Ayman F. Abouraddy

Role of Entanglement in Two-Photon Imaging

The use of entangled photons in an imaging system can exhibit effects that cannot be mimicked by any other two-photon source, whatever the strength of the correlations between the two photons. We consider a two-photon imaging system in which one photon is used to probe a remote (transmissive or scattering) object, while the other serves as a reference. We discuss the role of entanglement versus correlation in such a setting, and demonstrate that entanglement is a prerequisite for achieving distributed quantum imaging.

Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera

A single-photon-sensitive intensified charge-coupled-device (ICCD) camera has been used to simultaneously detect, over a broad area, degenerate and nondegenerate photon pairs generated by the quantum-optical process of spontaneous parametric down-conversion. We have developed a new method for determining the quantum fourth- order correlations in spatially extended detection systems such as this one. Our technique reveals the expected phase-matching-induced spa- tial correlations in a 2-f Fourier-transform system.

Decoherence-Free Subspaces in Quantum Key Distribution

We demonstrate that two recent innovations in the field of practical quantum key distribution (one-way autocompensation and passive detection) are closely related to the methods developed to protect quantum computations from decoherence. We present a new scheme that combines these advantages, and propose a practical implementation of this scheme that is feasible using existing technology.

Quantum-optical coherence tomography with dispersion cancellation

We propose a technique, called quantum-optical coherence tomography (QOCT), for carrying out tomographic measurements with dispersion-cancelled resolution. The technique can also be used to extract the frequency-dependent refractive index of the medium. QOCT makes use of a two-photon interferometer in which a swept delay permits a coincidence interferogram to be traced. The technique bears a resemblance to classical optical coherence tomography (OCT). However, it makes use of a nonclassical entangled twin-photon light source that permits measurements to be made at depths greater than those accessible via OCT, which suffers from the deleterious effects of sample dispersion. Aside from the dispersion cancellation, QOCT offers higher sensitivity than OCT as well as an enhancement of resolution by a factor of two for the same source bandwidth. QOCT and OCT are compared using an idealized sample.

Entangled-Photon Imaging of a Pure Phase Object

We demonstrate experimentally and theoretically that a coherent image of a pure phase object [implemented by a microelectromechanical system (MEMS) micromirror array] 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. One of the beams probes the phase object while the other is scanned. Though each of the beams is, in and of itself, spatially incoherent, the pair of beams exhibits higher-order interbeam coherence.

Degree of entanglement for two qubits

We demonstrate that any pure bipartite state of two qubits may be decomposed into a superposition of a maximally entangled state and an orthogonal factorizable one. Although there are many such decompositions, the weights of the two superposed states are, remarkably, unique. We propose a measure of entanglement based on this decomposition. We also demonstrate that this measure is connected to three measures of entanglement previously set forth: maximal violation of Bells inequality, concurrence, and two-particle visibility.

Biphoton focusing for two-photon excitation

We study two-photon excitation using biphotons generated via the process of spontaneous parametric down conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the crystal.

Quantum entanglement and the two-photon Stokes parameters

A formalism for two-photon Stokes parameters is introduced to describe the polarization entanglement of photon pairs. This leads to the definition of a degree of two-photon polarization, which describes the extent to which the two photons act as a pair and not as two independent photons. This pair-wise polarization is complementary to the degree of polarization of the individual photons. The approach provided here has a number of advantages over the density matrix formalism: it allows the one- and two-photon features of the state to be separated and offers a visualization of the mixedness of the state of polarization.

Polarization-assisted transverse and axial optical superresolution.

The superposition of two coaxial Gaussian beams with offset foci and orthogonal linear polarizations can be used to produce a right- or leftcircular polarization component with a focal spot of volume smaller than that of the Gaussian beam. This polarization-assisted axial and transverse superresolution effect is attributed to the differential Gouy phase shift within the focal region or to the non-Gaussian annular distribution of the circularlypolarized components in the far field.

Ellipsometric measurements by use of photon pairs generated by spontaneous parametric downconversion

We present a novel interferometric technique for performing ellipsometric measurements. This technique relies on the use of a nonclassical optical source, namely, polarization-entangled twin photons generated by spontaneous parametric downconversion from a nonlinear crystal, in conjunction with a coincidence-detection scheme. Ellipsometric measurements acquired with this scheme are absolute; i.e., they do not require source and detector calibration.