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We present analytic expressions for the coincidence detection probability amplitudes of photon pairs generated by spontaneous parametric down-conversion in both momentum and position spaces, without making use of the Gaussian approximation, and taking into account the effects of birefringence in the nonlinear crystal. We also present experimental data supporting our theoretical predictions, using Einstein-Podolsky-Rosen correlations as benchmarks, for 8 different pump beam configurations.

The Photon wave function Formalism provides an alternative description of some quantum optical phenomena in a more intuitive way. We use this formalism to describe the process of correlated Stokes--anti-Stokes Raman scattering. In this process, two photons from a laser beam are inelastically scattered by a phonon created by the first photon (Stokes processes) and annihilated by the second photon (anti-Stokes process), producing a Stokes--anti-Sokes (SaS) photon pair. We arrive at an expression for the two-photon wave function of the scattered SaS photon pair, which is in agreement with a number of experimental results., Comment: 8 pages, 1 figure

In the correlated Stokes--anti-Stokes scattering (SAS) an incident photon interacts with a Raman-active material, creating a Stokes photon and exciting a quantum vibrational mode in the medium, which is posteriorly annihilated on contact with a second incident photon, producing in turn an anti-Stokes photon. This can be accomplished by real and virtual processes. In real process the quantum mode shared between the Stokes and anti-Stokes events is a real particle, whereas in virtual processes the pair formation is mediated by the exchange of virtual particles. Here, we introduce a Hamiltonian to describe the pair production in SAS scattering, for both types of process, when stimulated by two orthogonally polarized laser pulses in a pump-and-probe configuration. We also model the effect of the natural decay of the vibration created in the Stokes event and compute the probability of producing SAS pairs. Additionally, we follow the dynamics of the vibration by considering the Stokes and anti-Stokes fields as external reservoirs, obtaining thus a master equation for the reduced density matrix for the vibrational population. Finally, we compare our theoretical results with recently published experimental data., Comment: 9 pages, 3 figures

We obtained the phase and intensity images of an object by detecting classical light which never interacted with it. With a double passage of a pump and a signal laser beams through a nonlinear crystal, we observe interference between the two idler beams produced by stimulated parametric down conversion. The object is placed in the amplified signal beam after its first passage through the crystal, and the image is observed in the interference of the generated idler beams. High contrast images can be obtained even for objects with small transmittance coefficient due to the geometry of the interferometer and to the stimulated parametric emission. Like its quantum counterpart, this three-colour imaging concept can be useful when the object must be probed with light at a wavelength for which detectors are not available., Comment: Just over 5 pages, 3 figures

The dynamics of systems subjected to noise is called Markovian in the absence of memory effects, i.e. when its immediate future only depends on its present. Time correlations in the noise source may generate non-Markovian effects that, sometimes, can be erased by appropriately coarse graining the time evolution of the system. In general, the coarse graining time $t_\text{CG}$ is taken to be much larger than the correlation time $\tau$ but no direct relation between them is established. Here we analytically obtain a relation between $t_\text{CG}$ and $\tau$ for the dynamics of a qubit subjected to a time correlated environment. Our results can be applied in principle to any distribution of the environmental correlations and can be tested through a collisional model where the qubit sequentially interacts with correlated qutrits.

Due to the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion the generated twin photons are entangled in Hermite-Gaussian (HG) modes. This enables one using HG modes as an alphabet for quantum communication. For global quantum communication purposes, we derive an analytic expression for two-photon detection probability in terms of HG modes taking into account the effects of the turbulent atmosphere. Our result is more general as it accounts for the propagation of both, signal and idler photons through the atmosphere, as opposed to other works considering one of the photons' propagation in vacuum. We show that while the restrictions on both the parity and order of the down-converted HG fields no longer hold due to the crosstalk between modes when propagating in the atmosphere, the crosstalk is not uniform: there are more robust modes that tend to keep the photons in them. These modes can be employed in order to increase the fidelity of quantum communication.

