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Imaging with undetected photons relies upon nonlinear interferometry to extract the spatial image from an infrared probe beam and reveal it in the interference pattern of an easier-to-detect visible beam. Typically, the transmission and phase images are extracted using phase-shifting techniques and combining interferograms from multiple frames. Here we show that off-axis digital holography enables reconstruction of both transmission and phase images at the infrared wavelength from a single interferogram, and hence a single frame, recorded in the visible. This eliminates the need for phase stepping and multiple acquisitions, thereby greatly reducing total measurement time for imaging with long acquisition times at low flux or enabling video-rate imaging at higher flux. With this single-frame acquisition technique, we are able to reconstruct transmission images of an object in the infrared beam with a signal-to-noise ratio of $1.78\,\pm\,0.06$ at 10 frames per second, and record a dynamic scene in the infrared beam at 33 frames per second., Comment: 8 pages, 5 figures, references added to page 1

Optical tweezers enable non-contact trapping of micro-scale objects using light. Despite their widespread use, it is currently not known how tightly it is possible to three-dimensionally trap micro-particles with a given photon budget. Reaching this elusive limit would enable maximally-stiff particle trapping for precision measurements on the nanoscale, and photon-efficient tweezing of light-sensitive objects. Here we solve this problem by customising a trapping light field to suit a specific particle, with the aim of simultaneously optimising trap stiffness in all three dimensions. Initially taking a theoretical approach, we develop an efficient multi-parameter optimisation routine to design bespoke optical traps for a wide range of micro-particles. We show that the confinement volume of micro-spheres held in these sculpted traps can be reduced by one-to-two orders-of-magnitude in comparison to a conventional optical tweezer of the same power. We go on to conduct proof-of-principle experiments, and use a wavefront shaping inspired strategy to suppress the Brownian fluctuations of optically trapped micro-spheres in every direction concurrently, thus demonstrating order-of-magnitude reductions in their confinement volumes. Our work paves the way towards the fundamental limits of optical control over the mesoscopic realm.

Conventional endoscopes comprise a bundle of optical fibers, associating one fiber for each pixel in the image. In principle, this can be reduced to a single multimode optical fiber (MMF), the width of a human hair, with one fiber spatial-mode per image pixel. However, images transmitted through a MMF emerge as unrecognizable speckle patterns due to dispersion and coupling between the spatial modes of the fiber. Furthermore, speckle patterns change as the fiber undergoes bending, making the use of MMFs in flexible imaging applications even more complicated. In this paper, we propose a real-time imaging system using flexible MMFs, but which is robust to bending. Our approach does not require access or feedback signal from the distal end of the fiber during imaging. We leverage a variational autoencoder (VAE) to reconstruct and classify images from the speckles and show that these images can still be recovered when the bend configuration of the fiber is changed to one that was not part of the training set. We utilize a MMF 300 mm long with a 62.5 um core for imaging 10 x 10 cm objects placed approximately at 20 cm from the fiber and the system can deal with a change in fiber bend of 50 degrees and range of movement of 8 cm.

Understanding quantum mechanics within curved spacetime is a key stepping stone towards understanding the nature of spacetime itself. Whilst various theoretical models have been developed, it is significantly more challenging to carry out actual experiments that probe quantum mechanics in curved spacetime. By adding Sagnac interferometers into the arms of a Hong-Ou-Mandel (HOM) interferometer that is placed on a mechanically rotating platform, we show that non-inertial motion modifies the symmetry of an entangled biphoton state. As the platform rotation speed is increased, we observe that HOM interference dips transform into HOM interference peaks. This indicates that the photons pass from perfectly indistinguishable (bosonic behaviour), to perfectly distinguishable (fermionic behavior), therefore demonstrating a mechanism for how spacetime can affect quantum systems. The work is increasingly relevant in the real world as we move towards global satellite quantum communications, and paves the way for further fundamental research that could test the influence of non-inertial motion (and equivalently curved spacetime) on quantum entanglement.

