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:0906.3273 · Journal of Physics B Atomic Molecular and Optical Physics

Gaussian modelling and Schmidt modes of SPDC biphoton states

Mikhail Vladimirovich Fedorov, J. M. Mikhailova, P. A. Volkov

Published Aug 12, 2009• 75 citations
arXivHTMLPDF

Abstract

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long.
DOI
10.1088/0953-4075/42/17/175503

Related papers

Biphoton wave packets in parametric down-conversion: Spectral and temporal structure and degree of entanglement

J. M. Mikhailova, P. A. Volkov, Mikhail Vladimirovich Fedorov

We investigate spectral and temporal features and entanglement of biphoton wave packets formed in spontaneous parametric down-conversion with a pulsed laser pump. The degree of entanglement is characterized by the experimentally measurable parameter $R$ defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration $\ensuremath{\tau}$. The function $R(\ensuremath{\tau})$ is shown to have a minimum and even in the minimum, at rather natural conditions, the degree of entanglement is found to be very high $({R}_{\mathrm{min}}=73)$. The Schmidt number $K$ is found analytically for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of $R$ and $K$ are found to be identical and numerical coefficients are found to be rather close. Two-time temporal wave function of a biphoton state is investigated in detail, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter ${R}_{t}$ (defined as the ratio of durations of the single-particle and coincidence signals) is shown to be very close to the Schmidt number $K$.

Physical Review A•Dec 16, 2008•99 citations

Schmidt Modes and the Time-Dependent Wavefunction of a Broadband Biphoton Field

Pavel A. Prudkovskii

The wavefunction of a broadband biphoton field arising in parametric down-conversion in an aperiodically polarized nonlinear crystal with a linear chirp under the action of a short pump pulse has been studied theoretically. The form of Schmidt modes has been determined in both the spectral and temporal representations. The dependence of the number of Schmidt modes on the duration of the pump pulse has been found and it has been shown that it is minimal at a quite short duration of the pump pulse of about 100 fs. The form of the wavefunction of biphotons in the time representation has been determined and it has been examined how the region of maximum correlation between the detection times of the down-converted signal and idler photons changes under the variation of the duration of the pump pulse. It has been shown that the maximum of the time correlation function of the signal and idler radiation intensities is significantly asymmetric. Its sharper edge in the case of sufficiently long pump pulses has a small width shorter than 30 fs and can be used to sy-nchronize events even without the compensation of the dispersion spreading of wave packets of the biphoton field.

Journal of Experimental and Theoretical Physics Letters•Nov 1, 2022•0 citations

Schmidt number for X-entanglement of photon pairs

D. B. Horoshko, Giuseppe Patera, A. Gatti +1 more

We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase- matching taking into consideration a major part of the broad spectral and angular bandwidth of the down- converted light. We derive an analytical expression for the Schmidt number as a function of the filter bandwidth in the limit of spectrally narrow pump.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 21, 2012•0 citations

Spontaneous parametric down-conversion using a pulse train

Amitabh Joshi, Shoukry S. Hassan

The process of spontaneous parametric down-conversion (SPDC) is studied for the case in which the pump is a train of pulses. Effects of such a train of pulses (equivalent to a frequency comb) on degenerate collinear type-II SPDC and degenerate collinear type-I SPDC are analyzed using the probability of photon coincidence counts and compared with the case when the medium is pumped by a single pulse.

Journal of Nonlinear Optical Physics & Materials•Sep 1, 2014•0 citations

Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone

James Schneeloch, John C Howell

Abstract As a tutorial to the spatial aspects of spontaneous parametric downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.

arXiv:1502.06996•Journal of Optics•Apr 4, 2016•142 citations

Introduction to the Transverse Spatial Correlations in Spontaneous Parametric Down-Conversion through the Biphoton Birth Zone

James Schneeloch, John C. Howell

As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.

•Jan 16, 2016•111 citations
We investigate spectral and temporal features and entanglement of biphoton wave packets formed in spontaneous parametric down-conversion with a pulsed laser pump. The degree of entanglement is characterized by the experimentally measurable parameter RRR defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration $\ensuremath{\tau}$. The function $R(\ensuremath{\tau})$ is shown to have a minimum and even in the minimum, at rather natural conditions, the degree of entanglement is found to be very high (Rmin=73)({R}_{\mathrm{min}}=73)(Rmin​=73). The Schmidt number KKK is found analytically for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of RRR and KKK are found to be identical and numerical coefficients are found to be rather close. Two-time temporal wave function of a biphoton state is investigated in detail, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter Rt{R}_{t}Rt​ (defined as the ratio of durations of the single-particle and coincidence signals) is shown to be very close to the Schmidt number KKK.
The wavefunction of a broadband biphoton field arising in parametric down-conversion in an aperiodically polarized nonlinear crystal with a linear chirp under the action of a short pump pulse has been studied theoretically. The form of Schmidt modes has been determined in both the spectral and temporal representations. The dependence of the number of Schmidt modes on the duration of the pump pulse has been found and it has been shown that it is minimal at a quite short duration of the pump pulse of about 100 fs. The form of the wavefunction of biphotons in the time representation has been determined and it has been examined how the region of maximum correlation between the detection times of the down-converted signal and idler photons changes under the variation of the duration of the pump pulse. It has been shown that the maximum of the time correlation function of the signal and idler radiation intensities is significantly asymmetric. Its sharper edge in the case of sufficiently long pump pulses has a small width shorter than 30 fs and can be used to sy-nchronize events even without the compensation of the dispersion spreading of wave packets of the biphoton field.
Abstract As a tutorial to the spatial aspects of spontaneous parametric downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.
As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.