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Optical vortex knots - one photon at a time.

Tempone-Wiltshire SJ, Johnstone SP, Helmerson K - Sci Rep (2016)

Bottom Line: The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated.Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot - one photon at a time.This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing.

View Article: PubMed Central - PubMed

Affiliation: School of Physics and Astronomy, Monash University, Victoria 3800, Australia.

ABSTRACT
Feynman described the double slit experiment as "a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which has in it the heart of quantum mechanics". The double-slit experiment, performed one photon at a time, dramatically demonstrates the particle-wave duality of quantum objects by generating a fringe pattern corresponding to the interference of light (a wave phenomenon) from two slits, even when there is only one photon (a particle) at a time passing through the apparatus. The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated. Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot - one photon at a time. This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing.

No MeSH data available.


Related in: MedlinePlus

Left: Optical set-up.Each photon passes through the spatial light modulator (SLM), which acts as a static phase element generating both a knot and a Gaussian reference beam, which is split and then spatially filtered such that one path contains the knot, and the other the reference beam. These two paths are then recombined at a small angle, which generates an interferogram that facilitates identification of the vortex structure, and then imaged onto the camera. The double headed arrow indicates the lens that is translated to image different transverse planes of the knot. The inset shows the hologram displayed on the SLM (available as supplementary material). Centre: Interferometric measurements of the knotted topology. Measurements of the optical field are made by summing multiple images that each contain an average of much less than one photon per pixel. (a) A single frame imaged by the camera in photon counting mode. (b–d) Measurements resulting from the summation of 100, 1000 and 8000 images, respectively, with the contrast of the resultant interference pattern increasing with increasing numbers of images making the forked vortex structure more visible (shown magnified in insets). Right: Normalised cross correlation (NCC) as a function of photon number. The peak value of the NCC between the interferometric measurement of the knotted optical field at Z = 0 with the expected theoretical intensity pattern of the knot, a Gaussian mode and the modal decomposition of the knot used in the ‘which path’ measurement, each interfered with a Gaussian mode to reproduce the global fringe pattern as a function of increasing number of summed images, displayed as increasing photon number.
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f2: Left: Optical set-up.Each photon passes through the spatial light modulator (SLM), which acts as a static phase element generating both a knot and a Gaussian reference beam, which is split and then spatially filtered such that one path contains the knot, and the other the reference beam. These two paths are then recombined at a small angle, which generates an interferogram that facilitates identification of the vortex structure, and then imaged onto the camera. The double headed arrow indicates the lens that is translated to image different transverse planes of the knot. The inset shows the hologram displayed on the SLM (available as supplementary material). Centre: Interferometric measurements of the knotted topology. Measurements of the optical field are made by summing multiple images that each contain an average of much less than one photon per pixel. (a) A single frame imaged by the camera in photon counting mode. (b–d) Measurements resulting from the summation of 100, 1000 and 8000 images, respectively, with the contrast of the resultant interference pattern increasing with increasing numbers of images making the forked vortex structure more visible (shown magnified in insets). Right: Normalised cross correlation (NCC) as a function of photon number. The peak value of the NCC between the interferometric measurement of the knotted optical field at Z = 0 with the expected theoretical intensity pattern of the knot, a Gaussian mode and the modal decomposition of the knot used in the ‘which path’ measurement, each interfered with a Gaussian mode to reproduce the global fringe pattern as a function of increasing number of summed images, displayed as increasing photon number.

Mentions: We generate our optical field employing methods similar to those of refs 15 and 16, using a complex valued, phase only hologram17 displayed upon a SLM. A reference Gaussian beam is also generated from the SLM and made to interfere with the knotted optical vortex field. The vortices leave a characteristic forked structure in the resulting interferogram, as shown in Fig. 1a, which facilitates identifying their locations. A schematic of the optical set up is shown on the left in Fig. 2, with the inset showing the hologram used to generate the knotted vortex structure and the reference Gaussian beam. A number of different transverse planes of the knotted optical field (Fig. 1) are imaged onto the camera by translating a final imaging lens (which also provides magnification of the field) in the direction of propagation. The vortices within each image plane are located and then ‘stitched’ together to visualise the three dimensional trefoil knot vortex structure (Fig. 1b).