We present a wide-field homodyne imaging system capable of recovering intensity and phase images of an object from a single camera frame at an illumination intensity significantly below the noise floor of the camera. By interfering a weak imaging signal with a much brighter reference beam we are able to image objects in the short-wave infrared down to signal intensity of $\sim$$1.1$ photons per pixel per frame incident on the sensor despite the camera having a noise floor of $\sim$$200$ photons per pixel. At this illumination level we operate under the conditions of a reference beam to probe beam power ratio of $\sim$$300$,$000$:$1$. There is a corresponding $29.2\%$ drop in resolution of the image due to the method implemented. For transmissive objects, in addition to intensity, the approach also images the phase profile of the object. We believe our demonstration could open the way to low-light imaging in domains where low noise cameras are not available, thus vastly extending the range of application for low-light imaging.

Time-of-flight (ToF) 3D imaging has a wealth of applications, from industrial inspection to movement tracking and gesture recognition. Depth information is recovered by measuring the round-trip flight time of laser pulses, which usually requires projection and collection optics with diameters of several centimetres. In this work we shrink this requirement by two orders of magnitude, and demonstrate near video-rate 3D imaging through multimode optical fibres (MMFs) - the width of a strand of human hair. Unlike conventional imaging systems, MMFs exhibit exceptionally complex light transport resembling that of a highly scattering medium. To overcome this complication, we implement high-speed aberration correction using wavefront shaping synchronised with a pulsed laser source, enabling random-access scanning of the scene at a rate of $\sim$23,000 points per second. Using non-ballistic light we image moving objects several metres beyond the end of a $\sim$40 cm long MMF of 50$\mu$m core diameter, with millimetric depth resolution, at frame-rates of $\sim$5Hz. Our work extends far-field depth resolving capabilities to ultra-thin micro-endoscopes, and will have a broad range of applications to clinical and remote inspection scenarios., Comment: Main text: 8 pages, 4 figures. Supplementary: 6 pages, 2 figures

The well-known linear Doppler effect arises from the linear motion between source and observer, while the less well-known rotational Doppler effect arises from the rotational motion. Here, we present both theories and experiments illustrating the relationship between the rotational and linear Doppler effects. A spiral phaseplate is used to generate a light beam carrying orbital angular momentum and the frequency shift is measured arising from its rotational and/or linear motion. By considering either the motion-induced time-evolving phase or the momentum and energy conservation in light-matter interactions, we derive the rotational Doppler shift, linear Doppler shift, and overall Doppler shift associated with rotational and linear motions. We demonstrate the relationship between rotational and linear Doppler shifts, either of which can be derived from the other effect, thereby illustrating their shared origin. Moreover, the close relationship between rotational and linear Doppler effects is also deduced for a more general moving rough surface.

Spontaneous downconversion is a versatile source for correlated biphotons that has been employed in many quantum sensing and imaging experiments. Spatially-resolved photon-counting detectors allow to access a large number of modes, posing the challenge of an accurate description of such systems. We propose a simple model to generate images as though acquired by a photon-counting camera, and allow to simulate and characterise the detection of quantum correlations. We derive quantitative parameters characteristic of the spatial correlations for a given experiment, comparing the images produced by our model to the frames acquired by an electron-multiplying CCD camera. Moreover we accurately predict the decreased detection of spatially correlated biphotons caused by introducing a variable amount of optical loss after the nonlinear crystal, even though the total number of detected events is kept constant, showing excellent agreement between model and experiment.

The production of pairs of entangled photons simply by focusing a laser beam onto a crystal with a non-linear optical response was used to test quantum mechanics and to open new approaches in imaging. The development of the latter was enabled by the emergence of single photon sensitive cameras able to characterize spatial correlations and high-dimensional entanglement. Thereby new techniques emerged such as the ghost imaging of objects - where the quantum correlations between photons reveal the image from photons that have never interacted with the object - or the imaging with undetected photons by using nonlinear interferometers. Additionally, quantum approaches in imaging can also lead to an improvement in the performance of conventional imaging systems. These improvements can be obtained by means of image contrast, resolution enhancement that exceed the classical limit and acquisition of sub-shot noise phase or amplitude images. In this review we discuss the application of quantum states of light for advanced imaging techniques.

