a, Bistable ANPs switch from a dark to a bright, stable state at high 1,064 nm pump intensity, which persists even after the power decreases. ANPs that have not been previously subjected to high intensities show much weaker emission under the same excitation conditions. b, Landscape of ANP states at different pump intensities. Quenching by MPR stabilizes the dark state (1). In contrast, the positive feedback loop of ESA and CR leads to PA and stabilizes the bright state (3). Intermediate excitation intensities result in a double well (2) in which the bistable dark and bright states are separated by a potential energy barrier that gives rise to instability and history dependence.

a, Pump power dependence of Nd³⁺ emission (810 nm, ⁴F_5/2 → ⁴I_9/2) in KPb₂Cl₅:Nd³⁺ ANPs at 77 K. The red data points represent the luminescence intensity acquired with increasing excitation intensity (up scan) and blue, with decreasing excitation intensity (down scan). The number indices represent the sequence of events. b, Luminescence spectra of KPb₂Cl₅:Nd³⁺ nanocrystals corresponding to power density and scan direction labelled in a by the number indices. c, Switch-on threshold, hysteresis width and switch-on contrast from n = 71 independent measurement spots on a film sample of KPb₂Cl₅:Nd³⁺ ANPs. Dots, experimental data points. The box plots display the mean (pink line), standard deviation (whiskers), and 25th and 75th percentiles (box bounds). The minima and maxima are shown as open circles. The measurement parameters are indicated below each box plot. d, Pump power dependence of Nd³⁺ emission (810 nm, ⁴F_5/2 → ⁴I_9/2) in KPb₂Cl₅:Nd³⁺ ANPs in the 110–170 K temperature range. Emission scaling at the switch-on threshold is derived from a linear fit of the log[light–light] curves; see the dashed lines and nonlinearity (s) values in a and d.

Reduction in the pump intensity below the 6.7 kW cm^–2 switch-on threshold does not reduce the ANP emission much until the irradiance decreases to 4.2 kW cm^–2, at which point the ANPs abruptly turn dark (Fig. 2a). This non-zero difference between the excitation intensity required to switch the ANPs on and off creates a hysteresis in their optical response, indicating optical bistability. Within this bistable region, the two stable states of the ANPs are manifested as dark or bright emission at intermediate pump intensity (for example, 5 kW cm^–2), depending on whether the luminescence is measured before or after reaching the switch-on threshold. Such bistability is spectrally observed in multiple Nd³⁺ emission lines, including the 810 nm (⁴F_5/2 → ⁴I_9/2) and 880 nm (⁴F_3/2 → ⁴I_9/2) transitions (Fig. 2b).

We observed this luminescence hysteresis on two different optical setups (Supplementary Fig. 4) and on different substrates (Supplementary Fig. 5). Furthermore, when we varied the acquisition dwell times (0.1–10 s) used for each pump power, the hysteresis widths and thresholds remained constant (Supplementary Fig. 6), indicating that the hysteresis does not originate from time-dependent factors such as laser-induced heating or slow PA rise times (~20 ms; Supplementary Fig. 21). Even room-temperature rise times (50–70 ms)²⁴ are shorter than the shortest dwell times (0.1 s), ensuring that samples are measured at steady state. All of these observations support our conclusion that the ANP emission signal is intrinsically bistable and not the result of experimental artefacts²⁷.

To obtain statistical information about the reproducibility of IOB and characteristics including the switch-on threshold, hysteresis width and intensity contrast, we measured the pump power dependence at multiple spots across a film of KPb₂Cl₅:Nd³⁺ ANPs (Supplementary Fig. 7 and Fig. 2c). The average switch-on power density is 5.2 kW cm^–2, corresponding to 64 μW, suitable for low-power requirements (microwatts to milliwatts) in optical computing²⁸. On average, the width of luminescence hysteresis is 1 kW cm^–2, and the photoswitching contrast of the KPb₂Cl₅:Nd³⁺ ANPs (that is, signal-to-noise ratio at the switch-on threshold) is 14 ± 4 dB, sufficiently high to unambiguously differentiate between the bright and dark ANP states²⁹. This contrast is one to two orders of magnitude greater than that of previously reported IOB nanomaterials, which were studied at room temperature (Supplementary Table 2 provides a comparison of KPb₂Cl₅:Nd³⁺ ANPs to other optically bistable materials).

To demonstrate the stability and reproducibility of this IOB, we repeated the optical hysteresis measurements on the same spot (Fig. 2a) 100 times over 12 h (Supplementary Fig. 8). Despite minor variations in the switch-on threshold (6.52 ± 0.21 kW cm^–2) and hysteresis width (2.20 ± 0.15 kW cm^–2), possibly due to sample drift, the IOB is consistently observed for every cycle. Notably, these ANPs show no photodarkening or blinking^30,31.

To probe how these nanocrystals give rise to IOB, we varied their Nd³⁺-doping levels. High nonlinearity and luminescence hysteresis are predominantly observed in samples with Nd³⁺ concentrations above 4 mol% (Supplementary Fig. 9), suggesting that the nonlinearity requisite for the IOB is driven by a mechanism such as PA that incorporates distance-dependent energy transfer processes^13,32. To understand the role of the host matrix, we measured the luminescence power dependence of Nd³⁺ ions doped in a higher-phonon-energy host, NaYF₄. However, we do not observe PA or luminescence hysteresis even when NaYF₄:Nd³⁺ nanocrystals are cooled to 8 K (Supplementary Fig. 10), underscoring the need for low-phonon-energy hosts to suppress MPR and observe PA and IOB. Thus, cryogenic temperatures alone are insufficient to promote IOB from nonlinear Nd³⁺ luminescence.

