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

Journal of the Physical Society of Japan

Multimode Theory of Up-Conversion of Two Photons

Masatoshi Nakatani, Ryōsuke Shimizu, Kazuki Koshino

Published Apr 27, 2009• 3 citations
Publisher

Abstract

The up-conversion dynamics of two photons in a three-level system is investigated theoretically. The analysis is based on a rigorous formalism that incorporates the multimode nature of the photon field, enabling quantitative handling of the spatial profiles of the photon pulses. We have derived an analytic formula that connects the wavefunction of two input photons to that of an up-converted output photon. The up-conversion efficiency and the output pulse profile are numerically calculated using this formula.

DOI
10.1143/jpsj.78.054401

Related papers

Up-conversion dynamics for temporally entangled two-photon pulses

Masatoshi Nakatani, Ryōsuke Shimizu, Kazuki Koshino

We analyze the up conversion of a two-photon pulse having temporal entanglement on the basis of a full quantum formalism that treats both photons and optical media quantum mechanically. We derive a formula of the up-converted photon wave function, which is applicable to arbitrary input two-photon states for a three-level system, as the simplest second-order nonlinear optical system. As the input, we employ three kinds of temporally entangled two-photon pulses: correlated, uncorrelated, and anticorrelated. We observe the up-conversion efficiency and the temporal profile of the up-converted photon. Our results reveal the crossover behavior of the up conversion from anticorrelation to correlation and show how the temporal correlation in the input is reflected in the up-conversion process.

Physical Review A•Jan 26, 2011•5 citations

Down-conversion of a single photon with unit efficiency

Kazuki Koshino

The down-conversion dynamics of a single photon in a single three-level system are investigated theoretically. The wave functions of the output photons are obtained analytically as functions of the input photon profile, and the down-conversion probability is evaluated from these output wave functions. It is demonstrated that down-conversion of a single photon with unit efficiency is possible and the necessary conditions are clarified.

Physical Review A•Jan 6, 2009•27 citations

Evaluation of multiphoton effects in down-conversion

Kazuyoshi Yoshimi, Kazuki Koshino

Multiphoton effects in down-conversion are investigated based on the full-quantum multimode formalism by considering a three-level system as a prototype nonlinear system. We analytically derive the three-photon output wave function for two input photons, where one of the two input photons is down-converted and the other one is not. Using this output wave function, we calculate the down-conversion probability, the purity, and the fidelity to evaluate the entanglement between a down-converted photon pair and a non-down-converted photon. It is shown that the saturation effect occurs by multiphoton input and that it affects both the down-conversion probability and the quantum correlation between the down-converted photon pair and the non-down-converted photon. We also reveal the necessary conditions for multiphoton effects to be strong.

Physical Review A•Apr 7, 2010•0 citations

Use of classical input for solving two-photon nonlinear dynamics

Kazuki Koshino

Optical nonlinear effects between several photons are usually negligibly small. Such nonlinear optical effects have been attracting much attention from the viewpoint of all-optical quantum computation. In order to analyze the nonlinear dynamics of photons quantitatively, it is essential to quantize both the photon field and the material system, and also to take account of the multimode nature of the photon field rigorously.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•0 citations

Refraction of the Two-Photon Multimode Field via a Three-Level Atom

Trever Harborth, Yuri V. Rostovtsev

Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes, and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level, two-photon system, but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.

Entropy•Jan 15, 2025•1 citation

Full two-photon down-conversion of a single photon

Eduardo Sánchez-Burillo, Luis Martín-Moreno, Juan José García‐Ripoll +1 more

We demonstrate, both numerically and analytically, that it is possible to deterministically generate two photons from one and only one photon. We characterize the output two-photon field and make our calculations close to reality by including losses. Our proposal relies on real or artificial three-level atoms with a cyclic transition strongly coupled to a one-dimensional waveguide. We show that almost perfect down-conversion, with efficiency over $99%$, is reachable using state-of-the-art waveguide QED architectures such as photonic crystals or superconducting circuits. In particular, we sketch an implementation in circuit QED, where the three-level atom is a transmon.

arXiv:1602.05603•Physical Review A•Nov 9, 2016•37 citations
The up-conversion dynamics of two photons in a three-level system is investigated theoretically. The analysis is based on a rigorous formalism that incorporates the multimode nature of the photon field, enabling quantitative handling of the spatial profiles of the photon pulses. We have derived an analytic formula that connects the wavefunction of two input photons to that of an up-converted output photon. The up-conversion efficiency and the output pulse profile are numerically calculated using this formula.
We analyze the up conversion of a two-photon pulse having temporal entanglement on the basis of a full quantum formalism that treats both photons and optical media quantum mechanically. We derive a formula of the up-converted photon wave function, which is applicable to arbitrary input two-photon states for a three-level system, as the simplest second-order nonlinear optical system. As the input, we employ three kinds of temporally entangled two-photon pulses: correlated, uncorrelated, and anticorrelated. We observe the up-conversion efficiency and the temporal profile of the up-converted photon. Our results reveal the crossover behavior of the up conversion from anticorrelation to correlation and show how the temporal correlation in the input is reflected in the up-conversion process.
Multiphoton effects in down-conversion are investigated based on the full-quantum multimode formalism by considering a three-level system as a prototype nonlinear system. We analytically derive the three-photon output wave function for two input photons, where one of the two input photons is down-converted and the other one is not. Using this output wave function, we calculate the down-conversion probability, the purity, and the fidelity to evaluate the entanglement between a down-converted photon pair and a non-down-converted photon. It is shown that the saturation effect occurs by multiphoton input and that it affects both the down-conversion probability and the quantum correlation between the down-converted photon pair and the non-down-converted photon. We also reveal the necessary conditions for multiphoton effects to be strong.
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes, and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level, two-photon system, but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.
We demonstrate, both numerically and analytically, that it is possible to deterministically generate two photons from one and only one photon. We characterize the output two-photon field and make our calculations close to reality by including losses. Our proposal relies on real or artificial three-level atoms with a cyclic transition strongly coupled to a one-dimensional waveguide. We show that almost perfect down-conversion, with efficiency over 9999%99, is reachable using state-of-the-art waveguide QED architectures such as photonic crystals or superconducting circuits. In particular, we sketch an implementation in circuit QED, where the three-level atom is a transmon.