The contrast of an image can be degraded by the presence of background light and sensor noise. To overcome this degradation, quantum illumination protocols have been theorised (Science 321 (2008), Physics Review Letters 101 (2008)) that exploit the spatial correlations between photon-pairs. Here we demonstrate the first full-field imaging system using quantum illumination, by an enhanced detection protocol. With our current technology we achieve a rejection of background and stray light of order 5 and also report an image contrast improvement up to a factor of 5.5, which is resilient to both environmental noise and transmission losses. The quantum illumination protocol differs from usual quantum schemes in that the advantage is maintained even in the presence of noise and loss. Our approach may enable laboratory-based quantum imaging to be applied to real-world applications where the suppression of background light and noise is important, such as imaging under low-photon flux and quantum LIDAR.

Extracting as much information as possible about an object when probing with a limited number of photons is an important goal with applications from biology and security to metrology. Imaging with a few photons is a challenging task as the detector noise and stray light are then predominant, which precludes the use of conventional imaging methods. Quantum correlations between photon pairs has been exploited in a so called 'heralded imaging scheme' to eliminate this problem. However these implementations have so-far been limited to intensity imaging and the crucial phase information is lost in these methods. In this work, we propose a novel quantum-correlation enabled Fourier Ptychography technique, to capture high-resolution amplitude and phase images with a few photons. This is enabled by the heralding of single photons combined with Fourier ptychographic reconstruction. We provide experimental validation and discuss the advantages of our technique that include the possibility of reaching a higher signal to noise ratio and non-scanning Fourier Ptychographic acquisition.

Although quantum physics is well understood in inertial reference frames (flat spacetime), a current challenge is the search for experimental evidence of non-trivial or unexpected behaviour of quantum systems in non-inertial frames. Here, we present a novel test of quantum mechanics in a non-inertial reference frame: we consider Hong-Ou-Mandel (HOM) interference on a rotating platform and study the effect of uniform rotation on the distinguishability of the photons. Both theory and experiments show that the rotational motion induces a relative delay in the photon arrival times at the exit beamsplitter and that this delay is observed as a shift in the position of the HOM dip. This experiment can be extended to a full general relativistic test of quantum physics using satellites in Earth orbit and indicates a new route towards the use of photonic technologies for investigating quantum mechanics at the interface with relativity.

Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean floor can generate random caustics and focus the energy of tsunami waves. Caustics share many similarities to rogue waves, as they both exhibit heavy-tailed distribution, i.e. an overpopulation of large events. Linear Schr\"odinger-type equations are usually used to explain the wave dynamics of caustics. However, in that the wave amplitude increases dramatically in caustics, nonlinearity is inevitable in many systems. In this Letter, we investigate the effect of nonlinearity on the formation of optical caustics. We show experimentally that, in contrast to linear systems, even small phase fluctuations can generate strong caustics upon nonlinear propagation. We simulated our experiment based on the nonlinear Schr\"odinger equation (NLSE) with Kerr-type nonlinearity, which describes the wave dynamics not only in optics, but also in some other physical systems such as oceans. Therefore, our results may also aid our understanding of ocean phenomena., Comment: 5 pages, 4 figures

Free electrons with a helical phase front, referred to as "twisted" electrons, possess an orbital angular momentum (OAM) and, hence, a quantized magnetic dipole moment along their propagation direction. This intrinsic magnetic moment can be used to probe material properties. Twisted electrons thus have numerous potential applications in materials science. Measuring this quantity often relies on a series of projective measurements that subsequently change the OAM carried by the electrons. In this Letter, we propose a nondestructive way of measuring an electron beam's OAM through the interaction of this associated magnetic dipole with a conductive loop. Such an interaction results in the generation of induced currents within the loop, which are found to be directly proportional to the electron's OAM value. Moreover, the electron experiences no OAM variations and only minimal energy losses upon the measurement, and, hence, the nondestructive nature of the proposed technique., Comment: 5 pages, 3 figures, and supplemental material that is comprised of text and 4 figures

