Photonic hyperentanglement in polarisation and frequency via joint spectrum shaping

Abstract

Hyperentanglement offers enhanced capacity for quantum information processing and communication protocols, especially in combination with robust high-dimensional degrees of freedom such as frequency-bin encoding. Here, we present a single-pass, unfiltered, down-conversion source of hyperentangled photon pairs in polarisation and frequency-bin degrees of freedom with dynamically tunable state dimension and composition at telecom wavelengths. We achieve this by optimal tailoring of the photons' joint spectral amplitude via pump and nonlinearity shaping. Using polarisation-resolved time-of-flight spectrometry and Hong-Ou-Mandel interference, we characterise the hyperentangled states and demonstrate for the polarisation component fidelities exceeding 99% averaged over frequency bins and concurrences above 98%. The degree of spectral entanglement, quantified by the Hong-Ou-Mandel visibility, is measured as 90%, well in line with numerical simulations. This approach provides a scalable route toward high-dimensional quantum states for quantum communication and computing applications.

Figures (8)

• Figure 1: Joint spectral amplitude engineering and hyperentanglement generation setup. (a) Spectral shaping is employed to tailor a multi-Gaussian spectrum (red line) from the unshaped laser pump spectrum (blue line). The corresponding simulated multi-Gaussian PEF is shown on the bottom panel. (b) The nonlinearity profile (blue line) is shaped to achieve a multi-Gaussian PMF (see bottom panel) by engineering the crystal's poling pattern, as depicted in the inset. Light and dark grey regions have inverted nonlinearity signs. The specific pattern used here introduces a phase shift of $\pi$ between the antinodes of the PMF. (c) The resulting joint spectral amplitude shows fully separate frequency bins, as shown in the marginal distributions of $|\text{JSA}|$. Schmidt decomposition yields a Schmidt number $K=2.033$ due to the symmetry of the JSA. (d) A femtosecond (fs)-pulsed laser is spectrally shaped with a pulse shaper Faleo2025 and the output is split at a beam splitter to pump two photon-pair sources, each consisting of a custom apodised-KTP crystal inside a Sagnac loop. A half-wave plate (HWP) controls the pump polarisation, determining whether separable or entangled photon pairs are generated. The hyperentangled down-converted photons are separated from the pump beam using a polarising beam splitter (PBS), a dichroic mirror (DM) and lowpass filters (LPF), and their polarisation state is tuned through fibre polarisation controllers (FPC).
• Figure 2: Spectral characterisation. (a)-(b) Simulated and experimental $\sqrt{\text{JSI}}$ obtained via TOFS, resulting in Schmidt numbers of $K_{\text{sim}}=2.088$ and $K_{\text{exp}}=2.098(2)$, respectively. (c) Intra-pair HOM interference at a fibre beam splitter (see upper inset). The simulation of the interference pattern assumes a JSA equivalent to $\sqrt{\text{JSI}}$ of panel (b) with a $\pi$-phase shift as shown in Fig. \ref{['fig:fig1']}(c). The interference visibility of the simulation and of the fit are 92.62(2) and 90.3(4), respectively. (d) Heralded inter-pair HOM interference (see upper inset). The red line shows the simulation of the interference assuming JSAs as in (c). The blue fit line is accompanied by a shaded area representing its one-sigma uncertainty region. The visibility of the simulation and fit are 47.65(1) and 44.2(1.2), respectively.
• Figure 3: Spectral shaping tunability. (a)-(b) Experimental $\sqrt{\text{JSI}}$ and marginal distributions for a double and triple Gaussian shaping, respectively, with a peak spacing equal to half that of the Gaussian PMF. (a) Schmidt decomposition results in a Schmidt number of $K=3.881(2)$. (b) Schmidt decomposition results in a Schmidt number of $K=3.701(2)$.
• Figure 4: Polarisation entanglement of individual frequency bins. (a) Photons pairs undergo a polarisation projection by employing a quarter-wave plate (QWP), HWP, and PBS combination. At the output, the photons propagate through dispersion modules and, for each projection, coincidence events are measured with SNSPDs to perform a TOFS measurement and reconstruct the JSI (see examples for H-H and H-V projections). Polarisation state tomography for each frequency bin is performed by using a set of 36 such polarisation projections. (b) Real and imaginary parts of the reconstructed density matrix in the polarisation DOF via polarisation-resolved TOFS for one of the four frequency bins ("Bin 1" in the subsequent panels). (c) Fidelities of the reconstructed polarisation states with respect to the target Bell state $\ket{\phi^+_{\text{p}}}$ of the four individual frequency bins. (d) Concurrence of the reconstructed polarisation-entangled states of the four individual frequency bins. (e) Spectral purity of the measured $\sqrt{\text{JSI}}$ for each of the required 36 polarisation projections. The red dashed line is the value obtained via simulation, $P_{\text{sim}}=K_{\text{sim}}^{-1}=0.4789$, dark orange bars are the raw measured values, and the light orange bars are the measured values corrected for counting statistic noise.
• Figure 5: Exchange symmetry of the hyperentangled photon pairs. (a) Photon pairs are interfered by scanning their temporal delay at the FBS. At each output, tomography stages perform a polarisation projection and two-fold coincidence counts between the four output ports (T1, R1, T2, R2) are recorded over 20s with SNSPDs. (b)-(e) Each panel displays three coincidence combinations: cross-polarisation-outputs (T1R1 & T2R2 in blue, T1R2 & R1T2 in orange) and same-polarisation-outputs (T1T2 & R1R2 in purple). The solid lines are the fits of the data (dots). The insets illustrate the beam splitter outputs at zero delay (highlighting bunching or antibunching behaviour) and the possible photons' polarisations. (b)-(c) In the H/V basis, both Bell states produce T-R coincidences since $\ket{\text{HV}}\pm\ket{\text{VH}}$ always pairs orthogonal polarisations. (d)-(e) In the D/A basis, $\ket{\psi^+_{\text{p}}}$ transforms to $\propto\ket{\text{DD}}+\ket{\text{AA}}$, yielding same-polarisation coincidences (purple trace in (d)), while $\ket{\psi^-_{\text{p}}}$ transforms to $\propto\ket{\text{AD}}-\ket{\text{DA}}$, yielding again cross-polarisation coincidences as in (c).