities of the interfering beams. We also theoretically establish that the magnification of the imaging system depends on two wavelengths: the average wavelength of the photon that illuminates the object and the average wavelength of the photon that is detected. Our analysis affirms that the imaging process is based on the principle that quantum interference occurs when interferometric path information is unavailable.

The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude. For unaccessible long times, however, the system recovers the regime of Josephson oscillations. The understanding of many-body quantum systems from the theoretical and experimental points of view has undergone a considerable development during the past decade. Unifying concepts of several branches of physics are under development, creating an interdisciplinary scenario for the understanding of quantum mechanical paradigms. One of the simplest many-body systems to be realized experimentally and studied theoretically are ultracold bosons in a double-well potential. This system is very rich exhibiting a great variety of quantum phenomena such as interference [1], tunneling/selftrapping [2,3,4,5,6,7], entanglement of macroscopic superpositions [8]. Lately this system has been extensively studied, especially after the implementation of several experiments in the area. The usual theoretical approach to weakly interacting Bose-Einstein condensates (BECs) is the mean-field approximation, a nonlinear Gross-Pitaevski equation [3,9,10,11,12,13,14,15,16], which has proven very adequate in explaining a wide variety of experiments.More recently, the dynamics of population distribution between two or more wells of an optical lattice have been experimentally investigated. In particular, Josephson oscillations have been observed in a 1D optical lattice [17,18] and recently the density distribution of tunneling 87 Rb particles is directly observed [2]. In this experiment, initial population differences between the left and right well components are controlled by loading the BEC into an asymmetric double-well potential. The Josephson dynamics is initiated at t = 0 by non-adiabatically changing the potential to a symmetric double-well. When the initial population imbalance is below a critical value, the system presents Josephson oscillations between the two sides of the well. However, above this critical value tunneling is not observed. Based on a mean field treatment, this is usually attributed to macroscopic self-trapping. In the present work, we discuss an alternative approach to this system based on exact numerical solutions of the two-mode Bose-Hubbard Hamiltonian [19]:

Wave-particle duality has become one of the flagships of quantum mechanics. This counterintuitive concept is highlighted in a delayed-choice experiment, where the experimental setup that reveals either the particle or wave nature of a quantum system is decided after the system has entered the apparatus. Here we consider delayed-choice experiments from the perspective of device-independent causal models and show their equivalence to a prepare-and-measure scenario. Within this framework, we consider Wheeler's original proposal and its variant using a quantum control and show that a simple classical causal model is capable of reproducing the quantum mechanical predictions. Nonetheless, among other results, we show that, in a slight variant of Wheeler's gedanken experiment, a photon in an interferometer can indeed generate statistics incompatible with any nonretrocausal hidden variable model, whose dimensionality is the same as that of the quantum system it is supposed to mimic. Our proposal tolerates arbitrary losses and inefficiencies, making it specially suited to loophole-free experimental implementations.

The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here we observe signatures of quantum nonlinear dynamics through the direct measurement of the time-evolved Wigner function of the quantum-kicked harmonic oscillator, implemented in the spatial degrees of freedom of light. Our setup is decoherence-free and we can continuously tune the semiclassical and chaos parameters, so as to explore the transition from regular to essentially chaotic dynamics. Owing to its robustness and versatility, our scheme can be used to experimentally investigate a variety of nonlinear quantum phenomena. As an example, we couple this system to a quantum bit and experimentally investigate the decoherence produced by regular or chaotic dynamics.

We report a measurement of the transverse momentum correlation between two photons by detecting only one of them. Our method uses two identical sources in an arrangement in which the phenomenon of induced coherence without induced emission is observed. In this way, we produce an interference pattern in the superposition of one beam from each source. We quantify the transverse momentum correlation by analyzing the visibility of this pattern. Our approach might be useful for the characterization of correlated photon pair sources and may lead to an experimental measure of continuous variable entanglement, which relies on the detection of only one of two entangled particles.quantum correlations | single-photon interference | complementarity principle | photon indistinguishability | photonic spatial modes S patial entanglement (1) of photon pairs plays an important role in fundamental quantum mechanics (2-4), quantum cryptography (5, 6), quantum teleportation (7), and quantum computation (8). A widely used strategy to test spatial entanglement is to directly measure intensity correlations in both near and far fields of the source plane, which are interpreted as correlations in the transverse positions and momenta of the two photons. Measurements of the transverse momentum correlation between two photons have been performed using a variety of experimental methods (3), including the scanning of two detectors (9, 10) or two slits (11), using detector arrays (12), spatial light modulators (13), and cameras (14). All of these methods rely on the detection of both of the correlated photons. This fact restricts their applicability to situations where the wavelength of both photons lies in a spectral range, for which sufficiently efficient detectors are available.If two spatially separated nonlinear crystals emit pairs of photons (signal and idler) by the process of spontaneous parametric down conversion (SPDC) (15, 16), the two resulting signal beams in general do not interfere in lowest order (17). The absence of interference can be understood by the fact that the measurement on an idler photon would provide which-path information about a signal photon. However, lowest-order interference between the signal beams occurs if the respective idler beams are indistinguishable. This phenomenon, known as induced coherence without induced emission, was first observed experimentally in ref. 18, following a suggestion by Z.-Y. Ou of aligning the two idler beams (18,19). The interferometric visibility is reduced if path-distinguishability is introduced via different transmissions (18,19), different temporal delays (20), or different transverse sizes of the two idler beams (21,22). Recently, the phenomenon led to applications in imaging (23), spectroscopy (24, 25), metrology (26), spectrum shaping (27), and fundamental tests of complementarity (e.g., refs. 28-30).In this paper, we introduce and experimentally demonstrate a method for measuring the transverse momentum correlation between two photons by detecting only one of them. Our me...

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...

We show that it is possible to generate a novel single-photon fringe pattern by using two spatially separated identical bi-photon sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties with potential applications. A striking feature of the fringes is that although the pattern is obtained by detecting only one photon of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon. The fringe shift is characterized by a combination of wavelengths of both photons, which implies that the wavelength of a photon can be measured without detecting it. Furthermore, the visibility of the fringes diminishes as the correlation between the transverse momenta of twin photons decreases: visibility is unity for maximum momentum correlation and zero for no momentum correlation. We also show that the momentum correlation between the two photons of a pair can be determined from the single-photon interference pattern. We thus for the first time propose a method of measuring a two-photon correlation without coincidence or heralded detection.