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arXiv:0802.3131 · Journal of Modern Optics

Properties of entangled photon pairs generated by a CW laser with small coherence time: theory and experiment

S. Cialdi, F. Castelli, Matteo G. A. Paris

Published Jan 16, 2009• 18 citations
arXivHTMLPDF

Abstract

The generation of entangled photon pairs by parametric down-conversion from solid state CW lasers with small coherence time is theoretically and experimentally analyzed. We consider a compact and low-cost setup based on a two-crystal scheme with Type-I phase matching. We study the effect of the pump coherence time over the entangled state visibility and over the violation of Bell's inequality, as a function of the crystal length. The full density matrix is reconstructed by quantum tomography. The proposed theoretical model is verified using a purification protocol based on a compensation crystal.

DOI
10.1080/09500340802187332

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The generation of entangled photon pairs by parametric down-conversion from solid state CW lasers with small coherence time is theoretically and experimentally analyzed. We consider a compact and low-cost setup based on a two-crystal scheme with Type-I phase matching. We study the effect of the pump coherence time over the entangled state visibility and over the violation of Bell's inequality, as a function of the crystal length. The full density matrix is reconstructed by quantum tomography. The proposed theoretical model is verified using a purification protocol based on a compensation crystal.
We address the generation of entangled photon pairs by parametric downconversion from solid state cw lasers with small coherence time. We consider a compact and low-cost setup based on a two-crystal scheme with type-I phase matching. We reconstruct the full density matrix by quantum tomography and analyze in detail the entanglement properties of the generated state as a function of the crystal's length and the coherence time of the pump. We verify the possibility to improve the visibility using a purification protocol based on a compensation crystal.
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.
Summary form only given. We have experimentally demonstrated that the two-photon probability amplitudes of photon pairs generated using spontaneous parametric down conversion from separate nonlinear crystals, under the conditions outlined above, remain independent and cannot be used to engineer more complex quantum states. The spontaneous nature of the down-conversion process prevents pairs of photons generated in unconnected regions of interaction from having a stable phase relationship between components of their probability amplitudes. The experiment has been performed using two BaB/sub 2/O/sub 4/ nonlinear crystals, of lengths 0.5 mm and 1.5 mm respectively. They have been cut to generate phase-matched type-II collinear down conversion.
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.
The purpose of this project is to set up a system for creating entangled photon pairs for use in various quantum mechanical experiments, including the testing of Bell’s inequalities which demonstrates the fundamentally indeterministic nature of quantum mechanics. The photons are created by pumping a beta barium borate crystal with 405 nm laser light then, due to a process called type 1 spontaneous parametric down conversion, a single pump photon can be converted into two 810 nm photons in an entangled state. In the same lab, a similar set up has already been achieved using a 474 nm pump laser, but by using a shorter wave length, a higher detection rate can be achieved. Two collimators are set up to collect the down converted photons and send them to two photon counting modules. The collimators need to be positioned precisely to detect any down converted photons because they emerge from the crystal in a narrow beam that is at an angle with respect to the pump beam and only a miniscule fraction of pump photons are down converted. The angle at which the down converted photons emerge is a function of how the crystal is prepared and the polarization orientation of the pump beam. It was calculated using a program by National Institute of Standards and Technology.
Two spatially separated type-I nonlinear crystals are pumped by femtosecond laser pulses to create entangled photon pairs in the process of spontaneous parametric down-conversion. The two-photon entangled state exhibits high-visibility quantum interference for both polarization and space-time variables without the need of stringent spectral postselection by using narrow-band filters. The visibility is insensitive to the thickness of the crystals, unlike in the case of pulse pumped type-II parametric down-conversion; therefore the intensity can be easily increased by using thick nonlinear crystals. This method will be indispensable in experiments that require a pulsed source of entangled photon pairs, such as generation of multiphoton entangled states, quantum teleportation, and quantum communications.