Quantum complementarity states that particles, e.g. electrons, can exhibit wave-like properties such as diffraction and interference upon propagation. \textit{Electron waves} defined by a helical wavefront are referred to as twisted electrons~\cite{uchida:10,verbeeck:10,mcmorran:11}. These electrons are also characterised by a quantized and unbounded magnetic dipole moment parallel to their propagation direction, as they possess a net charge of $-|e|$~\cite{bliokh:07}. When interacting with magnetic materials, the wavefunctions of twisted electrons are inherently modified~\cite{lloyd:12b,schattschneider:14a,asenjo:14}. Such variations therefore motivate the need to analyze electron wavefunctions, especially their wavefronts, in order to obtain information regarding the material's structure~\cite{harris:15}. Here, we propose, design, and demonstrate the performance of a device for measuring an electron's azimuthal wavefunction, i.e. its orbital angular momentum (OAM) content. Our device consists of nanoscale holograms designed to introduce astigmatism onto the electron wavefunctions and spatially separate its phase components. We sort pure and superposition OAM states of electrons ranging within OAM values of $-10$ and $10$. We employ the device to analyze the OAM spectrum of electrons having been affected by a micron-scale magnetic dipole, thus establishing that, with a midfield optical configuration, our sorter can be an instrument for nano-scale magnetic spectroscopy., Comment: 5 pages, 3 figures, 3 pages of supplementary materials

As an alternative to conventional multi-pixel cameras, single-pixel cameras enable images to be recorded using a single detector that measures the correlations between the scene and a set of patterns. However, to fully sample a scene in this way requires at least the same number of correlation measurements as there are pixels in the reconstructed image. Therefore single-pixel imaging systems typically exhibit low frame-rates. To mitigate this, a range of compressive sensing techniques have been developed which rely on a priori knowledge of the scene to reconstruct images from an under-sampled set of measurements. In this work we take a different approach and adopt a strategy inspired by the foveated vision systems found in the animal kingdom - a framework that exploits the spatio-temporal redundancy present in many dynamic scenes. In our single-pixel imaging system a high-resolution foveal region follows motion within the scene, but unlike a simple zoom, every frame delivers new spatial information from across the entire field-of-view. Using this approach we demonstrate a four-fold reduction in the time taken to record the detail of rapidly evolving features, whilst simultaneously accumulating detail of more slowly evolving regions over several consecutive frames. This tiered super-sampling technique enables the reconstruction of video streams in which both the resolution and the effective exposure-time spatially vary and adapt dynamically in response to the evolution of the scene. The methods described here can complement existing compressive sensing approaches and may be applied to enhance a variety of computational imagers that rely on sequential correlation measurements., Comment: 13 pages, 5 figures

Time-of-flight three dimensional imaging is an important tool for many applications, such as object recognition and remote sensing. Unlike conventional imaging approach using pixelated detector array, single-pixel imaging based on projected patterns, such as Hadamard patterns, utilises an alternative strategy to acquire information with sampling basis. Here we show a modified single-pixel camera using a pulsed illumination source and a high-speed photodiode, capable of reconstructing 128x128 pixel resolution 3D scenes to an accuracy of ~3 mm at a range of ~5 m. Furthermore, we demonstrate continuous real-time 3D video with a frame-rate up to 12 Hz. The simplicity of the system hardware could enable low-cost 3D imaging devices for precision ranging at wavelengths beyond the visible spectrum., Comment: 10 pages, 6 figures

