Odd-Order Aberration-Cancellation in Correlated-Photon Imaging

We discuss a correlated two-photon imaging apparatus that is capable of producing images that are free of the effects of odd-order aberration introduced by the optical system. We show that both quantum-entangled and classically correlated light sources are capable of producing the desired spatial-aberration cancelation

Twin-photon techniques for photo-detector calibration

The aim of this review paper is to enlighten some recent progresses in quantum optical metrology in the part of quantum efficiency measurements of photo-detectors performed with bi-photon states. The intrinsic correlated nature of entangled photons from Spontaneous Parametric Down Conversion phenomenon has opened wide horizons to a new approach for the absolute measurement of photo-detector quantum efficiency, outgoing the requirement for conventional standards of optical radiation; in particular the simultaneous feature of the creation of conjugated photons led to a well known technique of coincidence measurement, deeply understood and implemented for standard uses. On the other hand, based on manipulation of entanglement developed for Quantum Information protocols implementations, a new method has been proposed for quantum efficiency measurement, exploiting polarisation entanglement in addition to energy-momentum and time ones, that is based on conditioned polarisation state manipulation. In this review, after a general discussion on absolute photo-detector calibration, we compare these different methods, in order to give an accurate operational sketch of the absolute quantum efficiency measurement state of the art

Conditioned Unitary Transformation on biphotons

A conditioned unitary transformation ($90^o$ polarization rotation) is performed at single-photon level. The transformation is realized by rotating polarization for one of the photons of a polarization-entangled biphoton state (signal photon) by means of a Pockel's cell triggered by the detection of the other (idler) photon after polarization selection. As a result, polarization degree for the signal beam changes from zero to the value given by the idler detector quantum efficiency. This result is relevant to practical realization of various quantum information schemes and can be used for developing a new method of absolute quantum efficiency calibration

Two-Photon Spiral Imaging with Correlated Orbital Angular Momentum States

The concept of correlated two-photon spiral imaging is introduced. We begin by analyzing the joint orbital angular momentum (OAM) spectrum of correlated photon pairs. The mutual information carried by the photon pairs is evaluated, and it is shown that when an object is placed in one of the beam paths the value of the mutual information is strongly dependent on object shape and is closely related to the degree of rotational symmetry present. After analyzing the effect of the object on the OAM correlations, the method of correlated spiral imaging is described. We first present a version using parametric downconversion, in which entangled pairs of photons with opposite OAM values are produced, placing an object in the path of one beam. We then present a classical (correlated, but non-entangled) version. The relative problems and benefits of the classical versus entangled configurations are discussed. The prospect is raised of carrying out compressive imaging via twophoton OAM detection to reconstruct sparse objects with few measurements

Ghost imaging using homodyne detection

We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desired orthogonal quadrature components of the image. We point out an inherent link between the far-field bandwidth and the near-field resolution of the reproduced image, determined by the bandwidth of the source of the correlated beams. However, we show how to circumvent this limitation by using a spatial averaging technique which dramatically improves the imaging bandwidth of the far-field correlations as well as speeds up the convergence rate. The results are backed up by numerical simulations taking into account the finite size and duration of the pump pulse.Comment: 17 pages, 10 figures, submitted to Phys. Rev.

Efficient fiber coupling of down-conversion photon pairs

We develop and apply an effective analytic theory of a non-collinear, broadband type-I parametric down-conversion to study a coupling efficiency of the generated photon pairs into single mode optical fibers. We derive conditions necessary for highly efficient coupling for single and double type-I crystal producing polarization entangled states of light. We compare the obtained approximate analytic expressions with the exact numerical solutions and discuss the results for a case of BBO crystals.Comment: 15 pages, 4 figure

Entangled-Photon Imaging of a Pure Phase Object

We demonstrate experimentally and theoretically that a coherent image of a pure phase object may be obtained by use of a spatially incoherent illumination beam. This is accomplished by employing a two-beam source of entangled photons generated by spontaneous parametric down-conversion. Though each of the beams is, in and of itself, spatially incoherent, the pair of beams exhibits higher-order inter-beam coherence. One of the beams probes the phase object while the other is scanned. The image is recorded by measuring the photon coincidence rate using a photon-counting detector in each beam. Using a reflection configuration, we successfully imaged a phase object implemented by a MEMS micro-mirror array. The experimental results are in accord with theoretical predictions.Comment: 11 pages, 3 figures, submittedto Phys. Rev. Let

Ultranarrow resonance peaks in the transmission and reflection spectra of a photonic crystal cavity with Raman gain

The Raman gain of a probe light in a three-state $\Lambda$-scheme placed into a defect of a one-dimensional photonic crystal is studied theoretically. We show that there exists a pump intensity range, where the transmission and reflection spectra of the probe field exhibit \textit{simultaneously} occurring narrow peaks (resonances) whose position is determined by the Raman resonance. Transmission and reflection coefficients can be larger than unity at pump intensities of order tens of $\mu$W/cm$^{2}$. When the pump intensity is outside this region, the peak in the transmission spectrum turns into a narrow dip. The nature of narrow resonances is attributed to a drastic dispersion of the nonlinear refractive index in the vicinity of the Raman transition, which leads to a significant reduction of the group velocity of the probe wave.Comment: 9 pages, 3 figure

Measuring two-photon orbital angular momentum entanglement

We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of twin photons from a down-conversion source. Our estimate for the Schmidt number is substantially lower but still confirms the presence of high-dimensional entanglement.Comment: Extended paper of a published version in PRA, with some extra appendice

Analysis and interpretation of high transverse entanglement in optical parametric down conversion

Quantum entanglement associated with transverse wave vectors of down conversion photons is investigated based on the Schmidt decomposition method. We show that transverse entanglement involves two variables: orbital angular momentum and transverse frequency. We show that in the monochromatic limit high values of entanglement are closely controlled by a single parameter resulting from the competition between (transverse) momentum conservation and longitudinal phase matching. We examine the features of the Schmidt eigenmodes, and indicate how entanglement can be enhanced by suitable mode selection methods.Comment: 4 pages, 4 figure