Conservation of angular momentum on a single-photon level

Identifying conservation laws is central to every subfield of physics, as they illuminate the underlying symmetries and fundamental principles. A prime example can be found in quantum optics: The conservation of orbital angular momentum (OAM) during spontaneous parametric down-conversion (SPDC) enables the generation of a photon pair with entangled OAM. In this article, we report on the first study of OAM conservation in SPDC pumped by single photons. Our results present the first implementation of cascaded down-conversion without waveguides, setting the stage for experiments on the direct generation of multi-photon high-dimensional entanglement using all degrees of freedom of light.

💡 Research Summary

The paper presents the first experimental verification that orbital angular momentum (OAM) is conserved at the single‑photon level in spontaneous parametric down‑conversion (SPDC). While OAM conservation has long been demonstrated with strong classical laser pumps—where only the average OAM is guaranteed—the authors ask whether each individual quantum of OAM is transferred faithfully when the pump itself is a quantum state. To answer this, they construct a cascaded SPDC system: the first crystal generates photon pairs at 783 nm and 1588 nm from a continuous‑wave 524 nm pump. The 1588 nm photon serves as a herald, while the 783 nm photon is used as the pump for a second crystal. By switching between spontaneous emission (heralded single‑photon pump) and stimulated emission (coherent seed laser), they can prepare the pump in either a true single‑photon Fock state or a weak coherent state. The second crystal is a bulk periodically poled lithium niobate (ppLN) device that allows free‑space propagation of OAM‑carrying modes, unlike previous waveguide implementations that restrict spatial mode structure.

Theoretical analysis starts from the time‑dependent interaction Hamiltonian for a χ^(2) medium, expands the electric‑field operators in Laguerre‑Gaussian modes, and shows that the overlap integral enforces the selection rule ℓ_p = ℓ_s + ℓ_i due to rotational symmetry. The commutator