In order to investigate non-volatile optical memory functionality, we first measure the current-voltage (I-V) relationship as shown in Fig. 3a. By voltage cycling from 0→−21→0→15→0 V, a hysteresis curve is observed, therefore, confirming electrical memristor behavior. Figure 3b. illustrates the corresponding resistance indicating an initial high-resistance-state (HRS) which becomes a low-resistance-state (LRS) by applying a set voltage Vset = − 17.31 V. By applying a reset voltage of Vreset > 5 V, a transition from the LRS to HRS can occur, thus concluding a reset back to the original electrical state. While taking I–V data, we simultaneously measured the optical spectral response with an optical spectrum analyzer (OSA). The optical response is shown in Fig. 3c–f and is color-coded according to the I–V curves in Fig. 3a–b. Applying a bias from 0 to −21 V results in a non-volatile wavelength shift of Δλnon-volatile = 12.53 nm with near negligible optical losses (Fig. 3c). The wavelength shift is measured from the resonance dip (~1294.45 nm) where the arrow begins at 0 V and to the resonance dip (1306.98 nm) where the arrow ends with −21 V. Device insertion loss is discussed in supplementary note 5 and observed to be <0.5 dB. Ramping back down from −21 to 0 V does not shift the optical response back to the original state (Fig. 3d) and has a non-volatile wavelength stability of ~+/− 0.2 nm (35 GHz). This indicates a non-volatile phase shift of Δφ = 1.245π assuming a FSR = 20.13 nm, at essentially 0 power consumption (recorded current = 34 pA at 0 V). T 

Initial phase tuning measurements were performed on CTM cells integrated with ring resonator-based designs. One example consists of two cascaded double ring structures. The power coupling coefficients are chosen such that 𝜅1,2 = 0.25k𝜅0 4 results in a maximally flat filter condition if k = 2 and 𝜅0 2 = 0.35,[101,102] 𝜅1 is the electric field coupling coefficient between two rings. 𝜅0 is the field coupling coefficient between the input or output waveguides. Each cascade double ring structure can be divided into ′Ring bank 1″ and ′Ring bank 2″, with the first ring bank designed for a free-spectral range (FSR) of 130 GHz assuming a group index of ng = 3.78. Details of the directional coupler designs are shown in Figure 4c,d. Each ring bank consists of two III-V/Si ring resonators and three couplers as shown in Figure 4a,b. Optical measurements are performed on the port labeled “Out3” and yielded an FSR of ≈126 GHz most likely due to fabrication imperfections and unknown experimental group indices. ′Ring bank 2″ is shifted by a ΔL = 0.262 μm to offset resonances from ′Ring bank 1″ as shown in Figure 5a,d. Figure 5a,b shows the measured optical response before and after a non-volatile write operation of 0 → + 9 → 0 V. An ER of 7.11 dB was achieved with only a shift of Δ𝜆non-volatile = 0.041 nm. Transfer matrix calculations indicate an effective index change of Δneff ≈ 1.5 × 10−4 nm which is quite comparable to plasma dispersion-based phase shifters.[93] 

Simultaneous C–V curves and optical transmission spectra were also performed to track the evolution of optical non-volatility as shown in Figure 8c,d. A hysteresis curve in Figure 8c illustrates clear optical transmission non-volatility (at 𝜆 = 1289.57 nm) in the write to retention state (0 → +9 → 0 V). By applying an erase operation and observing the final state (0 → 5 → 0 V), we can see near perfect reset of the device with a slight difference in amplitude of ≈0.125 dB. Figure 8d shows measured C–V curves while tracking resonant wavelength minima. Near perfect reset states are also achieved. The measured C–V curves indicate significant smearing compared to theoretical curves and can be attributed to interface states at the p-Si/SiO2 and n-GaAs/HfO2 interface.