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

International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials)

Simultaneous Single- and Two-Mode Squeezing in Time-Varying Media

A. Stevens, Christophe Caloz

Published Sep 1, 2025• 0 citations
Publisher

Abstract

We study the squeezing of light beams in a system combining beam splitters and time-varying media. First, we derive the input-output operator transformations for time-varying media. Integrating these with the input-output operator transformations of beam splitters allows describing arbitrary sequences of beam splitters and time-varying media. We show that a specific configuration—beam splitter, time-varying medium, beam splitter, time-varying medium—enables simultaneous single- and two-mode squeezing. This dual squeezing mechanism leverages the benefits of both types of squeezing, offering potential advantages for high-precision, non-demolition measurements.

DOI
10.1109/metamaterials65622.2025.11174251

Related papers

Two-mode Squeezed Gaussons

Gordon Yeoman, Stephen Mark Barnett

Two-mode squeezed Gaussons are non-classical states of light which are intermediate between single-mode and two-mode squeezed states. They may be prepared by coherently mixing two single-mode squeezed states at a beam-splitter or via a frequency converter. When equally squeezed single-mode squeezed states are incident on a 50/50 beam-splitter the output will range between a two-mode squeezed state and two single-mode squeezed states as the phase of the input squeezed light is varied. This behaviour is reflected when the properties of such states are investigated.

Journal of Modern Optics•Aug 1, 1993•50 citations

Entangling the Whole by Beam Splitting a Part

Callum Croal, Christian Peuntinger, Vanessa Chille +4 more

A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.

arXiv:1506.08001•Physical Review Letters•Nov 4, 2015•11 citations

Beam splitter entangler for light fields

Xun‐Li Feng, Ruxin Li, Zhizhan Xu

We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.

arXiv:quant-ph/0306027•Physical Review A•Mar 23, 2005•12 citations

Hybrid quantum correlations from a single cavity: Generating simultaneously squeezed and entangled optical beams

Carlos Navarrete–Benlloch, Eugenio Quiros Roldan, Germán J. de Valcárcel

Quantum correlations, particularly squeezing and entanglement, are essential in quantum technologies such as metrology, computation, and simulation, as well as in foundational studies. In quantum optics, these phenomena are often intertwined: two squeezed beams can be transformed into entangled beams by mixing them at a beam splitter, and vice versa. However, it is less common to encounter states where two beams are simultaneously squeezed individually while retaining global entanglement. These hybrid states evidently present potential possibilities for applications. In this work, we propose a compact single-cavity source based on a nondegenerate optical parametric oscillator operated below threshold, capable of generating such light—signal and idler beams that are quadrature-squeezed individually while maintaining global entanglement. This behavior arises from an additional linear coupling between the signal and idler, resembling a beam-splitter interaction. We discuss two physical implementations of this system: one based on intra-cavity electro-optic modulators and the other on optomechanical interactions. This unique combination of local and non-local quantum correlations opens the door to novel quantum communication and metrology protocols.

•Sep 22, 2025•0 citations

Detaching two single-mode squeezing operators from the two-mode squeezing operator

Hong-Yi Fan, Cheng Da

It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within -ordering and -ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a -ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.

Chinese Physics B•Sep 1, 2013•10 citations

Entanglement properties of multi-cascaded beamsplitter and its applications

Fang Jia, Zhang Kui-Zheng, Yin-Quan Hu +3 more

Beam splitter,as a kind of linear optics instruments,has many applications such as in quantum optics and quantum information,including the preparation of nonclassical quantum states and entangled state representation.In Heisenberg picture,on the one hand,the relation of input-output of beam splitter can be easily obtained.Especially for the multicascaded beam-splitters,the input-output relation can also be directly obtained by the input-output relation of single beam splitter.On the other hand,we often need to calculate the probabilities of detecting photon number in many cases,thus we need to turn into Schrdinger picture for simplifying our calculation.Based on the equivalence between both pictures,the relation between transformation matrixes connecting these two pictures is derived.That is to say, the transform matrix corresponding to the Schrdinger picture can be obtained by transposing the transform matrix in Heisenberg picture.This concise relation constructs a bridge connecting two pictures and simplifies our calculation in the Schrdinger picture rather than step by step.Using the relation between transform matrixes of both pictures and combining the technique of integration within ordered product of operator,we further consider the coordination representation,normally ordering form and exponential expression of single beam-splitter.Then we further examine the coordination representation,normally ordering form and exponential expression of two-cascaded beam-splitters.As a generalization,the method is extended to the case of multi-cascaded beam-splitters.These investigations provide an effective way to prepare multi-mode entangled states and qubit states.In addition,a general method is shown of obtaining the total operator and its normally ordering form as well as Schmidt decomposition of the linear systems consisting of beam-splitters.As applications,2-cascaded beam-splitters is used to generate a new quantum mechanics representation and prepare the qubit states with the help of conditional measurement.The Schmidt decomposition of three-mode entangled state representation can be directly obtained by the coordination representation of 2-cascaded beam-splitters,which shows the property of entanglement.In addition,based on this representation we can clearly see that when the input states of first beam splitter are two coordinate states,the output states cannot be entangled.This implies that although the coordinate states are nonclassical,the entangled state can not be prepared either.The new proposed quantum mechanics representation will be further used to investigate the optical transformations,including wavelet transformation,Fourier transform,fractional Fourier transform,et al.Therelevant discussion will be our aim in the future research.