As normally used, no commercially available camera has a low-enough dark noise to directly produce video recordings of double-slit interference at the photon-by-photon level, because readout noise significantly contaminates or overwhelms the signal. In this work, noise levels are significantly reduced by turning on the camera only when the presence of a photon has been heralded by the arrival, at an independent detector, of a time-correlated photon produced via parametric down-conversion. This triggering scheme provides the improvement required for direct video imaging of Young's double-slit experiment with single photons, allowing clarified versions of this foundational demonstration. Further, we introduce variations on this experiment aimed at promoting discussion of the role spatial coherence plays in such a measurement. We also emphasize complementary aspects of single-photon measurement, where imaging yields (transverse) position information, while diffraction yields the transverse momentum, and highlight the roles of transverse position and momentum correlations between down-converted photons, including examples of "ghost" imaging and diffraction. The videos can be accessed at http://sun.iwu.edu/~gspaldin/SinglePhotonVideos.html online., Comment: 7 pages, 8 figures

Since the invention of digital cameras there has been a concerted drive towards detector arrays with higher spatial resolution. Microscanning is a technique that provides a final higher resolution image by combining multiple images of a lower resolution. Each of these low resolution images is subject to a sub-pixel sized lateral displacement. In this work we apply the microscanning approach to an infrared single-pixel camera. For the same final resolution and measurement resource, we show that microscanning improves the signal-to-noise ratio (SNR) of reconstructed images by approximately 50%. In addition, this strategy also provides access to a stream of low-resolution 'preview' images throughout each high-resolution acquisition. Our work demonstrates an additional degree of flexibility in the trade-off between SNR and spatial resolution in single-pixel imaging techniques.

Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate novel entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows for an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of $\sim60\%$ relative to $7344$ studied cases., Comment: V1: revtex4, 10 pages, 4 figures + supp. material (4 pages, 1 figure) V2: Substantial revisions implemented both in theory and experimental data analysis

That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using time-correlated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount., Comment: 8 pages, 4 figures

There is recent interest in the use of light beams carrying orbital angular momentum (OAM) for creating multiple channels within free-space optical communication systems. One limiting issue is that, for a given beam size at the transmitter, the beam divergence angle increases with increasing OAM, thus requiring a larger aperture at the receiving optical system if the efficiency of detection is to be maintained. Confusion exists as to whether this divergence scales linarly with, or with the square root of, the beam's OAM. We clarify how both these scaling laws are valid, depending upon whether it is the radius of the Gaussian beam waist or the rms intensity which is kept constant while varying the OAM., Comment: 4 pages, 2 figures

Low-light-level imaging techniques have application in many diverse fields, ranging from biological sciences to security. We demonstrate a single-photon imaging system based on a time-gated inten- sified CCD (ICCD) camera in which the image of an object can be inferred from very few detected photons. We show that a ghost-imaging configuration, where the image is obtained from photons that have never interacted with the object, is a useful approach for obtaining images with high signal-to-noise ratios. The use of heralded single-photons ensures that the background counts can be virtually eliminated from the recorded images. By applying techniques of compressed sensing and associated image reconstruction, we obtain high-quality images of the object from raw data comprised of fewer than one detected photon per image pixel., Comment: 9 pages, 4 figures

Quantum key distributions (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field, allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93\%. Through the use of a 7-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment shows that, in addition to having an increased information capacity, QKD systems based on spatial-mode encoding will be more tolerant to errors and thus more robust against eavesdropping attacks.

