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Journal of Lanzhou University of Technology

Two-Photon state function with spontaneous parametric down-conversion and its probability explanation

Xinli Ma

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The comprehensive action of monochromatic flux of pumping photons and quantum vacuum noise on nonlinear crystals without symmetric center is analyzed. The generating origin of the light field with SPDC expounded with the interaction of the pumping photons with the nonlinear crystals. The mathematic expression of two-photon state with SPDC is derived and its probability explanation is given.

Related papers

Study on generation mechanism and state function of spontaneous parametric down-conversion light field

Xinli Ma

Based on analyzing the interaction of pumping photons and a nonlinear crystal with no center of symmetry, an explanation about the generation mechanism of spontaneous parametric down-conversion (SPDC) light field was put forward. Then state function of SPDC biphoton light field was derived and a probability explanation was given.

Chinese Journal of Quantum Electronics•Jan 1, 2004•0 citations

Summarization of Investigation in Mechanism of Spontaneous Parametric Down-Conversion and Its Applications

Jianjun Li

Spontaneous parametric down-conversion is a non-classical optical field,which is generated by the interaction on nonlinear crystal of monochromatic flux of pumping photons and quantum vacuum noise.In this paper,the generation mechanism of spdc light field is interpreted by theory of quantum mechanics;the interpretation by classical theory is also given here.The paper also introduces roundly the non-classical characteristics and application advances of spdc light field in laser,remote sensing and quantum communication.Last but not least,SPDC′s application prospect and its developing direction are also given in this paper.

Acta Sinica Quantum Optica•Jan 1, 2006•0 citations

Quantum interference using ultrafast spontaneous parametric down-conversion

Mete Atatüre, Alexander V. Sergienko, Bradley M. Jost +2 more

Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations

Simulating the photon spatial distribution in spontaneous parametric down conversion (SPDC)

Sivan Trajtenberg‐Mills, Aviv Karnieli, Noa Voloch‐Bloch +4 more

We present a method for simulating the spatial distribution of the SPDC generated state based on classical equations. This enables the design of nonlinear crystals and pumping conditions for generating non-classical light with desired properties.

Quantum Information and Measurement (QIM)•Jan 1, 2019•0 citations

Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion

James Schneeloch, Samuel H. Knarr, Daniela F. Bogorin +6 more

Abstract As a tutorial, we examine the absolute brightness and number statistics of photon pairs generated in spontaneous parametric down-conversion (SPDC) from first principles. In doing so, we demonstrate how the diverse implementations of SPDC can be understood through a single common framework, and use this to derive straightforward formulas for the biphoton generation rate (pairs per second) in a variety of different circumstances. In particular, we consider the common cases of both collimated and focused Gaussian pump beams in a bulk nonlinear crystal, as well as in nonlinear waveguides and micro-ring resonators. Furthermore, we examine the number statistics of down-converted light using a non-perturbative approximation (the multi-mode squeezed vacuum), to provide quantitative formulas for the relative likelihood of multi-pair production events, and explore how the quantum state of the pump affects the subsequent statistics of the down-converted light. Following this, we consider the limits of the undepleted pump approximation, and conclude by performing experiments to test the effectiveness of our theoretical predictions for the biphoton generation rate in a variety of different sources.

arXiv:1807.10885•Journal of Optics•Feb 8, 2019•88 citations

Criteria on quantum fluctuations of vacuum and photons influence in Spontaneous-Parametric Down-Conversion and Four-Wave-Mixing

