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:physics/0604125 · Applied Physics Letters

Balanced homodyne detection of second-harmonic generation from isolated subwavelength emitters

Loc Le Xuan, Sophie Brasselet, François Treussart, Jean-François Roch, François Marquier, Dominique Chauvat, Sandrine Perruchas, Cédric Tard, Thierry Gacoin

Published Sep 18, 2006• 57 citations
arXivHTMLPDF

Abstract

The authors demonstrate the association of two-photon nonlinear microscopy with balanced homodyne detection for investigating second-harmonic radiation properties at nanoscale dimensions. Variation of the relative phase between second-harmonic and fundamental beams is retrieved, as a function of the absolute orientation of the nonlinear emitters. Sensitivity down to a few photons per second in the spatiotemporal mode of the local oscillator is obtained. This value is high enough to efficiently detect the coherent second-harmonic emission from a single KTiOPO4 crystal of subwavelength size.

DOI
10.1063/1.2356375

Related papers

Double balanced homodyne detection

Kouji Nakamura, Masa‐Katsu Fujimoto

In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_θ$ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators $\hat{b}_{1}$ and $\hat{b}_{2}$ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator $\hat{b}_θ$ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.

arXiv:1711.03713•Nov 10, 2017•3 citations

Quantum interference between heralded single photon state and coherent state

Lei Yang, Xiaoxin Ma, Xiaoying Li

Balanced homodyne detection has been introduced as a reliable technique of reconstructing the quantum state of a single photon Fock state, which is based on coupling the single photon state and a strong coherent local oscillator in a beam splitter and detecting the field quadrature at the output ports separately. The main challenge associated with a tomographic characterization of the single photon state is mode matching between the single photon state and the local oscillator. Utilizing the heralded single photon generated by the spontaneous parametric process, the multi-mode theoretical model of quantum interference between the single photon state and the coherent state in the fiber beam splitter is established. Moreover, the analytical expressions of the temporal-mode matching coefficient and interference visibility and relationship between the two parameters are shown. In the experimental scheme, the interference visibility under various temporal-mode matching coefficients is demonstrated, which is almost accordant with the theoretical value. Our work explores the principle of temporal-mode matching between the single photon state and the coherent photon state, originated from a local oscillator, and could provide guidance for designing the high-performance balanced homodyne detection system.

Chinese Physics B•Jun 1, 2017•1 citation

Design and simulation of a 300 MHz Balanced Homodyne Detector for quantum photonics

Jiayi Yang

Balanced Homodyne Detection (BHD), introduced in the 1970s, enables highly sensitive detection of phase and amplitude variations in weak light. Initially developed as an advanced optical detection technique, it rapidly became essential in quantum optics for accurately quantifying quadrature components and detecting squeezed states at the shot-noise limit. Today, BHD plays a critical role in diverse fields such as high-precision quantum metrology, gigabit speed optical communications, gravitational wave detection, and large-scale quantum information systems. In this study, a BHD simulation was implemented with a 90 phase difference between the local oscillator and the signal, thus enabling the extraction of the phase quadratureP^component of the optical field.

Advances in Engineering Innovation•Jul 10, 2025•0 citations

Experimental study of balanced optical homodyne and heterodyne detection by controlling sideband modulation

Li We

We experimentally study optical homodyne and heterodyne detections with the same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generates a single signal sideband, the light field measurement by mixing the single sideband at ω0 ±? with a strong local oscillator at the carrier frequency ω0on a beam splitter becomes balanced heterodyne detection. When two signal sidebands at ω0 ±? are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.

Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy•Jan 1, 2015•0 citations

QuaNtum-Enhanced Second Harmonic Generation beyond the Photon Pairs Regime

T. Dickinson, Ivi Afxenti, Giedre Astrauskaite +8 more

Long ago, it was predicted that stimulating two-photon processes such as two-photon absorption (TPA) and second harmonic generation (SHG) with entangled photons produced by parametric down-conversion (PDC) could result in higher efficiencies compared to classical illumination [1]. This was experimentally demonstrated for SHG [2] and TPA [3], where, however, the classical comparison was performed by adding losses to the PDC state rather than employing a true classical reference. In addition, these results considered spatially single-mode PDC radiation and were conducted at low photon fluxes, where the PDC modes are, on average, populated by less than one photon. This resulted in an extremely low SHG/TPA signal, considered of limited practical use for metrological applications (such as two-photon fluorescence microscopy or SHG imaging - see, e.g., [4]). A recent theoretical investigation [5] highlighted that a proper analysis of quantum-enhanced two-photon processes requires a fully spatiotemporal model of the nonlinear interactions. It further showed that highly multimode (in space and time) entangled PDC photons can provide a quantum advantage compared to an equivalent classical pulse, even in regimes well beyond the “one-photon-per-mode” limit, considered the boundary of quantum behavior.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 23, 2025•0 citations

Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection

D. F. McAlister, Michael G. Raymer

We propose and demonstrate a method for determining the two-time photon-number correlations of an optical field on ultrafast time scales. The method, which uses dual-pulse, phase-averaged, balanced-homodyne detection, is sensitive at the single-photon level and can have a quantum efficiency approaching 100%. Using this method we have determined the two-time, photon-number correlations on subpicosecond time scales of emission from a semiconductor optical amplifier.

Physical Review A•Mar 1, 1997•70 citations
The authors demonstrate the association of two-photon nonlinear microscopy with balanced homodyne detection for investigating second-harmonic radiation properties at nanoscale dimensions. Variation of the relative phase between second-harmonic and fundamental beams is retrieved, as a function of the absolute orientation of the nonlinear emitters. Sensitivity down to a few photons per second in the spatiotemporal mode of the local oscillator is obtained. This value is high enough to efficiently detect the coherent second-harmonic emission from a single KTiOPO4 crystal of subwavelength size.
In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator b^θ:=cos⁡θb^1+sin⁡θb^2\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}b^θ​:=cosθb^1​+sinθb^2​ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator b^θ\hat{b}_θb^θ​ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators b^1\hat{b}_{1}b^1​ and b^2\hat{b}_{2}b^2​ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator b^θ\hat{b}_θb^θ​ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.
Balanced homodyne detection has been introduced as a reliable technique of reconstructing the quantum state of a single photon Fock state, which is based on coupling the single photon state and a strong coherent local oscillator in a beam splitter and detecting the field quadrature at the output ports separately. The main challenge associated with a tomographic characterization of the single photon state is mode matching between the single photon state and the local oscillator. Utilizing the heralded single photon generated by the spontaneous parametric process, the multi-mode theoretical model of quantum interference between the single photon state and the coherent state in the fiber beam splitter is established. Moreover, the analytical expressions of the temporal-mode matching coefficient and interference visibility and relationship between the two parameters are shown. In the experimental scheme, the interference visibility under various temporal-mode matching coefficients is demonstrated, which is almost accordant with the theoretical value. Our work explores the principle of temporal-mode matching between the single photon state and the coherent photon state, originated from a local oscillator, and could provide guidance for designing the high-performance balanced homodyne detection system.
Balanced Homodyne Detection (BHD), introduced in the 1970s, enables highly sensitive detection of phase and amplitude variations in weak light. Initially developed as an advanced optical detection technique, it rapidly became essential in quantum optics for accurately quantifying quadrature components and detecting squeezed states at the shot-noise limit. Today, BHD plays a critical role in diverse fields such as high-precision quantum metrology, gigabit speed optical communications, gravitational wave detection, and large-scale quantum information systems. In this study, a BHD simulation was implemented with a 90 phase difference between the local oscillator and the signal, thus enabling the extraction of the phase quadratureP^component of the optical field.
We experimentally study optical homodyne and heterodyne detections with the same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generates a single signal sideband, the light field measurement by mixing the single sideband at ω0 ±? with a strong local oscillator at the carrier frequency ω0on a beam splitter becomes balanced heterodyne detection. When two signal sidebands at ω0 ±? are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.
Long ago, it was predicted that stimulating two-photon processes such as two-photon absorption (TPA) and second harmonic generation (SHG) with entangled photons produced by parametric down-conversion (PDC) could result in higher efficiencies compared to classical illumination [1]. This was experimentally demonstrated for SHG [2] and TPA [3], where, however, the classical comparison was performed by adding losses to the PDC state rather than employing a true classical reference. In addition, these results considered spatially single-mode PDC radiation and were conducted at low photon fluxes, where the PDC modes are, on average, populated by less than one photon. This resulted in an extremely low SHG/TPA signal, considered of limited practical use for metrological applications (such as two-photon fluorescence microscopy or SHG imaging - see, e.g., [4]). A recent theoretical investigation [5] highlighted that a proper analysis of quantum-enhanced two-photon processes requires a fully spatiotemporal model of the nonlinear interactions. It further showed that highly multimode (in space and time) entangled PDC photons can provide a quantum advantage compared to an equivalent classical pulse, even in regimes well beyond the “one-photon-per-mode” limit, considered the boundary of quantum behavior.