One-Photon Measurement of Two-Photon Entanglement.

Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.

Quantum imaging with undetected photons.

Information is central to quantum mechanics. In particular, quantum interference occurs only if there exists no information to distinguish between the superposed states. The mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Here we introduce and experimentally demonstrate a quantum imaging concept based on induced coherence without induced emission. Our experiment uses two separate down-conversion nonlinear crystals (numbered NL1 and NL2), each illuminated by the same pump laser, creating one pair of photons (denoted idler and signal). If the photon pair is created in NL1, one photon (the idler) passes through the object to be imaged and is overlapped with the idler amplitude created in NL2, its source thus being undefined. Interference of the signal amplitudes coming from the two crystals then reveals the image of the object. The photons that pass through the imaged object (idler photons from NL1) are never detected, while we obtain images exclusively with the signal photons (from NL1 and NL2), which do not interact with the object. Our experiment is fundamentally different from previous quantum imaging techniques, such as interaction-free imaging or ghost imaging, because now the photons used to illuminate the object do not have to be detected at all and no coincidence detection is necessary. This enables the probe wavelength to be chosen in a range for which suitable detectors are not available. To illustrate this, we show images of objects that are either opaque or invisible to the detected photons. Our experiment is a prototype in quantum information--knowledge can be extracted by, and about, a photon that is never detected.

Quantifying the momentum correlation between two light beams by detecting one.

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.

Experimental non-classicality of an indivisible quantum system.

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioglu and Shumovsky. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.

Generation and confirmation of a (100 x 100)-dimensional entangled quantum system.

Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.

Automated Search for new Quantum Experiments.

Quantum mechanics predicts a number of, at first sight, counterintuitive phenomena. It therefore remains a question whether our intuition is the best way to find new experiments. Here, we report the development of the computer algorithm Melvin which is able to find new experimental implementations for the creation and manipulation of complex quantum states. Indeed, the discovered experiments extensively use unfamiliar and asymmetric techniques which are challenging to understand intuitively. The results range from the first implementation of a high-dimensional Greenberger-Horne-Zeilinger state, to a vast variety of experiments for asymmetrically entangled quantum states-a feature that can only exist when both the number of involved parties and dimensions is larger than 2. Additionally, new types of high-dimensional transformations are found that perform cyclic operations. Melvin autonomously learns from solutions for simpler systems, which significantly speeds up the discovery rate of more complex experiments. The ability to automate the design of a quantum experiment can be applied to many quantum systems and allows the physical realization of quantum states previously thought of only on paper.

3D super-resolution optical fluctuation imaging with temporal focusing two-photon excitation.

3D super-resolution fluorescence microscopy typically requires sophisticated setups, sample preparation, or long measurements. A notable exception, SOFI, only requires recording a sequence of frames and no hardware modifications whatsoever but being a wide-field method, it faces problems in thick, dense samples. We combine SOFI with temporal focusing two-photon excitation - the wide-field method that is capable of exciting a thin slice in 3D volume. Temporal focusing is simple to implement whenever the excitation path of the microscope can be accessed. The implementation of SOFI is straightforward. By merging these two methods, we obtain super-resolved 3D images of neurons stained with quantum dots. Our approach offers reduced bleaching of out-of-focus fluorescent probes and an improved signal-to-background ratio that can be used when robust resolution improvement is required in thick, dense samples.

Noise-resistant phase imaging with intensity correlation.

Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.

Novel Design and Application of High-NA Fiber Imaging Bundles for In Vivo Brain Imaging with Two-Photon Scanning Fluorescence Microscopy.

Here, we provide experimental verification supporting the use of short-section imaging bundles for two-photon microscopy imaging of the mouse brain. The 8 mm long bundle is made of a pair of heavy-metal oxide glasses with a refractive index contrast of 0.38 to ensure a high numerical aperture NA = 1.15. The bundle is composed of 825 multimode cores, ordered in a hexagonal lattice with a pixel size of 14 µm and a total diameter of 914 µm. We demonstrate successful imaging through custom-made bundles with 14 µm resolution. As the input, we used a 910 nm Ti-sapphire laser with 140 fs pulse and a peak power of 9 × 104 W. The excitation beam and fluorescent image were transferred through the fiber imaging bundle. As test samples, we used 1 µm green fluorescent latex beads, ex vivo hippocampal neurons expressing green fluorescent protein and cortical neurons in vivo expressing the fluorescent reporter GCaMP6s or immediate early gene Fos fluorescent reporter. This system can be used for minimal-invasive in vivo imaging of the cerebral cortex, hippocampus, or deep brain areas as a part of a tabletop system or an implantable setup. It is a low-cost solution, easy to integrate and operate for high-throughput experiments.

Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information.

Photonics has become a mature field of quantum information science, where integrated optical circuits offer a way to scale the complexity of the set-up as well as the dimensionality of the quantum state. On photonic chips, paths are the natural way to encode information. To distribute those high-dimensional quantum states over large distances, transverse spatial modes, like orbital angular momentum possessing Laguerre Gauss modes, are favourable as flying information carriers. Here we demonstrate a quantum interface between these two vibrant photonic fields. We create three-dimensional path entanglement between two photons in a nonlinear crystal and use a mode sorter as the quantum interface to transfer the entanglement to the orbital angular momentum degree of freedom. Thus our results show a flexible way to create high-dimensional spatial mode entanglement. Moreover, they pave the way to implement broad complex quantum networks where high-dimensionally entangled states could be distributed over distant photonic chips.

Real-time imaging of quantum entanglement.

Quantum Entanglement is widely regarded as one of the most prominent features of quantum mechanics and quantum information science. Although, photonic entanglement is routinely studied in many experiments nowadays, its signature has been out of the grasp for real-time imaging. Here we show that modern technology, namely triggered intensified charge coupled device (ICCD) cameras are fast and sensitive enough to image in real-time the effect of the measurement of one photon on its entangled partner. To quantitatively verify the non-classicality of the measurements we determine the detected photon number and error margin from the registered intensity image within a certain region. Additionally, the use of the ICCD camera allows us to demonstrate the high flexibility of the setup in creating any desired spatial-mode entanglement, which suggests as well that visual imaging in quantum optics not only provides a better intuitive understanding of entanglement but will improve applications of quantum science.

Quantum entanglement of high angular momenta.

Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.