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/0507142 · Optics Letters

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

Brian J. Smith, I. A. Walmsley, K. Banaszek, Emmy Killett, M. G. Raymer

Published Dec 15, 2005• 54 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/ol.30.003365

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

The photon transverse wave function and its measurement

Brian J. Smith, M. G. Raymer, Bryan Killett +2 more

We report on a technique to measure the photon transverse wave function in coordinate space using a photon-counting, parity-inverting Sagnac interferometer. We present measurements of a TEM10 Hermite-Gaussian beam.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations

Measurement of the spatial shape of photons

Noemí González Rodríguez

Quantum systems entanglement in continuous variables has been receiving increasing attention from the scientific community. The transverse spatial shape of photons (i.e. transverse position and momentum degree of freedom) is such a continuous variable systems, which due to its ease of control is prone to be used for testing some of the new physical predictions that continuous variables quantum systems can offer, as the improvement of the security of quantum key distribution cryptography and the efficiency enhancement of quantum communication protocols. Following this line, the mean goal of this Thesis has been the characterization and measurement of the spatial shape of photons. Another outstanding problem in Quantum Optics Information Technology (QOIT) is the coherent and reversible storage of photons states in matter, i.e. the necessity of a quantum memory. Theoretical and experimental results about this topic have been showed. Below we summarize the more important contributions of this Thesis: Demonstration about the non-validity of the OAM transformation rule FORr highly focused light beams: We have shown from a theoretical and experimental point of view that the OAM transformation rule is not valid for highly focused light beams, since Dove prisms inherently introduce astigmatism, and therefore further OAM changes. We have analyzed how light beams with a well defined value of the OAM per photon, after traversing the Dove prism, are transformed into a superposition of states with well defined OAM. The violation of the rule, turns out to be more important for highly focused light beams. We have provided a quantitative study of the properties of the Dove prism, and we have verified experimentally the validity of the theoretical results in a series of experiments with a commercially available Dove prism. Presentation of a new method to measure the amplitude and phase of Laguerre-Gaussian like beams: A method to measure the amplitude an phase of Laguerre-Gaussian like beams have been presented, from a theoretical and experimental point of view. This method is based on a small variation of the spiral phase interferometry technique, which allows to avoid some technical problems that can be found in the reconstruction of finite sized beams and beams with phase singularities. A few examples of the use of our technique for the characterization of complex beams have been presented. Description of the transverse spatial shape of bipartite entangled photons generated in Spontaneous Parametric Down Conversion (SPDC) using the Wigner function formulism: We have show some theoretical and experimental results regarding the spatial Wigner function of entangled paired photons generated in SPDC. Concretely, we have studied the remote preparation of one of the photons of the pair, for the photon being in a Gaussian beam and in a superposition of two modes. Also, we have analyzed and measured the case of the Wigner function of only one of the two photons of the pair, which shows that one photon of the pair is in a statistical mixture of modes. Finally, an experiment to completely measure the spatial state of the two photons was proposed, and also analytical expressions for the results one would expect in this case were given. Investigation about the storage of spatial light polarization grating into the Zeeman ground states of cold cesium atoms: We have investigated theoretically and experimentally the dynamics of light grating stored in electromagnetically induced transparent (EIT) medium associated with a degenerate two-level system. The dependence of the stored light grating with the intensities of the incident and reading beams has been investigated. Bragg diffraction into the stored grating has been employed to probe the dynamics under different conditions showing reasonable results in agreement with the theoretical model developed. Moreover, we also have observed the coherent evolution of the stored grating in the presence of an applied magnetic field, which allows collapses and revivals of the stored grating, which is associated with the Larmor precession of the induced grating around the applied magnetic field. We think that the results of this Thesis are an important step in order to explore the quantum capabilities of the transverse spatial shape of photons and can encourage going further in this line of research. Moreover, the investigation on the dynamics of light grating stored in an EIT medium is of considerable importance for a better understanding of the coherent memory for multidimensional state spaces. Thus, a further and more detailed investigation of the topics presented here should be of special interest for the scientific community.

•Jan 1, 2010•1 citation

The Photon Transverse Wave Function and its Measurement

Brian J. Smith, Michael G. Raymer, Bryan Killett +2 more

We report on a technique to measure the photon transverse wave function in coordinate space using a photon-counting, parity-inverting Sagnac interferometer. We present measurements of a TEM10 Hermite-Gaussian beam.

