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:quant-ph/0302126 · Optics Letters

Direct measurement of the spatial Wigner function with area-integrated detection

Eran A. Mukamel, Konrad Banaszek, Ian A. Walmsley, Christophe Dorrer

Published Aug 1, 2003• 55 citations
arXivHTMLPDF

Abstract

We demonstrate experimentally a novel technique for characterizing transverse spatial coherence by using the Wigner distribution function. The method is based on the measurement of interference between a pair of rotated and displaced replicas of the input beam with an area-integrating detector, and it provides an optimal signal-to-noise ratio in regimes when array detectors are not available. We analyze the quantum-optical picture of the presented measurement for single-photon signals and discuss possible applications in quantum information processing.

DOI
10.1364/ol.28.001317

Related papers

Measurement of the transverse spatial quantum state of light at the single-photon level

Smith, B J, Killett, B, Raymer, M G +2 more

We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wave front, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared to theoretical predictions.

•Jul 14, 2005•39 citations

Measurement of the transverse spatial quantum state of light at the single-photon level

Brian J. Smith, I. A. Walmsley, K. Banaszek +2 more

We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wavefront, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared with theoretical predictions.

arXiv:quant-ph/0507142•Optics Letters•Dec 15, 2005•54 citations

Measuring quantum states: Experimental setup for measuring the spatial density matrix

Max Tegmark

To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wave function, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented that can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field, causing simple harmonic oscillation in the transverse direction. This corresponds to rotating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to recover the Wigner function by the standard inversion of the radon transform. By applying this technique to, for instance, double-slit experiments with various degrees of environment-induced decoherence, it should be possible to make our understanding of decoherence and apparent wave-function collapse less qualitative and more quantitative. \textcopyright{} 1996 The American Physical Society.

arXiv:quant-ph/9607021•Physical Review A•Oct 1, 1996•16 citations

Wigner function reconstruction by hybrid photodetectors in the linear regime

Maria Bondani, Alessia Allevi, Alessandra Andreoni

We present an experimental scheme for the reconstruction of the Wigner function of optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. We mix, at a beam-splitter, the signal state with a set of coherent probes of known complex amplitudes, and measure the probability distribution of the detected photons for each probe. The Wigner function is given by a suitable sum of those probability distributions. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 22, 2009•2 citations

WIGNER FUNCTION OF PULSED FIELDS RECONSTRUCTED BY DIRECT DETECTION

Alessia Allevi, Maria Bondani, Alessandra Andreoni

We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for different values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.

International Journal of Quantum Information•Jan 1, 2011•0 citations

Direct measurement of the Kirkwood-Rihaczek distribution for the spatial properties of a coherent light beam

Viktor Bollen, Yong Meng Sua, Kim Fook Lee

We present a direct measurement of the Kirkwood-Rihaczek (KR) distribution for spatial properties of a coherent light beam in terms of position and momentum (angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne detection (BHD) to simultaneously extract the distribution of the transverse position and momentum of a light beam. The two-LO BHD can measure the KR distribution for any complex wave field (including quantum mechanical wave function) without applying tomography methods (inverse Radon transformation). The transformation of the KR distribution to the Wigner, Glauber-Sudarshan $P$, and Husimi or $Q$ distributions in spatial coordinates are illustrated through experimental data. The KR distribution can provide the local information of a wave field, which is suitable for studying particle properties of a quantum system. Meanwhile, the Wigner function is suitable for studying wave properties such as interference, and hence provides nonlocal information of the wave field. The method developed here can be used for exploring the spatial quantum state for information processing and optical phase-space imaging for biomedical applications.

arXiv:0912.5251•Physical Review A•Jun 25, 2010•10 citations
We demonstrate experimentally a novel technique for characterizing transverse spatial coherence by using the Wigner distribution function. The method is based on the measurement of interference between a pair of rotated and displaced replicas of the input beam with an area-integrating detector, and it provides an optimal signal-to-noise ratio in regimes when array detectors are not available. We analyze the quantum-optical picture of the presented measurement for single-photon signals and discuss possible applications in quantum information processing.
We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wave front, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared to theoretical predictions.
We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wavefront, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared with theoretical predictions.
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wave function, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented that can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field, causing simple harmonic oscillation in the transverse direction. This corresponds to rotating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to recover the Wigner function by the standard inversion of the radon transform. By applying this technique to, for instance, double-slit experiments with various degrees of environment-induced decoherence, it should be possible to make our understanding of decoherence and apparent wave-function collapse less qualitative and more quantitative. \textcopyright{} 1996 The American Physical Society.
We present an experimental scheme for the reconstruction of the Wigner function of optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. We mix, at a beam-splitter, the signal state with a set of coherent probes of known complex amplitudes, and measure the probability distribution of the detected photons for each probe. The Wigner function is given by a suitable sum of those probability distributions. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.
We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for different values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.
We present a direct measurement of the Kirkwood-Rihaczek (KR) distribution for spatial properties of a coherent light beam in terms of position and momentum (angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne detection (BHD) to simultaneously extract the distribution of the transverse position and momentum of a light beam. The two-LO BHD can measure the KR distribution for any complex wave field (including quantum mechanical wave function) without applying tomography methods (inverse Radon transformation). The transformation of the KR distribution to the Wigner, Glauber-Sudarshan PPP, and Husimi or QQQ distributions in spatial coordinates are illustrated through experimental data. The KR distribution can provide the local information of a wave field, which is suitable for studying particle properties of a quantum system. Meanwhile, the Wigner function is suitable for studying wave properties such as interference, and hence provides nonlocal information of the wave field. The method developed here can be used for exploring the spatial quantum state for information processing and optical phase-space imaging for biomedical applications.