We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d+1) mutually unbiased measurements in a classical prepare and measure scheme and on a pair of entangled photons for dimensions ranging from d = 2 to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon up to a dimension of d = 4., Comment: Published in Phys. Rev. A

Photonics has become a mature field of quantum information science, where integrated optical circuits offer a way to scale the complexity of the setup 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 (OAM) 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 non-linear crystal and use a mode sorter as the quantum interface to transfer the entanglement to the OAM degree of freedom. Thus our results show a novel, 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., Comment: Journal reference added. Additonal measurements can be found in the journal version. 5 pages incl. 4 figures plus 2 pages supplementary information

One of the most widely used techniques for measuring the orbital angular momentum components of a light beam is to flatten the spiral phase front of a mode, in order to couple it to a single-mode optical fiber. This method, however, suffers from an efficiency that depends on the orbital angular momentum of the initial mode and on the presence of higher order radial modes. The reason is that once the phase has been flattened, the field retains its ringed intensity pattern and is therefore a nontrivial superposition of purely radial modes, of which only the fundamental one couples to a single mode optical fiber. In this paper, we study the efficiency of this technique both theoretically and experimentally. We find that even for low values of the OAM, a large amount of light can fall outside the fundamental mode of the fiber, and we quantify the losses as functions of the waist of the coupling beam of the orbital angular momentum and radial indices. Our results can be used as a tool to remove the efficiency bias where fair-sampling loopholes are not a concern. However, we hope that our study will encourage the development of better detection methods of the orbital angular momentum content of a beam of light., Comment: 5 pages, 4 figures

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks, a blazed axicon, binary axicon and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states., Comment: 8 pages, 10 figures

The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of "direct measurement" was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While this method has been used for measuring polarization states, its real potential lies in the measurement of states with a large dimensionality. Here we show the practical direct measurement of a high-dimensional state vector in the discrete basis of orbital-angular momentum. Through weak measurements of orbital-angular momentum and strong measurements of angular position, we measure the complex probability amplitudes of a pure state with a dimensionality, d=27. Further, we use our method to directly observe the relationship between rotations of a state vector and the relative phase between its orbital-angular-momentum components. Our technique has important applications in high-dimensional classical and quantum information systems, and can be extended to characterize other types of large quantum states., Comment: 8 pages, 3 figures

Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyse the measurement of intensity correlations using multi-element detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximises the visibility of the two photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying CCD camera, finding excellent agreement with the theoretical analysis., Comment: Some typos corrected, references added. 12 pages, 5 figures, revtex4; comments welcome

Computational ghost imaging retrieves the spatial information of a scene using a single pixel detector. By projecting a series of known random patterns and measuring the back reflected intensity for each one, it is possible to reconstruct a 2D image of the scene. In this work we overcome previous limitations of computational ghost imaging and capture the 3D spatial form of an object by using several single pixel detectors in different locations. From each detector we derive a 2D image of the object that appears to be illuminated from a different direction, using only a single digital projector as illumination. Comparing the shading of the images allows the surface gradient and hence the 3D form of the object to be reconstructed. We compare our result to that obtained from a stereo- photogrammetric system utilizing multiple high resolution cameras. Our low cost approach is compatible with consumer applications and can readily be extended to non-visible wavebands., Comment: 13pages, 4figures

We present an experimental comparison between different iterative ghost imaging algorithms. Our experimental setup utilizes a spatial light modulator for generating known random light fields to illuminate a partially-transmissive object. We adapt the weighting factor used in the traditional ghost imaging algorithm to account for changes in the efficiency of the generated light field. We show that our normalized weighting algorithm can match the performance of differential ghost imaging., Comment: 10 pages, 5 figures

Correlated-photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated-photon ghost-imaging experiments have scanned a single-pixel detector through the field of view to obtain the spatial information. However, scanning leads to a poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far-field of the photon pair source, taking advantage of the EPR-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing., Comment: Updated to published version; Advanced wave picture section removed; 7 pages and 4 figures

Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gauss (BG) basis. Having a readily adjustable radial scale, BG modes provide a more favourable basis for OAM entanglement over Laguerre-Gaussian (LG) modes. The OAM bandwidth in terms of BG modes can be increased by selection of particular radial modes and leads to a flattening of the spectrum. The flattening of the spectrum allows for higher entanglement. We demonstrate increased entanglement in terms of BG modes by performing a Bell-type experiment and violating the appropriate Clauser Horne Shimony Holt (CHSH) inequality. In addition, we reconstruct the quantum state of BG modes entangled in high-dimensions., Comment: 8 pages, 4 figures