Frontiers in Optics•Jan 1, 2004•0 citations

Interferometric scheme for direct measurement of moments of transverse spatial variables of photons

S. Machado, P. Milman, Stephen Patrick Walborn

We propose an interferometric method for the direct measurement of the moments of the transverse spatial variables of an optical field. The key elements are spatial light modulators, used to imprint a transverse phase on the field. We show that our measurement scheme can be used to measure the spatial correlation functions of a two-photon state directly, which allows for the identification of spatial entanglement without the need for partial state reconstruction. Our method can also be extended to $N$-photon states. We show that the method is more efficient than the measurement of marginal probability distributions, and that it can be made resilient to small alignment errors.

Physical Review A•May 24, 2013•6 citations

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

Eran A. Mukamel, Konrad Banaszek, Ian A. Walmsley +1 more

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.

arXiv:quant-ph/0302126•Optics Letters•Aug 1, 2003•55 citations
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.
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.
Quantum systems entanglement in continuous variables has been receiving increasing attention from the scientific community. The transverse spatial shape of photons (i.e. transverse position and momentum degree of freedom) is such a continuous variable systems, which due to its ease of control is prone to be used for testing some of the new physical predictions that continuous variables quantum systems can offer, as the improvement of the security of quantum key distribution cryptography and the efficiency enhancement of quantum communication protocols. Following this line, the mean goal of this Thesis has been the characterization and measurement of the spatial shape of photons. Another outstanding problem in Quantum Optics Information Technology (QOIT) is the coherent and reversible storage of photons states in matter, i.e. the necessity of a quantum memory. Theoretical and experimental results about this topic have been showed. Below we summarize the more important contributions of this Thesis: Demonstration about the non-validity of the OAM transformation rule FORr highly focused light beams: We have shown from a theoretical and experimental point of view that the OAM transformation rule is not valid for highly focused light beams, since Dove prisms inherently introduce astigmatism, and therefore further OAM changes. We have analyzed how light beams with a well defined value of the OAM per photon, after traversing the Dove prism, are transformed into a superposition of states with well defined OAM. The violation of the rule, turns out to be more important for highly focused light beams. We have provided a quantitative study of the properties of the Dove prism, and we have verified experimentally the validity of the theoretical results in a series of experiments with a commercially available Dove prism. Presentation of a new method to measure the amplitude and phase of Laguerre-Gaussian like beams: A method to measure the amplitude an phase of Laguerre-Gaussian like beams have been presented, from a theoretical and experimental point of view. This method is based on a small variation of the spiral phase interferometry technique, which allows to avoid some technical problems that can be found in the reconstruction of finite sized beams and beams with phase singularities. A few examples of the use of our technique for the characterization of complex beams have been presented. Description of the transverse spatial shape of bipartite entangled photons generated in Spontaneous Parametric Down Conversion (SPDC) using the Wigner function formulism: We have show some theoretical and experimental results regarding the spatial Wigner function of entangled paired photons generated in SPDC. Concretely, we have studied the remote preparation of one of the photons of the pair, for the photon being in a Gaussian beam and in a superposition of two modes. Also, we have analyzed and measured the case of the Wigner function of only one of the two photons of the pair, which shows that one photon of the pair is in a statistical mixture of modes. Finally, an experiment to completely measure the spatial state of the two photons was proposed, and also analytical expressions for the results one would expect in this case were given. Investigation about the storage of spatial light polarization grating into the Zeeman ground states of cold cesium atoms: We have investigated theoretically and experimentally the dynamics of light grating stored in electromagnetically induced transparent (EIT) medium associated with a degenerate two-level system. The dependence of the stored light grating with the intensities of the incident and reading beams has been investigated. Bragg diffraction into the stored grating has been employed to probe the dynamics under different conditions showing reasonable results in agreement with the theoretical model developed. Moreover, we also have observed the coherent evolution of the stored grating in the presence of an applied magnetic field, which allows collapses and revivals of the stored grating, which is associated with the Larmor precession of the induced grating around the applied magnetic field. We think that the results of this Thesis are an important step in order to explore the quantum capabilities of the transverse spatial shape of photons and can encourage going further in this line of research. Moreover, the investigation on the dynamics of light grating stored in an EIT medium is of considerable importance for a better understanding of the coherent memory for multidimensional state spaces. Thus, a further and more detailed investigation of the topics presented here should be of special interest for the scientific community.
We propose an interferometric method for the direct measurement of the moments of the transverse spatial variables of an optical field. The key elements are spatial light modulators, used to imprint a transverse phase on the field. We show that our measurement scheme can be used to measure the spatial correlation functions of a two-photon state directly, which allows for the identification of spatial entanglement without the need for partial state reconstruction. Our method can also be extended to NNN-photon states. We show that the method is more efficient than the measurement of marginal probability distributions, and that it can be made resilient to small alignment errors.
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.