Fig. 1: Design and performance of the multi-modal source.

a Schematic of the source. An input near-1550 nm pulsed pump laser (4.5 nm bandwidth), initially propagating in the TM0 mode, is split using a 50:50 beam-splitter (BS). The output in the upper arm of the BS is converted into the TM1 mode via a mode-converter (MC), while the TM0 output in the lower arm is delayed by a time τ = 1.46 ps. Due to the different group velocities, the two modes become overlapped and subsequently diverge again while propagating through the source, as qualitatively colour-coded in the figure. Photon pairs, with the signal photon (near 1588 nm) in the TM1 mode and the idler photon (near 1516 nm) in the TM0 mode, are emitted via inter-modal SFWM and finally deterministically separated via a MC. Inset: cross sections of the TM0 and TM1 modes in the MM waveguide. b Simulated JSI of the source in the presence of a delay τ = 1.46 ps (left) and with no delay (right), with corresponding single photon purities of 99.4% and 84.0%. c Optical microscope image of a single multi-modal source structure-waveguides are highlighted. d Set-up to characterise squeezed light via second-order correlation measurements, using a polarisation controller (PC), fibre pass-band filter (F), variable optical attenuator (VOA), and an optical power monitor (PM). e Measured squeezing as a function of (off-chip) pump power. Blue and red points are data measured in a source with and without delay, respectively, with a fit shown as a black line. The stars indicate the typical operating regime. Inset: measured heralded \({g}_{{\rm{h}}}^{(2)}(0)\) as a function of input powers. f Set-up for the characterisation of the emitted JSI, using a tunable filter (TF). g Measured JSI from the source with delay (left) and without delay (right), with respective corresponding spectral purities of 0.9904(6) and 0.931(2). h Set-up for purity characterisation via unheralded second-order correlation measurements. Idler photons are discarded via an absorbing termination (AT). i Measured unheralded \({g}_{{\rm{u}}}^{(2)}(\Delta t)\) in the source with delay. Each bar corresponds to a coincidence window of 2 ns (inset). The measured \({g}_{{\rm{u}}}^{(2)}(0)=1.97(3)\) corresponds to a photon spectral purity of 0.97(3). Error bars represent 1 s.d. and are calculated assuming Poissonian error statistics.