We describe an experimental implementation of a free-space 11-dimensional communication system using orbital angular momentum (OAM) modes. This system has a maximum measured OAM channel capacity of 2.12 bits/photon. The effects of Kolmogorov thin-phase turbulence on the OAM channel capacity are quantified. We find that increasing the turbulence leads to a degradation of the channel capacity. We are able to mitigate the effects of turbulence by increasing the spacing between detected OAM modes. This study has implications for high-dimensional quantum key distribution (QKD) systems. We describe the sort of QKD system that could be built using our current technology., Comment: 6 pages, 5 figures

The light produced by parametric down-conversion shows strong spatial entanglement that leads to violations of EPR criteria for separability. Historically, such studies have been performed by scanning a single-element, single-photon detector across a detection plane. Here we show that modern electron-multiplying charge-coupled device cameras can measure correlations in both position and momentum across a multi-pixel field of view. This capability allows us to observe entanglement of around 2,500 spatial states and demonstrate Einstein-Podolsky-Rosen type correlations by more than two orders of magnitude. More generally, our work shows that cameras can lead to important new capabilities in quantum optics and quantum information science., Comment: 5 pages, 4 figures

Holographic optical tweezers are used to construct a static bistable optical potential energy landscape where a Brownian particle experiences restoring forces from two nearby optical traps and undergoes thermally activated transitions between the two energy minima. Hydrodynamic coupling between two such systems results in their partial synchronisation. This is interpreted as an emergence of higher mobility pathways, along which it is easier to overcome barriers to structural rearrangement., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

Quantum entanglement plays a vital role in many quantum information and communication tasks. Entangled states of higher dimensional systems are of great interest due to the extended possibilities they provide. For example, they allow the realisation of new types of quantum information schemes that can offer higher information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems. Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher dimensional entangled systems are used. We have measured previously untested correlations between two photons to experimentally demonstrate high-dimensional entangled states. We obtain violations of Bell-type inequalities generalised to d-dimensional systems with up to d = 12. Furthermore, the violations are strong enough to indicate genuine 11-dimensional entanglement. Our experiments use photons entangled in orbital angular momentum (OAM), generated through spontaneous parametric down-conversion (SPDC), and manipulated using computer controlled holograms.

We demonstrate electromagnetic quantum states of single photons and of correlated photon pairs exhibiting "hybrid" entanglement between spin and orbital angular momentum. These states are obtained from entangled photon pairs emitted by spontaneous parametric down conversion, by employing a $q$-plate for coupling the spin and orbital degrees of freedom of a photon. Entanglement and contextual quantum behavior (that is also non-local, in the case of photon pairs) is demonstrated by the reported violation of the Clauser-Horne-Shimony-Holt inequality. In addition a classical analog of the hybrid spin-orbit photonic entanglement is reported and discussed., Comment: 5 pages, 3 figures

Microrheology is a branch of rheology having the same principles as conventional bulk rheology, but working on micron length scales and micro-litre volumes. Optical tweezers have been successfully used with Newtonian fluids for rheological purposes such as determining fluid viscosity. Conversely, when optical tweezers are used to measure the viscoelastic properties of complex fluids the results are either limited to the material's high-frequency response, discarding important information related to the low-frequency behavior, or they are supplemented by low-frequency measurements performed with different techniques, often without presenting an overlapping region of clear agreement between the sets of results. We present a simple experimental procedure to perform microrheological measurements over the widest frequency range possible with optical tweezers. A generalised Langevin equation is used to relate the frequency-dependent moduli of the complex fluid to the time-dependent trajectory of a probe particle as it flips between two optical traps that alternately switch on and off., Comment: 13 pages, 6 figures, submitted to Special Issue of the Journal of Optics

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalised Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers., Comment: 5 pages, 3 figures