Entangled ripples and twists of light: radial and azimuthal Laguerre–Gaussian mode entanglement

Abstract

It is well known that photons can carry a spatial structure akin to a ‘twisted’ or ‘rippled’ wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light–matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre–Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field LG entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between nine LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication.

Radially and Azimuthally Pure Vortex Beams from Phase-Amplitude Metasurfaces

“…In fact, the ability to perform phase and amplitude modulation allows us to sculpt many other families of paraxial beams. Exploiting the control over the complete transverse spatial degree of freedom is significant for the emerging field of high-dimensional quantum information, boosting communication channels with higher encoding capacities and increasing noise robustness in entanglement distributions . We foresee these devices as a very convenient and powerful approach, which could further drive the uptake of higher-order vortex modes.…”

Radially and azimuthally pure vortex beams from phase-amplitude metasurfaces

“…Exploiting the control over the complete transverse spatial degreeof-freedom is significant for the emerging field of high-dimensional quantum information, boosting communication channels with higher encoding capacities 23 and increasing noise robustness in entanglement distributions. 35 We foresee these devices as a very convenient and powerful approach, which could further drive the uptake of higher order vortex modes.…”

Inverse-design of high-dimensional quantum optical circuits in a complex medium

“…In contrast, our programmable circuit T performs generalised basis transformations to a localised "pixel" basis with a maximum theoretical efficiency of unity (see Section III), enabling multi-outcome measurements in any given basis. The circuit is programmed to operate on two different input bases, the macro-pixel basis [41] and the orbital-angularmomentum (OAM) basis [54], while the target output modes are randomly selected from the set of all possible foci at the output of the circuit. We then implement a variety of different target gates including the identity-I, Pauli-Z, Pauli-X, Fourier-F, and random unitaries-R by programming the circuit using the wavefront-matching algorithm.…”

“…The main characteristics of the entanglement source, i.e., the strength of transverse-momentum correlation, generated beam waist, and the position of the beams, are determined by using our developed 2Dπmeasurement [77] which is the joint coincidence measurement of local π-phase step knife-edge scans across the SLMs at each party. The two-photon state is then characterised via quantum state tomography (S.4) and the entanglement dimensionality is certified [78] using a high-dimensional entanglement witness in two discrete spatial-mode bases-the Macro-pixel basis [41] and the orbital-angular-momentum (OAM) basis [79]. We utilise these two bases as the set of input target modes for constructing the programmable circuits.…”

“…In this article, we harness light scattering through an off-the-shelf multi-mode fibre to program generalised quantum circuits for transverse spatial photonic modes in dimensions up to seven. We apply these circuits for the manipulation of high-dimensional entangled states of light in multiple spatial-mode bases, demonstrating highdimensional Pauli-Z and X gates, discrete Fourier transforms, and random unitaries in the macro-pixel and OAM spatial-mode bases [41,54]. Furthermore, in contrast with single-outcome projective measurements that are inherently inefficient [55], our technique realises generalised transformations to a spatially localised "pixel" ba-sis, effectively turning the channel itself into a generalised multi-outcome measurement device.…”