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

Physical Review A

Temporal beam splitter and temporal interference

José Tito Mendonça, Ana María Guerra Martins, Ariel Guerreiro

Published Oct 3, 2003• 69 citations
Publisher

Abstract

The effect of photon beam splitting in a time-varying medium is described by classical and quantum theoretical models. It generalizes the concept of time refraction, introduced recently by the authors as a natural extrapolation of the usual concepts of refraction and reflection into the time domain. Total time reflection is shown to exist. A sequence of time refraction processes is shown to lead to temporal interference effects. The concept of temporal beam splitter is introduced. Bogoliubov transformations for the temporal beam splitter are derived. Resonant amplification of light by change in time in the optical medium is shown to exist.

DOI
10.1103/physreva.68.043801

Related papers

Quantum theory of time refraction

José Tito Mendonça, Ariel Guerreiro, Ana María Guerra Martins

The concept of time refraction is introduced to describe the effects of a sudden change of the optical properties of a dielectric medium. This can be seen as the most elementary process associated with photon acceleration and frequency upshifting. The quantum theory of such a process shows that the initial wave splits into time-transmitted and time-reflected waves propagating in opposite directions after the occurrence of a time discontinuity of the refractive index. The time refraction laws, analogous to the well known Fresnel formulas and Snell's law, are also derived. It is shown that, in quantum terms, time refraction is equivalent to a squeezing transformation.

Physical Review A•Aug 10, 2000•89 citations

Second-order temporal interference of two independent light beams at an asymmetrical beam splitter

Jianbin Liu, Jingjing Wang, Zhuo Xu

The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds the classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when an asymmetrical beam splitter is employed.

arXiv:1608.07941•Chinese Physics B•Jan 1, 2017•4 citations

The Quantum Regime Operation of Beam Splitters and Interference Filters

Andre Vatarescu

The presence of the quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter, prevents a single-photon from propagating in a straight-line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are: 1) the quantum Rayleigh stimulated emission which can form groups of photons of the same frequencies, and 2) the unavoidable parametric amplification of single-photons in the original parametric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single-photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with statistical ensemble probability amplitudes leads to the counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements which are afterwards averaged.

•Feb 2, 2023•10 citations

Two-boson quantum interference in time

Nicolas J. Cerf, Michael G. Jabbour

The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum interference. It has its roots in the symmetry of identical quantum particles, as dictated by the Pauli principle. Two identical bosons impinging on a beam splitter (of transmittance 1/2) cannot be detected in coincidence at both output ports, as confirmed in numerous experiments with light or even matter. Here, we establish that partial time reversal transforms the beam splitter linear coupling into amplification. We infer from this duality the existence of an unsuspected two-boson interferometric effect in a quantum amplifier (of gain 2) and identify the underlying mechanism as time-like indistinguishability. This fundamental mechanism is generic to any bosonic Bogoliubov transformation, so we anticipate wide implications in quantum physics.

arXiv:2012.15165•Proceedings of the National Academy of Sciences•Dec 11, 2020•13 citations

The Quantum Regime Operation of Beam Splitters and Interference Filters

Andre Vatarescu

The presence of quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter prevents a single photon from propagating in a straight line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are the quantum Rayleigh-stimulated emission, which can form groups of photons of the same frequency, and the unavoidable parametric amplification of single photons in the original parame-tric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with probability amplitudes of a statistical ensemble leads to counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements whose values are afterwards averaged.

Quantum Beam Science•Apr 2, 2023•3 citations

A quantum optical shutter

Samuel L. Braunstein

A time-dependent dielectric cmedium is used to model a time-varying beam-splitter inside a cavity. The time-varying boundary conditions smoothly evolve from a highly transmitting to a highly reflecting beam-splitter. These approximately correspond to a transformation from a single cavity to a pair of cavities. Quantum field-theoretic calculations show that such a smooth change yields non-singular evolution of the field. However, it predicts a production of photons up to frequencies comparable to the rate of change of the transition. We find that a time-varying beam-splitter operating at optical frequencies would produce an observable number of photons.

Journal of Optics B Quantum and Semiclassical Optics•Mar 1, 2005•4 citations
The effect of photon beam splitting in a time-varying medium is described by classical and quantum theoretical models. It generalizes the concept of time refraction, introduced recently by the authors as a natural extrapolation of the usual concepts of refraction and reflection into the time domain. Total time reflection is shown to exist. A sequence of time refraction processes is shown to lead to temporal interference effects. The concept of temporal beam splitter is introduced. Bogoliubov transformations for the temporal beam splitter are derived. Resonant amplification of light by change in time in the optical medium is shown to exist.
The concept of time refraction is introduced to describe the effects of a sudden change of the optical properties of a dielectric medium. This can be seen as the most elementary process associated with photon acceleration and frequency upshifting. The quantum theory of such a process shows that the initial wave splits into time-transmitted and time-reflected waves propagating in opposite directions after the occurrence of a time discontinuity of the refractive index. The time refraction laws, analogous to the well known Fresnel formulas and Snell's law, are also derived. It is shown that, in quantum terms, time refraction is equivalent to a squeezing transformation.
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds the classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when an asymmetrical beam splitter is employed.
The presence of the quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter, prevents a single-photon from propagating in a straight-line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are: 1) the quantum Rayleigh stimulated emission which can form groups of photons of the same frequencies, and 2) the unavoidable parametric amplification of single-photons in the original parametric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single-photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with statistical ensemble probability amplitudes leads to the counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements which are afterwards averaged.
The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum interference. It has its roots in the symmetry of identical quantum particles, as dictated by the Pauli principle. Two identical bosons impinging on a beam splitter (of transmittance 1/2) cannot be detected in coincidence at both output ports, as confirmed in numerous experiments with light or even matter. Here, we establish that partial time reversal transforms the beam splitter linear coupling into amplification. We infer from this duality the existence of an unsuspected two-boson interferometric effect in a quantum amplifier (of gain 2) and identify the underlying mechanism as time-like indistinguishability. This fundamental mechanism is generic to any bosonic Bogoliubov transformation, so we anticipate wide implications in quantum physics.
The presence of quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter prevents a single photon from propagating in a straight line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are the quantum Rayleigh-stimulated emission, which can form groups of photons of the same frequency, and the unavoidable parametric amplification of single photons in the original parame-tric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with probability amplitudes of a statistical ensemble leads to counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements whose values are afterwards averaged.
A time-dependent dielectric cmedium is used to model a time-varying beam-splitter inside a cavity. The time-varying boundary conditions smoothly evolve from a highly transmitting to a highly reflecting beam-splitter. These approximately correspond to a transformation from a single cavity to a pair of cavities. Quantum field-theoretic calculations show that such a smooth change yields non-singular evolution of the field. However, it predicts a production of photons up to frequencies comparable to the rate of change of the transition. We find that a time-varying beam-splitter operating at optical frequencies would produce an observable number of photons.