Reconfigurable circuit for mode tunable topological structured light

Abstract

Structured light in the quantum regime has garnered considerable attention due to the opportunities it offers when mixing light's internal degrees of freedom, for high-dimensional and multi-dimensional quantum states of light. A popular example is to harness polarisation and spatial entangled photons with a shared topological invariant that is robust against numerous families of noisy quantum channels. Yet, producing such states with high purity and adaptability remains challenging. Here we introduce a compact, self-locking Mach-Zehnder interferometer that integrates digital spatial light modulators with static beam displacers to map spatial-mode entanglement from a parametric down-conversion source onto topological entanglement with high fidelity. The device also mimics the action of a reprogrammable controlled-unitary gate, digitally driven by the spatial light modulator. This approach is an enabling platform and provides a practical route to generating reliable, high-purity quantum-structured light with topological features, both at the single-photon level and as entangled states, a direction of growing topical interest.

Figures (3)

• Figure 1: (a) Hybrid biphoton states possessing nonlocal correlations between the polarisation of one photon (Photon A) and the spatial mode of the other photon (Photon B), exhibit tunable topological structures. (b) Schematic for generating hybrid entanglement using SPDC states initially entangled in the OAM Dof. NLC: nonlinear crystal; BPF: band-pass filter; M: mirror; SLM: spatial light modulator; BC: BBO birefringent crystal; APD: avalanche photo diodes; HWP: half-wave plate; QWP: quarter-wave plate; LP: linear polarizer; PBD: polarization beam displacers; SMF: single-mode fiber; CC: coincidence counter. (c) Digital self-locking Mach–Zehnder interferometer for performing the spatial-to-polarisation mode mapping constructed using two PBDs a HWP and a an SLM. A BBO crystal was used to compensate for the mode-dependent delay. (d) Circuit representation of the interferometer acting as a controlled unitary operator in the polarisation and spatial mode of photon A, performing a conditional unitary operation (OAM modulation), depending on the input polarisation state of photon A. (e) At the end of this process, photon A is measured in the polarisation DoF using a QWP, HWP and LP while photon B is measured in the spatial DoF using SLM2.
• Figure 2: State reconstruction and characterisation across multiple subspaces $(\ell_{1}, \ell_{2})$ for states of the form$\ket{\Phi}_{AB} = \ket{H}\ket{\ell_1} + \ket{V}\ket{\ell_2}$. (a) Joint projective measurement outcomes on photon A (polarization, rows) and B (OAM, columns) with their corresponding (b) reconstructed density matrices for the states with $(\ell_1,\ell_2) \in \{(1,0), (-1,1), (2,0), (3,-2)\}$. The magnitude $(\text{abs}(\rho))$$(\text{Re}(\rho))$ and imaginary, $(\text{Im}(\rho))$, components of the density matrix are shown. (c) Joint detection measurement outcomes for the CHSH Bell-inequality test for subspaces $(1,0)$, $(1,-1)$, $(2,0)$, and $(3,-2)$ respectively, with the associated angles for photon A ($\theta_{A}$) shown in the legend below. The measured subspaces admit visibilities of $V = 0.86, 0.90, 0.91, 0.91$, and Bell parameters, $S = 2.35\pm0.02, 2.49\pm0.02, 2.56\pm0.02 , 2.56 \pm0.03$, respectively.
• Figure 3: The reconstructed quantum Stokes vector field, $\vec{S}_A(\vec{r}_B)$, for every state with the associated vector components, $S_{x,y,z}$ and Stokes phases $\phi_{ij}=\tan^{-1}\left(\frac{S_j}{S_i}\right)$, for states with topological numbers $N\in \{0.9932, 0.0027, 2.9971, 4.90\}$ found in the upper panel and $N\in \{-0.9932, -1.9987, -3.9957, -4.9037\}$ found in the lower panel.