Acta Physica Sinica•Jan 1, 2018•3 citations
We study the squeezing of light beams in a system combining beam splitters and time-varying media. First, we derive the input-output operator transformations for time-varying media. Integrating these with the input-output operator transformations of beam splitters allows describing arbitrary sequences of beam splitters and time-varying media. We show that a specific configuration—beam splitter, time-varying medium, beam splitter, time-varying medium—enables simultaneous single- and two-mode squeezing. This dual squeezing mechanism leverages the benefits of both types of squeezing, offering potential advantages for high-precision, non-demolition measurements.
Two-mode squeezed Gaussons are non-classical states of light which are intermediate between single-mode and two-mode squeezed states. They may be prepared by coherently mixing two single-mode squeezed states at a beam-splitter or via a frequency converter. When equally squeezed single-mode squeezed states are incident on a 50/50 beam-splitter the output will range between a two-mode squeezed state and two single-mode squeezed states as the phase of the input squeezed light is varied. This behaviour is reflected when the properties of such states are investigated.
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.
We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.
Quantum correlations, particularly squeezing and entanglement, are essential in quantum technologies such as metrology, computation, and simulation, as well as in foundational studies. In quantum optics, these phenomena are often intertwined: two squeezed beams can be transformed into entangled beams by mixing them at a beam splitter, and vice versa. However, it is less common to encounter states where two beams are simultaneously squeezed individually while retaining global entanglement. These hybrid states evidently present potential possibilities for applications. In this work, we propose a compact single-cavity source based on a nondegenerate optical parametric oscillator operated below threshold, capable of generating such light—signal and idler beams that are quadrature-squeezed individually while maintaining global entanglement. This behavior arises from an additional linear coupling between the signal and idler, resembling a beam-splitter interaction. We discuss two physical implementations of this system: one based on intra-cavity electro-optic modulators and the other on optomechanical interactions. This unique combination of local and non-local quantum correlations opens the door to novel quantum communication and metrology protocols.
It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within -ordering and -ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a -ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.
Beam splitter,as a kind of linear optics instruments,has many applications such as in quantum optics and quantum information,including the preparation of nonclassical quantum states and entangled state representation.In Heisenberg picture,on the one hand,the relation of input-output of beam splitter can be easily obtained.Especially for the multicascaded beam-splitters,the input-output relation can also be directly obtained by the input-output relation of single beam splitter.On the other hand,we often need to calculate the probabilities of detecting photon number in many cases,thus we need to turn into Schrdinger picture for simplifying our calculation.Based on the equivalence between both pictures,the relation between transformation matrixes connecting these two pictures is derived.That is to say, the transform matrix corresponding to the Schrdinger picture can be obtained by transposing the transform matrix in Heisenberg picture.This concise relation constructs a bridge connecting two pictures and simplifies our calculation in the Schrdinger picture rather than step by step.Using the relation between transform matrixes of both pictures and combining the technique of integration within ordered product of operator,we further consider the coordination representation,normally ordering form and exponential expression of single beam-splitter.Then we further examine the coordination representation,normally ordering form and exponential expression of two-cascaded beam-splitters.As a generalization,the method is extended to the case of multi-cascaded beam-splitters.These investigations provide an effective way to prepare multi-mode entangled states and qubit states.In addition,a general method is shown of obtaining the total operator and its normally ordering form as well as Schmidt decomposition of the linear systems consisting of beam-splitters.As applications,2-cascaded beam-splitters is used to generate a new quantum mechanics representation and prepare the qubit states with the help of conditional measurement.The Schmidt decomposition of three-mode entangled state representation can be directly obtained by the coordination representation of 2-cascaded beam-splitters,which shows the property of entanglement.In addition,based on this representation we can clearly see that when the input states of first beam splitter are two coordinate states,the output states cannot be entangled.This implies that although the coordinate states are nonclassical,the entangled state can not be prepared either.The new proposed quantum mechanics representation will be further used to investigate the optical transformations,including wavelet transformation,Fourier transform,fractional Fourier transform,et al.Therelevant discussion will be our aim in the future research.