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to system backflow of information (strong non-Markovianity) have been experimentally simulated. In this work, using an all-optical setup we simulate and observe the so-called weak non-Markovian dynamics. Through full process tomography, we experimentally demonstrate that the dynamics of a qubit can be non-Markovian despite an always increasing correlation between the system and its environment which, in our case, denotes no information backflow. We also show the transition from the weak to the strong regime by changing a single parameter in the environmental state, leading us to a better understanding of the fundamental features of non-Markovianity., Comment: v2: final version

In a recent work, Aharonov et al. suggested that a photon could be separated from its polarization in an experiment involving pre- and post-selection [New J. Phys 15, 113015 (2013)]. They named the effect 'quantum Cheshire Cat', in a reference to the cat that is separated from its grin in the novel Alice's Adventures in Wonderland. Following these ideas, Denkmayr et al. performed a neutron interferometric experiment and interpreted the results suggesting that neutrons were separated from their spin [Nat. Commun. 5, 4492 (2014)]. Here we show that these results can be interpreted as simple quantum interference, with no separation between the quantum particle and its internal degree of freedom. We thus hope to clarify the phenomenon with this work, by removing these apparent paradoxes., Comment: 5 pages, 3 figures

We investigate the smallest set of requirements for inducing non-Markovian dynamics in a collisional model of open quantum systems. This is done by introducing correlations in the state of the environment and analyzing the divisibility of the quantum maps from consecutive time steps. Our model and results serve as a platform for the microscopic study of non-Markovian behavior as well as an example of a simple scenario of non-Markovianity with purely contractive maps, i.e. with no back-flow of information between system and environment., Comment: Revised version, session added, references added

The state of the spatially correlated down-converted photons is usually treated as a two-mode Gaussian entangled state. While intuitively this seems to be reasonable, it is known that new structures in the spatial distributions of these photons can be observed when the phase-matching conditions are properly taken into account. Here, we study how the variances of the near- and far-field conditional probabilities are affected by the phase-matching functions, and we analyze the role of the EPR-criterion regarding the non-Gaussianity and entanglement detection of the spatial two-photon state of spontaneous parametric down-conversion (SPDC). Then we introduce a statistical measure, based on the negentropy of the joint distributions at the near- and far-field planes, which allows for the quantification of the non-Gaussianity of this state. This measure of non-Gaussianity requires only the measurement of the autocorrelation covariance sub-matrices, and will be relevant for new applications of the spatial correlation of SPDC in CV quantum information processing., Comment: 20 pages, 5 figures

We present a simple treatment for the phenomenon of parametric downconversion considering the coherent scattering of one pump photon into a photon pair by a nonlinear crystal. The energy and momentum entanglement of the quantum state of the generated twin photons are seen as a consequence of the fundamental indistinguishability of the time and the position in which the photon pair is created inside the crystal. We also discuss some consequences of the system entanglement., Comment: 6 pages, 2 figures. v3: Minor changes on the text. Some references were included

The Bialynicki-Birula-Sipe photon wave function formalism is extended to include the interaction between photons and continuous non-absorptive media. When the second quantization of this formalism is introduced, a new way of describing the quantum interactions between light and matter emerges. As an example of application, the quantum state of the twin photons generated by parametric down conversion is obtained in agreement with previous treatments, but with a more intuitive interpretation., Comment: 13 pages, no figures. To appear in New Journal of Physics

The transverse spatial effects observed in photon pairs produced by parametric down-conversion provide a robust and fertile testing ground for studies of quantum mechanics, non-classical states of light, correlated imaging and quantum information. Over the last 20 years there has been much progress in this area, ranging from technical advances and applications such as quantum imaging to investigations of fundamental aspects of quantum physics such as complementarity relations, Bell's inequality violation and entanglement. The field has grown immensely: a quick search shows that there are hundreds of papers published in this field. The objective of this article is to review the building blocks and major theoretical and experimental advances in the field, along with some possible technical applications and connections to other research areas., Comment: 116 pages, 35 figures. To appear in Physics Reports

