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Journal of Physics A Mathematical and General

Enhanced generation rate of the coherent entanglement photon pairs in parametrical down-conversion

N. A. Enaki, Viorel Ciornea

Published May 24, 2001• 3 citations
Publisher

Abstract

The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with a nonlinear dispersive medium is studied in this paper. Taking into account the second- and third-order susceptibility tensors of the crystal, it is demonstrated that in the good cavity approximation the bistable behaviour of the two-photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of anharmonicity terms in polarization.

DOI
10.1088/0305-4470/34/22/302

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The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with a nonlinear dispersive medium is studied in this paper. Taking into account the second- and third-order susceptibility tensors of the crystal, it is demonstrated that in the good cavity approximation the bistable behaviour of the two-photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of anharmonicity terms in polarization.
The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with nonlinear dispersive medium is studied in this paper. Taking into account the second and third order of the susceptibility tensor of the crystal, it is demonstrated that in good cavity approximation the bistable behavior of the two photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of an harmonicity terms in polarization.
A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
The effect of the quantum properties of light on nonlinear processes has been well studied theoretically. It has been shown that the efficiency of n-photon nonlinear processes in many cases scales as the normalized n-th order correlation function. For light with high intensity correlation function, the efficiency of the n-th harmonic generation will be considerably higher than for coherent light. The experimental observation of this effect remained difficult until recently, because of the absence of bright sources with strong and fast intensity fluctuations. For the experimental demonstration of statistical effects in optical harmonic generation we use as a pump the radiation of high-gain parametric down conversion. Such light shows quantum properties (e.g. quadrature or two-mode squeezing) and has large number of photons in one mode. The normalized n-th order correlation function for this light is (2n - 1)!!, which makes it more attractive for nonlinear processes than both coherent and thermal light. For the generation of optical harmonics we used broadband parametric down conversion around frequency-degeneracy (1600 nm) produced in 1cm BBO crystal from Ti:Sapphire laser (800 nm, 1.6ps, 5kHz, 3W mean intensity). Due to spectral filtering and post-selection technique we could vary the statistics of light from coherent to super-bunched, which allowed us to demonstrate the efficiency enhancement for second-, third-, and fourth-harmonic generation. The obtained experimental results show a good agreement with the theory.
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.
The harnessing of the nonclassical properties in photon pairs generated by the process of Spontaneous Parametric Down Conversion (SPDC) to enhance two-photon interactions has long intrigued researchers. Their use in light-matter interactions has been proven to improve efficiency either by increasing the rate of generation or by suppressing noise. Namely, the processes of Entangled Sum Frequency Generation (eSFG) and Entangled Two Photon Absorption (eTPA) have been shown to produce more photons when stimulated with entangled photons than the classical versions of the effects. This has only been effective so far at very low intensities, which, alongside the inability to reproduce previous experimental results, has caused debates about the usefulness of the effect. In the presented work, I aim to shed light on the topic by employing a carefully crafted source of entangled photon pairs to improve two-photon effects. I attempt to demonstrate, through a series of experiments, that the quantum enhancement can be observed at an order of magnitude higher than previously thought possible. To solidify the results, a direct comparison of the quantum effect was conducted by investigating the performance of the phenomenon when it is stimulated by classical radiation from a laser. Our results confirm a quantum improvement in a regime previously considered impossible, and they enabled us to examine the ramifications of the effect on imaging. By doing so, we consider real-life microscopy applications, and therefore, we can set limits to the effect.
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.