Fig. 4: High-speed characterization of MO modulator at cryogenic temperatures.

a, Frequency response (S₂₁ coefficient) of the MO modulator at 4 K measured with a vector network analyser (VNA). The red dashed line highlights the point where S₂₁ has decreased by 3 dB relative to the low-frequency value. The roll-off in this regime is 3 dB per decade, which is much less than the 20 dB per decade expected for a single-pole filter function. A sharper roll-off sets in at a frequency of 5 GHz. b,c, Spectral response of the microring resonator near 1,500 nm (b) and 1,550 nm (c). Although the spectrum near 1,500 nm shows sharper resonance, the characterization is performed near 1,550 nm because this wavelength is better suited for the testing apparatus. d, Eye diagram at bit rates of 1 Gbps (first column) and 2 Gbps (second column) measured at temperatures of 77 K (first row) and 4 K (second row). The eye diagram at 4 K shows a smaller ER compared with 77 K, which is mainly due to the difficulties in finely controlling the fibre-to-chip alignment at this temperature (Supplementary Section 3 provides more details on the measurement setup). In the inset, we report the energy consumption per bit computed from the independent measurements of R and L. The value of energy per bit, E_b, does not substantially change between 77 and 4 K because the ohmic dissipation in the electromagnet is the dominating contribution of the energy consumption and the resistance saturates below ~100 K (Supplementary Section 3).