We demonstrate experimentally how orbital-angular-momentum entanglement of two photons evolves under influence of atmospheric turbulence. We find that the quantum channel capacity is surprisingly robust: Its typical horizontal decay distance is of the order of 2 kilometers, demonstrating the potential of photonic orbital angular momentum for free-space quantum communication in a metropolitan environment., Comment: 4 pages, 5 figures

In this work we study the transverse spatial correlation of the pair of photons generated via the process of spontaneous parametric frequency down-conversion, in periodically poled non-linear crystals illuminated by a pulsed laser beam. It is well known that the two-photon state generated in quasi-phase matching (QPM) configurations depends explicitly on the characteristics of the pump beam, on the crystal modulated non-linearity, and on the detection geometry. This has allowed the development of several techniques for controlling the biphoton spectral and spatial properties. Here we discuss another technique for implementing the spatial entanglement modification in QPM gratings. We show, theoretically and experimentally, that in nearly collinear geometries, the spatial shape modulation of the pump beam allows for the control of the biphoton transverse spatial correlation.

We present a detailed account of the two-photon states generated by SPDC in both type I and type II phase matching, including the effects of anisotropy of the nonlinear medium and the frequency spread of the down-converted fields. Accurate as well as simplified expressions are derived for type I and type II phase matching in the context of Fourier Optics. The main results are compared with experimental data available in the literature, showing good agreement in all cases., Comment: 11 pages 16 figures

We show that the well known geometric phase, the Gouy phase in optics can be defined for matter waves in vacuum as well. In particular we show that the underlying physics for the "matter waves" Gouy phase is the generalized Schroedinger-Robertson uncertainty principle, more specifically, the off diagonal elements of the covariance matrix. Recent experiments involving the diffraction of fullerene molecules and the uncertainty principle are shown to be quantitatively consistent with the existence of a Gouy phase for matter waves., Comment: 9 pages, 3 figures

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models., Comment: v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1 and tomographic results were included, Propostion 2 was removed and the references were fixed

This paper has been withdrawn due to a crucial theoretical error., Comment: This paper has been withdrawn

This paper has been withdrawn due to a crucial theoretical and experimental error., Comment: This paper has been withdrawn

We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam-splitter exit is calculated. In the regime where the cavity length are larger than the one-photon coherence length, photon coalescence and anti-coalescence interference is observed. Feynman's path diagrams for the indistinguishable processes that lead to quantum interference are presented. As application for the Hong-Ou-Mandel interferometer with two cavities, it is discussed the construction of an optical XOR gate.

Controlling the pump beam transverse profile in multimode Hong-Ou-Mandel interference, we generate a ''localized" two-photon singlet state, in which both photons propagate in the same beam. This type of multi-photon singlet beam may useful in quantum communication to avoid decoherence. We show that although the photons are part of the same beam, they are never in the same plane wave mode, which is characterized by spatial antibunching behavior in the plane normal to the propagation direction., Comment: 4 pages, 4 figures

We show that the transfer of the plane wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum., Comment: 6 pages, 5 figures

We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong-Ou-Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information., Comment: 20 pages, 14 figures, Brief Review to be published in Modern Physics Letters B

We report an experiment to generate maximally entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D-slits in the arms of the twin fotons define the qudit space. By manipulating the pump beam correctly the twin photons will pass only by symmetrically opposite slits, generating entangled states between these differents paths. Experimental results for qudits with D=4 and D=8 are shown. We demonstrate that the generated states are entangled states., Comment: 04 pages, 04 figures

We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and non-maximally entangled pure states of first order Hermite-Gaussian modes., Comment: 9 pages, 4 figures. Corrections made as per referee comments, references updated. Submitted PRA

We propose a simple scheme for complete Bell-state measurement of photons using hyperentangled states - entangled in multiple degrees of freedom. In addition to hyperentanglement, our scheme requires only linear optics and single photon detectors, and is realizable with current technology. At the cost of additional classical communication, our Bell-state measurement can be implemented non-locally. We discuss the possible application of these results to quantum dense coding and quantum teleportation.

