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SPIE Conference on Nonlinear Optics and its Applications

Tunable spatial compensation for polarization entangled photons

Salem F. Hegazy, Salah S. A. Obayya

Published May 14, 2018• 1 citation
Publisher

Abstract

The polarization entangled state produced via spontaneous parametric downconversion (SPDC) has relativephase maps in frequency and momentum domains which give an almost complete picture about the distinguishability and purity loss in the conjugate time and space domains. We demonstrate experimentally the tunable compensation of directional relative-phase profile for entangled photons generated by two cascaded / crossed crystals and captured over ultra-wide spatial window. We use a phase-only spatial light modulator (SLM) programmable via a personal computer to flatten (or correct for) the spatial relative-phase profile and also to add on-demand spatial phase profile. A fast, yet accurate, technique is introduced for frequent relative-phase measurements based on the tilt angle of a quarter wave plate (QWP) acting on the diagonally polarized pump beam and nulling the relative-phase of the entangled state at that direction. Our experimental measurements verify previous theoretical models for tunable compensation of the polarization two-photon state produced by the cascaded crystals arrangement.

DOI
10.1117/12.2306942

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The polarization entangled state produced via spontaneous parametric downconversion (SPDC) has relativephase maps in frequency and momentum domains which give an almost complete picture about the distinguishability and purity loss in the conjugate time and space domains. We demonstrate experimentally the tunable compensation of directional relative-phase profile for entangled photons generated by two cascaded / crossed crystals and captured over ultra-wide spatial window. We use a phase-only spatial light modulator (SLM) programmable via a personal computer to flatten (or correct for) the spatial relative-phase profile and also to add on-demand spatial phase profile. A fast, yet accurate, technique is introduced for frequent relative-phase measurements based on the tilt angle of a quarter wave plate (QWP) acting on the diagonally polarized pump beam and nulling the relative-phase of the entangled state at that direction. Our experimental measurements verify previous theoretical models for tunable compensation of the polarization two-photon state produced by the cascaded crystals arrangement.
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The simultaneous production of a set of arbitrary hyperentangled states is crucial for quantum machines running variant quantum protocols concurrently, like universal quantum computers and quantum communication hubs. We present an experimental method to prepare a set of arbitrary path-polarization hyperentangled states concurrently using non-collinear spontaneous parametric down-conversion (SPDC). A cascaded pair of type-I crystals are pumped by 405-nm diagonally-polarized beam to produce a noncollinear stream of photon pairs. Compensation crystals are inserted to correct for the angular slope of the relative phase of the produced polarization entangled state. The pathentangled states are created over four pairs of slits positioned at conjugate locations to the pump beam. The local relative-phases of the path and polarization states can be independently tailored by intercepting the SPDC emission by tiltable birefringent and glass plates. The amplitudes of the polarization states is controlled by the manipulation of the polarization state of the pump. Also, the amplitudes of the path states is accessed by translating the slits over the SPDC cone. Here, while a pure state describes the whole SPDC emission, the produced states can be deemed an independent set by avoiding paths balanced to less than the coherence-length.
The two-photon state generated by overlapping the noncollinear spontaneous parametric down conversion (SPDC) emissions of two coherently pumped type-I crystals undergoes spatial and spectral decoherence precluding the capture of high pair counts with high state fidelity. Here we present a tunable compensation method for tackling the rising state decoherence in the two degrees of freedom in the case of crystals with negative birefringence. We determine the directional-spectral phase function of the two-photon state initially and after compensation, taking into account the finite spectral width of the pump beam. Subsequently, the optimal characteristics of the compensation crystals are computed by criteria of flat phase function in spectrum and space. The results of our model are compared with measurements of some recent experiments.
We suggest and demonstrate a novel source of two-photon multipartite entangled states which exploits the transverse spatial structure of spontaneous parametric down-conversion together with a programmable spatial light modulator (SLM). The one-dimensional SLM is used to perform polarization entanglement purification and to realize arbitrary phase gates between polarization and momentum degrees of freedom of photons. We experimentally demonstrate our scheme by generating two-photon three-qubit linear cluster states with high fidelity using a diode laser pump with a limited coherence time and power on the crystal as low as  2.5~2.5 2.5 mW.
Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time-polarization mapping, offering a promising route toward stable, low-QBER quantum communication.