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### Imaging symmetric and antisymmetric behavior of orbital-angular-momentum-entangled two-photon states

##### Zeferino Ibarra-Borja, Pablo Yepiz-Graciano, Nicolas Claro-Rodríguez, Alfred B. U’Ren, and Roberto Ramírez-Alarcón

##### Phys. Rev. Applied **22**, 024068 – Published 27 August 2024

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#### Abstract

We report on an experiment in which orbital-angular-momentum (OAM)-entangled photon pairs generated by the spontaneous parametric down-conversion process can be engineered to have particular symmetry properties. Our method is based on the use of a Dove-prism pair in conjunction with Hong-Ou-Mandel (HOM) interferometry resolved in transverse position and OAM. The latter allows us to engineer the postselected two-photon state to exhibit a specific type of symmetry. By selecting particular topological charge values for the pump and for the postselected two-photon state, we can transition from a symmetric two-photon state and a HOM dip to an antisymmetric state and a HOM peak. Spatial resolution allows us to obtain the HOM interferogram both at the single-pixel level and globally by summing over all sensor pixels. Furthermore, through spatially selective OAM projection of the detected photon pairs, we can define multiple transverse regions with different symmetry properties, as verified by our spatially resolved HOM apparatus. Although we used two transverse regions for this proof-of-concept demonstration, this method could in principle be scaled to a larger number of regions, leading to a new technique to be added to the existing toolbox for quantum technologies in the photonic domain.

- Received 21 March 2024
- Revised 12 July 2024
- Accepted 29 July 2024

DOI:https://doi.org/10.1103/PhysRevApplied.22.024068

© 2024 American Physical Society

#### Physics Subject Headings (PhySH)

- Research Areas

Quantum communicationQuantum correlations in quantum informationQuantum measurements

Quantum Information, Science & Technology

#### Authors & Affiliations

Zeferino Ibarra-Borja^{1,2}, Pablo Yepiz-Graciano^{1,2}, Nicolas Claro-Rodríguez^{1}, Alfred B. U’Ren^{2}, and Roberto Ramírez-Alarcón^{1,*}

^{1}Centro de Investigaciones en Óptica A. C., León, Guanajuato 37150, Mexico^{2}Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX 04510, Mexico

^{*}Contact author: roberto.ramirez@cio.mx

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##### Issue

Vol. 22, Iss. 2 — August 2024

##### Subject Areas

- Optics
- Quantum Physics
- Quantum Information

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Article part of CHORUS

Accepted manuscript will be available starting27 August 2025.#### Images

###### Figure 1

Polar diagrams showing the properties of the postselected SPDC state for (a) ${\ell}_{p}=0$ and (b) ${\ell}_{p}=1$. The radius of the polar diagram (indicated in the horizontal axis) represents the SPDC topological charge projection value $\ell $. Along a circumference for a specific $\ell $, the symmetric and antisymmetric coefficients define a point, and if this lies on the horizontal (vertical) axis, the postselected state is purely symmetric (antisymmetric). Points defined by the same interprism angle $\varphi $ are joined together smoothly to form the spiral shapes shown.

###### Figure 2

Experimental setup. OAM-entangled photon pairs are generated by the SPDC process. The signal photon is transmitted through a Dove-prism pair (${\mathrm{DP}}_{1}$ and ${\mathrm{DP}}_{2}$) to manipulate the properties of the resulting photon pair, and the photon pairs interfere in a beam splitter (BS). While one of the photons emerging from the BS is spatially resolved upon detection by an ICCD camera, upon transmission through the image-preserving optical delay line (DL), the other photon is projected to a user-selected topological charge value prior to detection by an avalanche photodiode (APD).

###### Figure 3

HOM interference behavior for ${\ell}_{p}=\ell =0$ and $\varphi ={45}^{\circ}$. Panel (a) shows the spatially resolved HOM interferograms for a selection of seven different signal-idler $\tau $ values, with the case $\tau =0$ corresponding to the central plot; the green dot in this plot indicates the pixel used for the single-pixel interferogram, as described in the main text. (b) Single-pixel HOM interferogram (black dots), along with the global interferogram obtained by summing over all ICCD pixel readouts (red dots), for temporal delay $\tau $ values ranging from $-200\phantom{\rule{0ex}{0ex}}\mathrm{fs}$ ($-60\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$) to $+200\phantom{\rule{0ex}{0ex}}\mathrm{fs}$ ($+60\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$). The curves are fits to sinc-squared functions for comparison purposes only, as detailed in the main text. (c) Transverse intensity of the two portions of the SPDC ring (for each of the signal and idler photons) clipped by the triangular mirror, one of which is rotated by the Dove-prism pair. The image shown was taken on the plane of the BS (${\mathrm{IP}}_{1}$) and has dimensions of $1.5\phantom{\rule{0ex}{0ex}}\mathrm{mm}\times 1.4\phantom{\rule{0ex}{0ex}}\mathrm{mm}$ ($119\times 110$ pixels of the ICCD sensor).

###### Figure 4

HOM interference behavior for ${\ell}_{p}=0$, $\ell =1$, and $\varphi ={45}^{\circ}$. Panel (a) shows the spatially resolved HOM interferograms for a selection of seven different signal-idler $\tau $ values, with the case $\tau =0$ corresponding to the central plot; the green dot in this plot indicates the pixel used for the single-pixel interferogram, as described in the main text. (b) Single-pixel HOM interferogram (black dots), along with the global interferogram obtained by summing over all ICCD pixel readouts (red dots), for temporal delay $\tau $ values ranging from $-200\phantom{\rule{0ex}{0ex}}\mathrm{fs}$ ($-60\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$) to $+200\phantom{\rule{0ex}{0ex}}\mathrm{fs}$ ($+60\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$). The curves are fits to sinc-squared functions for comparison purposes only.

###### Figure 5

HOM interference behavior for ${\ell}_{p}=0$ and $\ell =0,1,2,3,4$ and $\varphi ={45}^{\circ}$. Panel (a) shows the spatially resolved HOM interferograms at a delay value corresponding to $\mathrm{\Delta}z=-56\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$ ($\tau =-186$ fs) outside of the dip/peak area for each value of $\ell $. Panel (b) shows the HOM interferograms for $\ell =0,1,2,3,4$, demonstrating an alternation between dips (for $\ell =0,2,4$) and peaks (for $\ell =1,3$).

###### Figure 6

(a) The red dots indicate the observed visibility for the HOM interferograms from the previous figure, while the curve indicates the best fit to the relationship in Eq.(6), yielding an interprism angle of $\varphi ={47.9}^{\circ}$. (b) Spiral polar diagram plotted for ${\ell}_{p}=0$ and $\varphi ={47.9}^{\circ}$.

###### Figure 7

HOM interference behavior for ${\ell}_{p}=0$ and an SPDC topological charge projected in a spatially selective manner to $\ell =1$ within a circumference on the SLM plane and to $\ell =0$ outside of this circumference [see inset of panel (a)]. We show the spatially resolved HOM interferograms for two values of temporal delay, corresponding to (a) $\mathrm{\Delta}z=60\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$ ($\tau =200$ fs) and (b) $\mathrm{\Delta}z=0\phantom{\rule{0ex}{0ex}}\text{\mu}\mathrm{m}$ ($\tau =0$ fs). The resulting HOM visibility is shown in panel (c), with positive (negative) values in the internal (external) region. In panel (d), we show the interferograms resulting from adding up the pixels in the two regions denoted by green boxes in panel (c), showing a peak for the internal region and a dip for the external region.