Adaptive Quantum Optics with Spatially Entangled Photon Pairs

Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement. By modulating spatially entangled photon pairs, we create periodic, topological, and random patterns of quantum illumination, without effect on intensity. We then structure the quantum illumination to simultaneously compensate for entanglement that has been randomized by a scattering medium and to characterize the medium's properties via a quantum measurement of the optical memory effect. The results demonstrate fundamental aspects of spatial coherence and open the field of adaptive quantum optics

General model of photon-pair detection with an image sensor

We develop an analytic model that relates intensity correlation measurements performed by an image sensor to the properties of photon pairs illuminating it. Experiments using both an effective single-photon counting (SPC) camera and a linear electron-multiplying charge-coupled device (EMCCD) camera confirm the model

Quantum Phase Imaging using Spatial Entanglement

Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control

Optimizing the signal-to-noise ratio of biphoton distribution measurements

Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and faster acquisition speeds than traditional raster scanning of point detectors; to date, however, there has been no general formula available to optimize data collection. Here we analyze the dependence of such measurements on count rate, detector noise properties, and threshold levels. We derive expressions for the biphoton joint probability distribution and its signal-to-noise ratio (SNR), valid beyond the low-count regime up to detector saturation. The analysis gives operating parameters for global optimum SNR that may be specified prior to measurement. We find excellent agreement with experimental measurements within the range of validity, and discuss discrepancies with the theoretical model for high thresholds. This work enables optimized measurement of the biphoton joint probability distribution in high-dimensional joint Hilbert spaces.Comment: 9 pages, 5 figures, 1 tabl

Biphoton transmission through non-unitary objects

Losses should be accounted for in a complete description of quantum imaging systems, and yet they are often treated as undesirable and largely neglected. In conventional quantum imaging, images are built up by coincidence detection of spatially entangled photon pairs (biphotons) transmitted through an object. However, as real objects are non-unitary (absorptive), part of the transmitted state contains only a single photon, which is overlooked in traditional coincidence measurements. The single photon part has a drastically different spatial distribution than the two-photon part. It contains information both about the object, and, remarkably, the spatial entanglement properties of the incident biphotons. We image the one- and two-photon parts of the transmitted state using an electron multiplying CCD array both as a traditional camera and as a massively parallel coincidence counting apparatus, and demonstrate agreement with theoretical predictions. This work may prove useful for photon number imaging and lead to techniques for entanglement characterization that do not require coincidence measurements.Comment: 7 pages, 5 figure

Quantum image distillation

Imaging with quantum states of light promises advantages over classical approaches in terms of resolution, signal-to-noise ratio, and sensitivity. However, quantum detectors are particularly sensitive sources of classical noise that can reduce or cancel any quantum advantage in the final result. Without operating in the single-photon counting regime, we experimentally demonstrate distillation of a quantum image from measured data composed of a superposition of both quantum and classical light. We measure the image of an object formed under quantum illumination (correlated photons) that is mixed with another image produced by classical light (uncorrelated photons) with the same spectrum and polarization, and we demonstrate near-perfect separation of the two superimposed images by intensity correlation measurements. This work provides a method to mix and distinguish information carried by quantum and classical light, which may be useful for quantum imaging, communications, and security

3-D IR imaging with uncooled GaN photodiodes using nondegenerate two-photon absorption

We utilize the recently demonstrated orders of magnitude enhancement of extremely nondegenerate two-photon absorption in direct-gap semiconductor photodiodes to perform scanned imaging of 3D structures using IR femtosecond illumination pulses (1.6 um and 4.93 um) gated on the GaN detector by sub-gap, femtosecond pulses. While transverse resolution is limited by the usual imaging criteria, the longitudinal or depth resolution can be less than a wavelength, dependent on the pulsewidths in this nonlinear interaction within the detector element. The imaging system can accommodate a wide range of wavelengths in the mid-IR and near-IR without the need to modify the detection and imaging systems.Comment: 9 pages, 6 figure

Massively parallel coincidence counting of high-dimensional entangled states

Entangled states of light are essential for quantum technologies and fundamental tests of physics. Current systems rely on entanglement in 2D degrees of freedom, e.g., polarization states. Increasing the dimensionality provides exponential speed-up of quantum computation, enhances the channel capacity and security of quantum communication protocols, and enables quantum imaging; unfortunately, characterizing high-dimensional entanglement of even bipartite quantum states remains prohibitively time-consuming. Here, we develop and experimentally demonstrate a new theory of camera detection that leverages the massive parallelization inherent in an array of pixels. We show that a megapixel array, for example, can measure a joint Hilbert space of 1012 dimensions, with a speed-up of nearly four orders-of-magnitude over traditional methods. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, generalizes readily to arbitrary numbers of entangled photons, and opens previously inaccessible regimes of high-dimensional quantum optics

3-(1-Methyl-3-imidazolio)propane­sulfonate: a precursor to a Brønsted acid ionic liquid

The title compound, C7H12N2O3S, is a zwitterion precursor to a Brønsted acid ionic liquid with potential as an acid catalyst. The C—N—C—C torsion angle of 100.05 (8)° allows the positively charged imidazolium head group and the negatively charged sulfonate group to inter­act with neighboring zwitterions, forming a C—H⋯O hydrogen-bonding network; the shortest among these inter­actions is 2.9512 (9) Å. The C—H⋯O inter­actions can be described by graph-set notation as two R 2 2(16) and one R 2 2(5) hydrogen-bonded rings