$\ell 00\ell$entanglement and the twisted quantum eraser

We demonstrate the generation of unbalanced two-photon entanglement in the Laguerre–Gaussian (LG) transverse-spatial degree-of-freedom, where one photon carries a fundamental (Gauss) mode and the other a higher-order LG mode with a non-zero azimuthal ($\ell$) component. Taking a cue from the $N00N$ state nomenclature, we call these types of states $\ell 00\ell$-entangled. They are generated by shifting one photon in the LG mode space and combining it with a second (initially uncorrelated) photon at a beamsplitter, followed by coincidence detection. In order to verify two-photon coherence, we demonstrate a two-photon “twisted” quantum eraser, where Hong–Ou–Mandel interference is recovered between two distinguishable photons by projecting them into a rotated LG superposition basis. Using an entanglement witness, we find that our generated states have fidelities of 95.31% and 89.80% to their respective ideal maximally entangled states. In addition to being of fundamental interest, this type of entanglement will likely have a significant impact on tickling the average quantum physicist’s funny bone.