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Physical Review A

Quantum delocalization in photon-pair generation

Kayn A. Forbes, Jack Ford, Garth A. Jones, Davıd L. Andrews

Published Aug 23, 2017• 6 citations
Publisher

Abstract

The generation of correlated photon pairs is a key to the production of entangled quantum states, which have a variety of applications within the area of quantum information. In spontaneous parametric down-conversion---the primary method of generating correlated photon pairs---the associated photon annihilation and creation events are generally thought of as being colocated: The correlated pair of photons is localized with regards to the pump photon and its positional origin. A detailed quantum electrodynamical analysis highlights a mechanism exhibiting the possibility of a delocalized origin for paired output photons: The spatial extent of the region from which the pair is generated can be much larger than previously thought. The theory of both localized and nonlocalized degenerate down-conversion is presented, followed by a quantitative analysis using discrete-volume computational methods. The results may have significant implications for quantum information and imaging applications, and the design of nonlinear optical metamaterials.

DOI
10.1103/physreva.96.023850

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The generation of correlated photon pairs is a key to the production of entangled quantum states, which have a variety of applications within the area of quantum information. In spontaneous parametric down-conversion---the primary method of generating correlated photon pairs---the associated photon annihilation and creation events are generally thought of as being colocated: The correlated pair of photons is localized with regards to the pump photon and its positional origin. A detailed quantum electrodynamical analysis highlights a mechanism exhibiting the possibility of a delocalized origin for paired output photons: The spatial extent of the region from which the pair is generated can be much larger than previously thought. The theory of both localized and nonlocalized degenerate down-conversion is presented, followed by a quantitative analysis using discrete-volume computational methods. The results may have significant implications for quantum information and imaging applications, and the design of nonlinear optical metamaterials.
The achievement of optimum conversion efficiency in conventional spontaneous parametric down-conversion requires consideration of quantum processes that entail multisite electrodynamic coupling, actively taking place within the conversion material. The physical mechanism, which operates through virtual photon propagation, provides for photon pairs to be emitted from spatially separated sites of photon interaction; occasionally pairs are produced in which each photon emerges from a different point in space. The extent of such nonlocalized generation is influenced by individual variations in both distance and phase correlation. Mathematical analysis of the global contributions from this mechanism provides a quantitative measure for a degree of positional uncertainty in the origin of down-converted emission.
Efficient Generation of Entangled Photon-Pairs The first experiments with correlated photons have been performed in the context of EPR-Bell experiments on the realistic and local properties of quantum mechanics. The source used there produced pairs of polarization entangled photons from a 2-photon decay of Calcium atoms. The technical requirements of these experiments were high (vacuum systems, stronge dye-lasers, etc.) whereas the efficiency of the source was quite low. An important step forward was the introduction of spontaneous parametric down conversion (SPDC), which has become the most common source in quantum optics for generating correlated or entangled photon pairs. In this process photons of an intense pump laser convert to photon pairs in an optical nonlinear crystal. Conservation of energy and momentum leads to strong correlations between the generated photons. With this kind of two-photon source it was possible to realize or improve many experiments on the foundations of quantum mechanics addressing the EPR-Paradoxon and in the new field of quantum information. But again, more advanced experiments and applications suffer from the limited ef- ficiency of the fluorescence process. Many photon pairs are lost by spatial and spectral filtering, which is necessary to achieve polarization entanglement and long coherence times. Different techniques have been implemented to increase the number of photon pairs using two-crystal arrangements, focusing techniques or periodically poled crystals. Most of these methods have the disadvantage that no entangled photons have been observed. It is the aim of this work to increase the yield and to improve the mode definition of entangled photon pairs generated by resonant enhancement of the pump mode and the fluorescence modes. As a first step a linear cavity for the pump mode was realized. Since the conversion probability is proportional to the pump power it was possible to increase the photon pair count rate by factor of 7 over the previous source. Besides the possibility of further improvement on already established pair correlation experiments, such an enhancement allows to build a compact source for photon pairs, in which an expensive argon-ion laser is replaced by a cheap diode laser. Among other applications such sources are of strong interest for quantum cryptography. 