Optical vortex knots - one photon at a time.

Tempone-Wiltshire SJ, Johnstone SP, Helmerson K - Sci Rep (2016)

Left: Optical set-up.Each photon passes through the spatial light modulator (SLM), which acts as a static phase element generating both a knot and a Gaussian reference beam, which is split and then spatially filtered such that one path contains the knot, and the other the reference beam. These two paths are then recombined at a small angle, which generates an interferogram that facilitates identification of the vortex structure, and then imaged onto the camera. The double headed arrow indicates the lens that is translated to image different transverse planes of the knot. The inset shows the hologram displayed on the SLM (available as supplementary material). Centre: Interferometric measurements of the knotted topology. Measurements of the optical field are made by summing multiple images that each contain an average of much less than one photon per pixel. (a) A single frame imaged by the camera in photon counting mode. (b–d) Measurements resulting from the summation of 100, 1000 and 8000 images, respectively, with the contrast of the resultant interference pattern increasing with increasing numbers of images making the forked vortex structure more visible (shown magnified in insets). Right: Normalised cross correlation (NCC) as a function of photon number. The peak value of the NCC between the interferometric measurement of the knotted optical field at Z = 0 with the expected theoretical intensity pattern of the knot, a Gaussian mode and the modal decomposition of the knot used in the ‘which path’ measurement, each interfered with a Gaussian mode to reproduce the global fringe pattern as a function of increasing number of summed images, displayed as increasing photon number.
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f2: Left: Optical set-up.Each photon passes through the spatial light modulator (SLM), which acts as a static phase element generating both a knot and a Gaussian reference beam, which is split and then spatially filtered such that one path contains the knot, and the other the reference beam. These two paths are then recombined at a small angle, which generates an interferogram that facilitates identification of the vortex structure, and then imaged onto the camera. The double headed arrow indicates the lens that is translated to image different transverse planes of the knot. The inset shows the hologram displayed on the SLM (available as supplementary material). Centre: Interferometric measurements of the knotted topology. Measurements of the optical field are made by summing multiple images that each contain an average of much less than one photon per pixel. (a) A single frame imaged by the camera in photon counting mode. (b–d) Measurements resulting from the summation of 100, 1000 and 8000 images, respectively, with the contrast of the resultant interference pattern increasing with increasing numbers of images making the forked vortex structure more visible (shown magnified in insets). Right: Normalised cross correlation (NCC) as a function of photon number. The peak value of the NCC between the interferometric measurement of the knotted optical field at Z = 0 with the expected theoretical intensity pattern of the knot, a Gaussian mode and the modal decomposition of the knot used in the ‘which path’ measurement, each interfered with a Gaussian mode to reproduce the global fringe pattern as a function of increasing number of summed images, displayed as increasing photon number.
Mentions: We generate our optical field employing methods similar to those of refs 15 and 16, using a complex valued, phase only hologram17 displayed upon a SLM. A reference Gaussian beam is also generated from the SLM and made to interfere with the knotted optical vortex field. The vortices leave a characteristic forked structure in the resulting interferogram, as shown in Fig. 1a, which facilitates identifying their locations. A schematic of the optical set up is shown on the left in Fig. 2, with the inset showing the hologram used to generate the knotted vortex structure and the reference Gaussian beam. A number of different transverse planes of the knotted optical field (Fig. 1) are imaged onto the camera by translating a final imaging lens (which also provides magnification of the field) in the direction of propagation. The vortices within each image plane are located and then ‘stitched’ together to visualise the three dimensional trefoil knot vortex structure (Fig. 1b).

Bottom Line: The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated.Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot - one photon at a time.This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing.

View Article: PubMed Central - PubMed

Affiliation: School of Physics and Astronomy, Monash University, Victoria 3800, Australia.

ABSTRACT
Feynman described the double slit experiment as "a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which has in it the heart of quantum mechanics". The double-slit experiment, performed one photon at a time, dramatically demonstrates the particle-wave duality of quantum objects by generating a fringe pattern corresponding to the interference of light (a wave phenomenon) from two slits, even when there is only one photon (a particle) at a time passing through the apparatus. The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated. Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot - one photon at a time. This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing.

No MeSH data available.


Related in: MedlinePlus