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Frontiers in Optics

Manipulating Incident Light to Create Complex States and Control Spatial Correlations in SPDC

Tianhong Wang, Pascal Bassène, Moussa N’Gom

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We use a spatial light modulator (SLM) to precisely control the pump beam of a type-I spontaneous parametric down-conversion (SPDC) process and generate complex SPDC signals. The method can be extended to a type-II phase-matching and stacked type-I crystals.
DOI
10.1364/fio.2024.jw4a.28

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We present a simple way of simulating Spontaneous parametric down-conversion (SPDC) by modulating a classical laser beam with two spatial light modulators (SLM) through a back projection setup. This system has the advantage of having very high photon count rates, it can simulate a large range of pump beam profiles simply by modifying the hologram on the SLM, and it can be easily converted to a SPDC setup by simply changing only two of its components without the need to perform realignment. This setup can be used to give an indication whether a SPDC experiment will be feasible in a very short amount of time.
The two-photon state generated by spontaneous parametric down-conversion (SPDC) exhibit spatial entanglement embedded in the corresponding mode function. The control of the spatial characteristics of the generated two-photon state is an issue of paramount importance. For example, the spatial entanglement of the two down converted photons forms the basis of quantum imaging, and entanglement in orbital angular momentum has opened a new scenario for implementing multidimensional Hilbert spaces. We put forward several techniques to engineer the spatial structure of entangled two-photon states generated in SPDC. The first strategy we consider for spatial control of the quantum state makes use of the direct manipulation of the pump beam. This technique makes feasible to prepare arbitrary engineered entangled states in any d-dimensional Hilbert space. The second strategy is based on the proper preparation of the down-converting crystal itself, namely quantum state manipulation by quasi-phase-matching (QPM) engineering. We use properly designed transversely varying QPM gratings in nonlinear crystals.
In this thesis we demonstrate experimentally the implementation of quantum processes and simulation of complex dynamics, through the manipulation of a quantum system. Pairs of entangled photons generated by spontaneous parametric down conversion (SPDC) were used as the quantum system. The entangled state in the transversal path has been manipulated using programmable spatial light modulators (SLM). A nonlinear crystal with phase matching type I and a continuouslaser beam with wavelength in the violet region were used for the generation of twin photons in entangled path states that allow us to vary the Hilbert space dimension. Three quantum protocols were experimentally studied in this thesis: minimum Deutsch algorithm, entanglement concentration and simulation of dissipative dynamics. In the Deutsch algorithm implementation were used twin photons generated by SPDC and a double slit to encode a spatial qubit were used. The second photon was used as a trigger to prepare a conditional state of the first. The SLM was used as the oracle mentioned in the algorithm, i. e., it is responsible for implementing the balancedand constant functions. The entanglement concentration protocol for two-qutrit states was also implemented. Partially entangled path states were generated using SPDC along with a SLM that modules amplitude only. A second SLM phase modulator inside a Sagnac interferometer was used to implement the protocol using the method known as Procustean. The third protocol demonstrated experimentally was the simulation of two dissipative dynamics in qudits: dephasing and amplitude. One of the photons passes through a noisy channel, implemented using a SLM, and the transmitted state is characterized allowing us to identify the noisy channel properties.
Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.