3 In many quantum information experiments optical fibers are use to carry the photons over long distance. Therefore, light from the parametric down-conversion source has to be efficiently coupled into fibers. In the second part we report on a new method to optimize collection efficiency by matching the angular distribution of the parametric fluorescence to the spatial mode of an optical fiber. By using this technique, we detected 366500 polarization-entangled photon pairs per second in the near-infrared region in single-mode optical fibers for 465 mW pump power (at 351.1 nm) with a 2 mm BBOcrystal. The entanglement of the photon pairs was verified by measuring polarization correlations of more than 96% in a HV-basis and in a ±45◦-basis. To our knowledge, such enormous count rates of highly entangled photon pairs have not been reached yet with any other technique. In the third part of this thesis we investigated the process of parametric downconversion in a cavity which is resonant to certain longitudinal down-conversion modes only. The idea of placing the parametric down-conversion source inside a cavity is not new. Such a device is usually referred to as a single or double resonant optical parametric oscillator (OPO) and is mainly used to generate squeezed quantum states. In that kind of application the system is operating close to but still under the threshold of oscillation. In our application the situation is quite different. The system is operating far below threshold so that mainly spontaneous emission occurs. In that mode correlations between single photons can still be observed. But bouncing the light back and forth inside the cavity increases the interaction length and hence enhances the signal levels of the down-conversion fields. Further, by resonating two certain modes only, the bandwidth is reduced by orders of magnitude and the coherence time is found to be inverse proportional to the bandwidth. A similar experiment has already been realized with a type-I parametric down-converter in the resonator. We have tried to realize a compact double resonant OPO far below threshold with a type-II parametric down-converter in a high-finesse cavity to realize a bright source of entangled photon pairs with extremely narrow bandwidth.
Summary form only given. Correlated photons are a key ingredient of many experiments testing the foundations of quantum mechanics and in quantum information processing. Many of these experiments harness entanglement by means of the nonclassical interference of photon pairs. A critical issue for such experiments is the mode matching of the photonic wave packets. Spontaneous parametric down-conversion is a well-established and practical method for generating pairs of correlated photons. High visibility interference of photon pairs generated by down-conversion in bulk crystals, a standard source for this type of experiments, can be achieved only by significant spatial filtering, which dramatically reduces the useful fraction of photon pairs. It also reduces the correlations between the presence of photons, thus opening for example the efficiency loophole in tests of Bell's inequalities. Nonlinear waveguides, compared to bulk crystals, offer several advantages as a source of correlated photon pairs. Most importantly, the waveguide structure provides a means to control precisely the spatial characteristics of generated photons, because of the well-defined transverse modes of the guide. in addition, nonlinear waveguides offer both higher pair production rates by utilizing the technique of quasiphase matching, and possibilities for spectral mode engineering.
A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.
Scattering of non-classical light is enabling new ways to study and control photon transport. However, advances in this field often rely on simplifying assumptions regarding the quantum light's generation and its source. In this work, we relax some of these assumptions and probe the behavior of entangled photon pairs passing through a disordered layer after being generated by a randomly scattered pump via spontaneous parametric down conversion. We experimentally demonstrate that, even when both the pump and the down-converted photons propagate through a dynamic scattering medium, the pairs maintain a sharp peak in their correlations. A comprehensive theoretical and numerical analysis shows that these correlations persist regardless of when the pairs are generated, whether immediately after the pump is scattered or under other conditions. More specifically, we detail how the shape of the angular correlation depends on the pump's scattering and how it varies with the distance between the pair-generation region and the entrance of the disordered medium. These findings represent a crucial step toward understanding quantum light generation in complex media, and potentially exploiting it for quantum technologies.
We report an experiment to generate and propagate two entangled spatial qudits, [Formula: see text]-dimensional quantum systems, using spontaneous parametric down-conversion. The manipulation, via pump beam, of the transverse spatial correlation between the photon pairs is explored. Inserting apertures with [Formula: see text]-slits in the arms of the down-converted photons, we associate the qudit space with the [Formula: see text] possible paths followed by each photon. Experimental results for qudits with [Formula: see text] and 8 are shown. We demonstrate that the generated states cannot be classically correlated. We also show the propagation of entangled states of spatial qudits. Their free-space distribution is performed at the laboratory scale and the propagated states maintain a high fidelity with their original form.