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Photonics for Quantum (PfQ)

Effect of phase and spatial distinguishability of photon pairs on the entanglement fidelity

Hashir Kuniyil, Kadir Durak

Published Jul 9, 2021• 0 citations
Publisher

Abstract

Polarization entanglement based cryptography uses the photon pairs generated in a spontaneous paramet- ric down-conversion process and guarantees the security through the violation of Bell’s inequality. Certain experimental parameters affects the entanglement fidelity and leads to a possible information leakage. The optical path difference of photons born at different crystals contributes to reduced fidelity, due to the extra birefringence of the nonlinear crystal. Although previous studies suggested methods to erase the distinguishability of photons by introducing compensation crystals, the phase difference, which is due to the lateral ray distribution is not studied. We used two commercially available collection optics; an aspheric and an achromatic lens. With these collection optics, the effect of collection optics on the entanglement fidelity is studied. We developed a simulation of such a system and found that aspheric collection optics is more suitable to achieve high fidelity.

DOI
10.1117/12.2600933

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Polarization entanglement based cryptography uses the photon pairs generated in a spontaneous paramet- ric down-conversion process and guarantees the security through the violation of Bell’s inequality. Certain experimental parameters affects the entanglement fidelity and leads to a possible information leakage. The optical path difference of photons born at different crystals contributes to reduced fidelity, due to the extra birefringence of the nonlinear crystal. Although previous studies suggested methods to erase the distinguishability of photons by introducing compensation crystals, the phase difference, which is due to the lateral ray distribution is not studied. We used two commercially available collection optics; an aspheric and an achromatic lens. With these collection optics, the effect of collection optics on the entanglement fidelity is studied. We developed a simulation of such a system and found that aspheric collection optics is more suitable to achieve high fidelity.
In this report,decoherence sources for entangled photons created by spontaneous parametricdown-conversion phenomenon are studied. The phase and spatial distinguishability of photon pairs from orthogonal crystals reduce the maximum achievable entanglement fidelity. Carefully chosen compensation crystals are used to erase the phase and spatial traces of down-conversion origins. Emission angle of photon pairs also leads to optical path difference and results in phase distinguishability. A realistic scenario is numerically modelled, where the photon pairs with nonzero emission angle gather a phase difference. These pairs can still be collected and manipulated for practical use but the collection optics adds upon the phase difference. Two commercially available optics for collection; aspheric and achromatic lenses are compared. The numerical simulation results are compared with the experimental results to validate the built model for predicting the maximum achievable entanglement fidelity. The results indicate that the fidelity can be accurately estimated with the presented model by inserting the experimental parameters to it. The study is expected to be very useful for preparation and optimization of entangled photon pair sources in critical phase-matching configuration.
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Photon-based entanglement sources, crucial for obtaining entangled states, are typically generated via spontaneous parametric down-conversion. However, birefringence in nonlinear crystals causes spatial or temporal walk-off, reducing entangled photon quality. The theoretical analysis attributes birefringent walk-off to dispersive materials curbed by pre- and post-compensation. We experimentally validate this method, enhancing polarization-entangled photon quality. We measured the Bell state along with a violation of CHSH-Bell's inequality by ∼366 standard deviations (S = 2.623 ± 0.0017). Our approach, simple and stable, does not complicate setups. Its applicability extends to optimizing various entanglement source schemes, aiding optical quantum technologies such as computation, sensing, and communication.
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.
Using the process of spontaneous parametric down-conversion in a two-crystal geometry, we have generated a source of polarization-entangled photon pairs that is more than ten times brighter, per unit of pump power, than previous sources, with another factor of 30 to 75 expected to be readily achievable. We have measured a high level of entanglement between photons emitted over a relatively large collection angle, and over a 10-nm bandwidth. As a demonstration of the source capabilities, we obtained a 242-\ensuremath{\sigma} violation of Bell's inequalities in less than three minutes, and observed near-perfect photon correlations when the collection efficiency was reduced. In addition, both the degree of entanglement and the state purity should be readily tunable.
Quantum computation and quantum communication require sources of entangled photons, especially from low-cost diode lasers. This study considered a polarization entangled photons pulse source produced via a spontaneous parametric down-conversion process in the type-I phase-matching of two nonlinear crystals, incorporating a continuous wave laser diode operating in pulse mode as a pump. The generated photons were measured based on visibility as a function of the pump frequency and collection apertures. A polarization correlation between photon pairs of approximately 93% and a Bell parameter S value of 2.56 ± 0.05 were obtained using the source described here.