Conditional interference patterns can be obtained with twin photons from spontaneous parametric down-conversion and the phase of the pattern can be controlled by the relative transverse position of the signal and idler detectors. Using a configuration that produces entangled photons in both polarization and transverse momentum we report on the control of the conditional patterns by acting on the polarization degree of freedom., Comment: Submitted for publication in Optics Communications

We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure classical architecture, no matter how few qubits are available and, therefore, it suggests an easier implementable technology than a pure quantum computer with arbitrary number of qubits., Comment: 5 pages, 4 figures, 2 tables; final version: International Journal of Quantum Information, 1,2(2003)279-288

Many quantum information protocols require a Bell-state measurement of entangled systems. Most optical Bell-state measurements utilize two-photon interference at a beam splitter. By creating polarization-entangled photons with spontaneous parametric down-conversion using a first-order Hermite-Gaussian pump beam, we invert the usual interference behavior and perform an incomplete Bell-state measurement in the coincidence basis. We discuss the possibility of a complete Bell-state measurement in the coincidence basis using hyperentangled states [Phys. Rev. A, \textbf{58}, R2623 (1998)]., Comment: 5 pages, 5 figures

We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging., Comment: 4 pages, 6 figures, submitted to PRL

We study theoretical and experimentally the propagation of the angular spectrum of the light produced in the up-conversion process. The connection between the angular spectrum of the fundamental and the second harmonic is derived and measured. We show that even though they are connected, it is not possible to directly transfer images from the fundamental to the second harmonic., Comment: Submitted for publication in Phys. Rev. A

We report an interference experiment that shows transverse spatial antibunching of photons. Using collinear parametric down-conversion in a Young-type fourth-order interference setup we show interference patterns that violate the classical Schwarz inequality and should not exist at all in a classical description., Comment: 4 pages, 7 figures

The theoretical framework behind a recent experiment by Nogueira et. al. [Phys. Rev. Lett. 86}, 4009 (2001)] of spatial antibunching in a two-photon state generated by collinear type II parametric down-conversion and a birefringent double-slit is presented. The fourth-order quantum correlation function is evaluated and shown to violate the classical Schwarz-type inequality, ensuring that the field does not have a classical analog. We expect these results to be useful in the rapidly growing fields of quantum imaging and quantum information., Comment: 5 pages, 3 figures. Minor changes made, accepted for publication in PRA

We report a quantum eraser experiment which actually uses a Young double-slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert and Walther. One photon of an entangled pair is incident on a Young double-slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the interference pattern. To recover interference, we measure the polarization of the other entangled photon. In addition, we perform the experiment under delayed erasure circumstances., Comment: 7 pages, 9 figures, Submitted to Phys. Rev. A

The intensity transverse profile of the light produced in the process of stimulated down-conversion is derived. A quantum-mechanical treatment is used. We show that the angular spectrum of the pump laser can be transferred to the stimulated down-converted beam, so that images can also be transferred from the pump to the down-converted beam. We also show that the transfer can occur from the stimulating beam to the down-converted one. Finally, we study the process of diffraction through an arbitrarily shaped screen. For the special case of a double-slit, the interference pattern is explicitly obtained. The visibility for the spontaneous emitted light is in accordance with the van Cittert - Zernike theorem for incoherent light, while the visibility for the stimulated emitted light is unity. The overall visibility is in accordance with previous experimental results.

We show that the first experiment with double-slits and twin photons detected in coincidence can be understood as a quantum eraser. The ``which path'' information is erased by transverse indistinguishability obtained by means of mode filtering in the twin conjugated beam. A delayed choice quantum eraser based on the same scheme is proposed., Comment: Submitted for publication in Optics Communications