Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2006.12271 · Journal of the Optical Society of America B

Dependence of the photon statistics of down-converted field-modes on the photon statistics of the pump field-mode

Nilakantha Meher, Anand K. Jha

Published Jun 18, 2020• 5 citations
arXivHTMLPDF

Abstract

Using the zero time-delay second-order correlation function for studying photon statistics, we investigate how the photon statistics of field-modes generated by the parametric down-conversion (PDC) process depends on the photon statistics of the pump field-mode. We derive general expressions for the zero time-delay second-order correlation function of the down-converted field-modes for both multi-mode and single-mode PDC processes. We further study these expressions in the weak down-conversion limit. We show that for a two-photon two-mode PDC process, in which a pump photon splits into two photons into two separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to twice that of the pump field-mode. Furthermore, for an n -photon n -mode down-conversion process, in which a pump photon splits into n photons into n separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to 2 ( n − 1 ) times that of the pump field- mode. However, in contrast to multi-mode PDC processes, for a single-mode PDC process, in which a pump photon splits into two or more photons into a single mode, the zero time-delay second-order correlation function of the down-converted field-mode is not proportional to that of the pump in the weak down-conversion limit. Nevertheless, we find it to be inversely proportional to the average number of photons in the pump field-mode.

DOI
10.1364/josab.396618

Related papers

Photon statistics in parametric down-conversion process

Nilakantha Meher, Anand K. Jha

Using the zero time-delay second-order correlation function, we investigate how the photon statistics of the field-modes generated by parametric down-conversion (PDC) process depends on photon statistics of the pump field-mode.

Frontiers in Optics•Jan 1, 2020•0 citations

Time-resolved second-order autocorrelation function of parametric down-conversion

D. B. Horoshko, Shivang Srivastava, Filip Sośnicki +4 more

We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.

arXiv:2502.07691•Physical Review A•Jul 14, 2025•2 citations

Transfer of temporal coherence in parametric down-conversion

Girish Ashok Kulkarni, Prashant Kumar, Anand K. Jha

We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.

arXiv:1704.01786•Journal of the Optical Society of America B•Jul 17, 2017•16 citations

Theory of parametric frequency down conversion of light

C. K. Hong, L. Mandeļ

A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.

Physical Review A•Apr 1, 1985•464 citations

Multiphoton correlations in parametric down-conversion and their measurement in the pulsed regime

Olga Aleksandrovna Ivanova, T. Sh. Iskhakov, Alexander N. Penin +1 more

We consider normalised intensity correlation functions (CFs) of different orders for light emitted via parametric down-conversion (PDC) and their dependence on the number of photons per mode. The main problem in measuring such correlation functions is their extremely small width, which considerably reduces their contrast. It is shown that if the radiation under study is modulated by a periodic sequence of pulses that are short compared to the CF width, no decrease in the contrast occurs. A procedure is proposed for measuring normalised CFs of various orders in the pulsed regime. For nanosecond-pulsed PDC radiation, normalised second-order CF is measured experimentally as a function of the mean photon number.

Quantum Electronics•Oct 31, 2006•62 citations

Photon statistics in parametric interaction of three waves

Yu A Il'inskiĭ, Давид Николаевич Клышко, Vera M. Petnikova

The parametric approximation is used in a statistical analysis of the frequency conversion of an optical field by a noncentrosymmetric crystal which couples an input wave of frequency 0 < ω < ωL/2 to output waves of frequency ω+nωL(n = 0, ±1, ±2, ...; ωL is the pump frequency). An expression is obtained for the characteristic function of the output field which is described in terms of a matrix of the coupling coefficients in the case of Gaussian (displaced) statistics of the input field with independent modes. The mutual statistics of the output waves with n ≥ 0 and n' < 0 is not Gaussian but corresponds, in the lowest approximation with respect to the pump wave and in the absence of the input field, to a spontaneous (direct or cascade) decay of pump photons into photon pairs. The intensity of the radiation represented by the n ≥ 0 modes is equal to the intensity of the radiation emerging from a classical converter which receives one photon in each mode with n' < 0. The special case of three interacting modes with n = −1, 0, 1 (upconverter or light modulator) is considered in detail. The noise intensities and correlations between the numbers of photons in two and three modes are found for this case, and the spatial-temporal correlation function of the fields of the Stokes (n' = −1) and anti-Stokes (n = 1) frequencies is determined.

Soviet Journal of Quantum Electronics•Nov 30, 1975•6 citations
Using the zero time-delay second-order correlation function for studying photon statistics, we investigate how the photon statistics of field-modes generated by the parametric down-conversion (PDC) process depends on the photon statistics of the pump field-mode. We derive general expressions for the zero time-delay second-order correlation function of the down-converted field-modes for both multi-mode and single-mode PDC processes. We further study these expressions in the weak down-conversion limit. We show that for a two-photon two-mode PDC process, in which a pump photon splits into two photons into two separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to twice that of the pump field-mode. Furthermore, for an n -photon n -mode down-conversion process, in which a pump photon splits into n photons into n separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to 2 ( n − 1 ) times that of the pump field- mode. However, in contrast to multi-mode PDC processes, for a single-mode PDC process, in which a pump photon splits into two or more photons into a single mode, the zero time-delay second-order correlation function of the down-converted field-mode is not proportional to that of the pump in the weak down-conversion limit. Nevertheless, we find it to be inversely proportional to the average number of photons in the pump field-mode.
We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.
We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.
A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.
We consider normalised intensity correlation functions (CFs) of different orders for light emitted via parametric down-conversion (PDC) and their dependence on the number of photons per mode. The main problem in measuring such correlation functions is their extremely small width, which considerably reduces their contrast. It is shown that if the radiation under study is modulated by a periodic sequence of pulses that are short compared to the CF width, no decrease in the contrast occurs. A procedure is proposed for measuring normalised CFs of various orders in the pulsed regime. For nanosecond-pulsed PDC radiation, normalised second-order CF is measured experimentally as a function of the mean photon number.
The parametric approximation is used in a statistical analysis of the frequency conversion of an optical field by a noncentrosymmetric crystal which couples an input wave of frequency 0 < ω < ωL/2 to output waves of frequency ω+nωL(n = 0, ±1, ±2, ...; ωL is the pump frequency). An expression is obtained for the characteristic function of the output field which is described in terms of a matrix of the coupling coefficients in the case of Gaussian (displaced) statistics of the input field with independent modes. The mutual statistics of the output waves with n ≥ 0 and n' < 0 is not Gaussian but corresponds, in the lowest approximation with respect to the pump wave and in the absence of the input field, to a spontaneous (direct or cascade) decay of pump photons into photon pairs. The intensity of the radiation represented by the n ≥ 0 modes is equal to the intensity of the radiation emerging from a classical converter which receives one photon in each mode with n' < 0. The special case of three interacting modes with n = −1, 0, 1 (upconverter or light modulator) is considered in detail. The noise intensities and correlations between the numbers of photons in two and three modes are found for this case, and the spatial-temporal correlation function of the fields of the Stokes (n' = −1) and anti-Stokes (n = 1) frequencies is determined.