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:0910.4929 · Journal of Modern Optics

Multimode spontaneous parametric down-conversion in a lossy medium

Radosław Chrapkiewicz, Wojciech Wasilewski

Published Mar 10, 2010• 6 citations
arXivHTMLPDF

Abstract

We study the process of multimode spontaneous parametric down–conversion (SPDC) in a lossy, one-dimensional waveguide. We propose a description using first-order correlation functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three-wave mixing with ultrashort pump, linear propagation and attenuation, and we are able to divide the evolution into three stages and predict it qualitatively. We find that losses do not destroy the quantum properties of SPDC but stabilize the final state.

DOI
10.1080/09500341003642588

Related papers

Multimode Spontaneous Parametric Down-Conversion in the Lossy Medium

Rados Law Chrapkiewicz, Wojciech Wasilewski

We study the process of multimode spontaneous parametric down–conversion (SPDC) in a lossy, one-dimensional waveguide. We propose a description using first-order correlation functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three-wave mixing with ultrashort pump, linear propagation and attenuation, and we are able to divide the evolution into three stages and predict it qualitatively. We find that losses do not destroy the quantum properties of SPDC but stabilize the final state.

•Jan 1, 2009•6 citations

Spectral and temporal properties of type-II parametric down-conversion: The impact of losses during state generation

Denis A. Kopylov, Michael Stefszky, Torsten Meier +2 more

In this paper, we theoretically study the spectral and temporal properties of pulsed spontaneous parametric down-conversion (SPDC) generated in lossy waveguides. Our theoretical approach is based on the formalism of Gaussian states and the Langevin equation, which is elaborated for weak parametric down-conversion and photon-number-unresolved click detection. Using the example of frequency-degenerate type-II SPDC generated under the pump-idler group-velocity-matching condition, we show how the joint-spectral intensity, mode structure, normalized second-order correlation function, and Hong-Ou-Mandel interference pattern depend on internal losses of the SPDC process. We found that the joint-spectral intensity is almost insensitive to internal losses, while the second-order correlation function shows a strong dependence on them, being different for the signal and idler beams in the presence of internal losses. Based on the sensitivity of the normalized second-order correlation function, we show how its measurement can be used to experimentally determine internal losses.

arXiv:2501.08917•Physical Review Research•Jun 18, 2025•4 citations

Simple way to incorporate loss when modeling multimode-entangled-state generation

Colin Vendromin, Marc M. Dignam

We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations for the time-dependent squeezing parameters and thermal photon numbers of the state. The benefit of this semianalytic approach is that the number of coupled equations scales linearly with the number of modes and is independent of the number of photons generated. With this analytic form of the state, correlation variances are easily expressed as analytic functions of the time-dependent mode parameters. Thus, our solution makes it computationally tractable and relatively straightforward to calculate the generation and evolution of multimode entangled states in multiple coupled, lossy cavities, even when there are a large number of modes and/or photons.

arXiv:2112.12044•Physical Review A•Jun 6, 2022•5 citations

Spontaneous parametric downconversion in waveguides: what's loss got to do with it?

L. G. Helt, Michael J. Steel, John E. Sipe

We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss.Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients.In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator, and we find that this density operator is naturally composed of two photon, one photon, and zero photon contributions.The biphoton probability density, or joint spectral intensity (JSI), associated with the two-photon contribution is determined not only by a phase matching term, but also by a loss matching term.The relative sizes of the loss coefficients within this term lead to three qualitatively different regimes of SPDC JSIs.If either the pump or generated photon loss is much higher than the other, the side lobes of the phase matching squared sinc function are washed out.On the other hand, if pump and generated photon loss are appropriately balanced, the lossy JSI is identical to the lossless JSI.Finally, if the generated photon loss is frequency dependent, the shape of the JSI can be altered more severely, potentially leading to generated photons that are less frequency correlated though also produced less efficiently when compared to photons generated in low-loss waveguides.

arXiv:1407.4219•New Journal of Physics•Jan 27, 2015•32 citations

Theory of spontaneous parametric down-conversion from photonic crystals

A. Nick Vamivakas, Bahaa E. A. Saleh, Alexander V. Sergienko +1 more

An effective-medium approach is used to derive a set of coupled-mode equations describing quadratic parametric interactions in a one-dimensional inhomogeneous medium of finite length. The solutions for both copropagating and counterpropagating interactions are used to study the quantum-mechanical process of spontaneous parametric down-conversion (SPDC). An example is studied in which the inhomogeneous medium is a photonic crystal. The effect that device geometry has on both the efficiency and bandwidth of SPDC is explored. With appropriate design, we find that it is possible not only to enhance the efficiency of SPDC, but also to generate broadband copropagating and narrowband counterpropagating down-converted light. A setup is proposed with the potential to act as a source of entangled photon pairs.