Benoît Boulanger, Gaspar Mougin-Trichon, Véronique Boutou

This article is a theoretical and quantitative exploration of the limit regarding the pump intensity between the two regimes of spontaneous-parametric down-conversion (SPDC) as well as of four-wave-mixing (FWM) in the framework of a semi-classical model and analytical calculations. A dimensionless parameter has been defined at this limit, corresponding to the photon-pairs flux per frequency unit: it has been found equal to 0.369. The ratio between the electric field of the generated photons and the quantum fluctuations of vacuum calculated at the limit is equal to 1.718. These quantitative results confirm that below the limit, the pump photon splitting leading to photon-pairs can be considered as spontaneous, i.e. mainly seeded by the quantum fluctuations of vacuum, while it is stimulated by the generated signal and idler photons above the limit, which corresponds to an optical parametric amplification regime. Our calculations also show that this limit can be easily reached in the case of SPDC according to the typical values of non-linearities and available crystal dimensions. In the case of FWM, it would be only possible in kilometric optical fibers. This corpus is a useful tool box for designing further quantum experiments performed from either side of the limit, as well as at the limit it-self where the influence of the quantum fluctuations of vacuum and of the generated photons should have the same weight. Furthermore, the quantum significance of the numerical values of the two criteria defined here remains to be established, which should motivate future theoretical quantum studies.

quant-pharXiv:2601.08349•Jan 14, 2026•0 citations
The comprehensive action of monochromatic flux of pumping photons and quantum vacuum noise on nonlinear crystals without symmetric center is analyzed. The generating origin of the light field with SPDC expounded with the interaction of the pumping photons with the nonlinear crystals. The mathematic expression of two-photon state with SPDC is derived and its probability explanation is given.
Spontaneous parametric down-conversion is a non-classical optical field,which is generated by the interaction on nonlinear crystal of monochromatic flux of pumping photons and quantum vacuum noise.In this paper,the generation mechanism of spdc light field is interpreted by theory of quantum mechanics;the interpretation by classical theory is also given here.The paper also introduces roundly the non-classical characteristics and application advances of spdc light field in laser,remote sensing and quantum communication.Last but not least,SPDC′s application prospect and its developing direction are also given in this paper.
Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.
Abstract As a tutorial, we examine the absolute brightness and number statistics of photon pairs generated in spontaneous parametric down-conversion (SPDC) from first principles. In doing so, we demonstrate how the diverse implementations of SPDC can be understood through a single common framework, and use this to derive straightforward formulas for the biphoton generation rate (pairs per second) in a variety of different circumstances. In particular, we consider the common cases of both collimated and focused Gaussian pump beams in a bulk nonlinear crystal, as well as in nonlinear waveguides and micro-ring resonators. Furthermore, we examine the number statistics of down-converted light using a non-perturbative approximation (the multi-mode squeezed vacuum), to provide quantitative formulas for the relative likelihood of multi-pair production events, and explore how the quantum state of the pump affects the subsequent statistics of the down-converted light. Following this, we consider the limits of the undepleted pump approximation, and conclude by performing experiments to test the effectiveness of our theoretical predictions for the biphoton generation rate in a variety of different sources.
This article is a theoretical and quantitative exploration of the limit regarding the pump intensity between the two regimes of spontaneous-parametric down-conversion (SPDC) as well as of four-wave-mixing (FWM) in the framework of a semi-classical model and analytical calculations. A dimensionless parameter has been defined at this limit, corresponding to the photon-pairs flux per frequency unit: it has been found equal to 0.369. The ratio between the electric field of the generated photons and the quantum fluctuations of vacuum calculated at the limit is equal to 1.718. These quantitative results confirm that below the limit, the pump photon splitting leading to photon-pairs can be considered as spontaneous, i.e. mainly seeded by the quantum fluctuations of vacuum, while it is stimulated by the generated signal and idler photons above the limit, which corresponds to an optical parametric amplification regime. Our calculations also show that this limit can be easily reached in the case of SPDC according to the typical values of non-linearities and available crystal dimensions. In the case of FWM, it would be only possible in kilometric optical fibers. This corpus is a useful tool box for designing further quantum experiments performed from either side of the limit, as well as at the limit it-self where the influence of the quantum fluctuations of vacuum and of the generated photons should have the same weight. Furthermore, the quantum significance of the numerical values of the two criteria defined here remains to be established, which should motivate future theoretical quantum studies.