Physical Review A•Oct 14, 2004•36 citations

Spontaneous parametric down conversion in a doubly resonant one-dimensional photonic crystal

Viola Introini, Michael J. Steel, John E. Sipe +2 more

We study spontaneous parametric down conversion (SPDC) in a one-dimensional photonic crystal designed to operate in a doubly resonant configuration, where the frequencies of the pump and the generated photons are both tuned to band-edge resonances. We investigate the spectral correlations of the generated photons as a function of the spectral width of the pump, and demonstrate that the SPDC generation rate can scale with the fifth power of the structure length in the limit of a quasi-continuous-wave pump. We show that such an unusual scaling can be simply connected with the scaling of second-harmonic generation in the same structure, illustrating the general link between spontaneous and stimulated parametric nonlinear processes.

Optics Letters•Jan 31, 2020•9 citations
We study the process of multimode spontaneous parametric down–conversion (SPDC) in a lossy, one-dimensional waveguide. We propose a description using first-order correlation functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three-wave mixing with ultrashort pump, linear propagation and attenuation, and we are able to divide the evolution into three stages and predict it qualitatively. We find that losses do not destroy the quantum properties of SPDC but stabilize the final state.
We study the process of multimode spontaneous parametric down–conversion (SPDC) in a lossy, one-dimensional waveguide. We propose a description using first-order correlation functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three-wave mixing with ultrashort pump, linear propagation and attenuation, and we are able to divide the evolution into three stages and predict it qualitatively. We find that losses do not destroy the quantum properties of SPDC but stabilize the final state.
In this paper, we theoretically study the spectral and temporal properties of pulsed spontaneous parametric down-conversion (SPDC) generated in lossy waveguides. Our theoretical approach is based on the formalism of Gaussian states and the Langevin equation, which is elaborated for weak parametric down-conversion and photon-number-unresolved click detection. Using the example of frequency-degenerate type-II SPDC generated under the pump-idler group-velocity-matching condition, we show how the joint-spectral intensity, mode structure, normalized second-order correlation function, and Hong-Ou-Mandel interference pattern depend on internal losses of the SPDC process. We found that the joint-spectral intensity is almost insensitive to internal losses, while the second-order correlation function shows a strong dependence on them, being different for the signal and idler beams in the presence of internal losses. Based on the sensitivity of the normalized second-order correlation function, we show how its measurement can be used to experimentally determine internal losses.
We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations for the time-dependent squeezing parameters and thermal photon numbers of the state. The benefit of this semianalytic approach is that the number of coupled equations scales linearly with the number of modes and is independent of the number of photons generated. With this analytic form of the state, correlation variances are easily expressed as analytic functions of the time-dependent mode parameters. Thus, our solution makes it computationally tractable and relatively straightforward to calculate the generation and evolution of multimode entangled states in multiple coupled, lossy cavities, even when there are a large number of modes and/or photons.
We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss.Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients.In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator, and we find that this density operator is naturally composed of two photon, one photon, and zero photon contributions.The biphoton probability density, or joint spectral intensity (JSI), associated with the two-photon contribution is determined not only by a phase matching term, but also by a loss matching term.The relative sizes of the loss coefficients within this term lead to three qualitatively different regimes of SPDC JSIs.If either the pump or generated photon loss is much higher than the other, the side lobes of the phase matching squared sinc function are washed out.On the other hand, if pump and generated photon loss are appropriately balanced, the lossy JSI is identical to the lossless JSI.Finally, if the generated photon loss is frequency dependent, the shape of the JSI can be altered more severely, potentially leading to generated photons that are less frequency correlated though also produced less efficiently when compared to photons generated in low-loss waveguides.
An effective-medium approach is used to derive a set of coupled-mode equations describing quadratic parametric interactions in a one-dimensional inhomogeneous medium of finite length. The solutions for both copropagating and counterpropagating interactions are used to study the quantum-mechanical process of spontaneous parametric down-conversion (SPDC). An example is studied in which the inhomogeneous medium is a photonic crystal. The effect that device geometry has on both the efficiency and bandwidth of SPDC is explored. With appropriate design, we find that it is possible not only to enhance the efficiency of SPDC, but also to generate broadband copropagating and narrowband counterpropagating down-converted light. A setup is proposed with the potential to act as a source of entangled photon pairs.
We study spontaneous parametric down conversion (SPDC) in a one-dimensional photonic crystal designed to operate in a doubly resonant configuration, where the frequencies of the pump and the generated photons are both tuned to band-edge resonances. We investigate the spectral correlations of the generated photons as a function of the spectral width of the pump, and demonstrate that the SPDC generation rate can scale with the fifth power of the structure length in the limit of a quasi-continuous-wave pump. We show that such an unusual scaling can be simply connected with the scaling of second-harmonic generation in the same structure, illustrating the general link between spontaneous and stimulated parametric nonlinear processes.