We further investigated the impact of thermal phonons on the quenching of Nd³⁺ energy levels (for example, ⁴I_11/2) by measuring the power-dependent luminescence of KPb₂Cl₅:Nd³⁺ ANPs at different temperatures. We find that higher temperatures lead to a lower degree of nonlinearity and narrowing of luminescence hysteresis (Fig. 2d), making thermal contributions to IOB unlikely. Importantly, we observe IOB at temperatures as high as 150 K (Fig. 2d). The switch-on threshold also shifts to lower power densities with increasing temperatures, correlating with an enhanced phonon-assisted ground-state absorption (GSA). In particular, at 160 K, ANPs do not show luminescence hysteresis despite their highly nonlinear (s = 70) luminescence, suggesting that extreme nonlinearities (s ≥ 100) are required to induce IOB in KPb₂Cl₅:Nd³⁺ ANPs.

Mechanism of IOB in ANPs

To corroborate these experimental results and better understand this observed IOB, we used a differential rate equation model³³ to numerically simulate the time-dependent population of the 4f^N energy levels of Nd³⁺ ions in a KPb₂Cl₅ host (Supplementary Note 1). Our simulations reproduce the nonlinear power scaling of KPb₂Cl₅:Nd³⁺ luminescence and, most importantly, the luminescence hysteresis of experimental observations (Supplementary Fig. 11). Similar results were also found using a simplified rate equation model (Supplementary Note 2). These simulations do not incorporate thermal phenomena, highlighting that IOB in KPb₂Cl₅:Nd³⁺ ANPs is governed only by the optical activation of electronic 4f energy levels, which distinguishes this system from thermal IOB in other materials^19,23.

The photophysical mechanism (Supplementary Fig. 13) extracted from these simulations³³ resembles the canonical PA process in which excited-state absorption (ESA; Fig. 3a, thick orange arrow) dominates over GSA (thin orange arrow) and couples to a cascade of cross-relaxation (CR) processes (dashed arrows, CR1–5) to form an ‘energy loop’¹³. Each CR process multiplies the population of low-lying excited manifolds of Nd³⁺ ions, like ⁴I_11/2, increasing the rates of ESA and CR from those levels. Repeated CR + ESA amplifies those populations exponentially in a positive feedback loop, resulting in the observed nonlinear behaviour.

Fig. 3: Model of IOB in KPb₂Cl₅:Nd³⁺ ANPs.

a, Simplified energy-level diagram of Nd³⁺ ions showing GSA, CR, ESA and emission. ESA and a collection of CR processes (CR1-5) form a positive feedback loop, leading to giant signal amplification and IOB. Competing MPR (wavy arrow) is also shown. b, Pump power dependence of Nd³⁺ excited (⁴I_11/2) versus ground (⁴I_9/2) energy-level population ratio in a simulated KPb₂Cl₅:20 mol% Nd³⁺ system. The dashed line corresponds to the power-up scan and the solid line to the power-down scan. c, Influence of CR pathway knock-outs (KOs) on the hysteresis width and nonlinearity for ⁴F_3/2 → ⁴I_9/2 radiative transition. WT, wild type; CR#, CR1-5 as shown in a.

Such looping is supported by our observation that simulated populations of the Nd³⁺ ground (⁴I_9/2) and first-excited (⁴I_11/2) 4f electronic levels are inverted at the switch-on pump threshold (Fig. 3b). In particular, this population inversion (PI) is maintained even when the power is reduced below that threshold, resulting in hysteresis in the power dependence of the population ratio between the ⁴I_11/2 and ⁴I_9/2 energy levels. The PI is correlated with the emergence of the bright state of ANPs, suggesting that bright and dark steady states of these bistable ANPs are distinguished by their inverted and non-inverted excited-level populations, respectively.

To identify the critical transitions responsible for IOB, we performed a series of ‘knock-out’ simulations in which we systematically deactivate individual CR pathways in the CR cascade (CR1–5) that drives the PA (additional knock-out methods and results provided in the Supplementary Information)³⁴. When MPR and other parameters are held constant, the simulated power-dependent luminescence of the knock-out systems reveals that among the CR processes, CR1 (Fig. 3a; [(⁴I_9/2 → ⁴I_11/2):(⁴I_13/2 → ⁴I_11/2)]) has the most impact on the performance of bistable ANPs. Deactivating CR1 reduces the nonlinearity by 5.8-fold (to s = 17) and eliminates luminescence hysteresis (Fig. 3c). Although CR processes from the ⁴F_3/2 excited energy level (Fig. 3a, CR3–5) are not essential to establish PI, knocking them out shifts the switch-on threshold to higher values (Supplementary Fig. 11). We believe that these pathways are needed to repopulate the lower Nd³⁺ energy levels (⁴I_11/2, ⁴I_13/2 and ⁴I_15/2) after photon absorption and they contribute to the nonlinear behaviour of ANPs through a CR cascade. Finally, we compared the rate of CR1 in the wild-type (no knock-outs) KPb₂Cl₅:Nd³⁺ with that of other transitions. We find that within the bistable region of luminescence, the ⁴I_11/2 energy level is populated via CR1 faster than it is depopulated via MPR (Supplementary Figs. 14 and 15). This dominance of CR1 over quenching processes appears to be a necessary condition for IOB, which is satisfied in low-phonon-energy matrices that result in low MPR rates (Supplementary Table 4).

On the basis of these mechanistic observations, we construct a conceptual scheme explaining how IOB occurs in KPb₂Cl₅:Nd³⁺ ANPs (Fig. 1b). These bistable ANPs exhibit two stable macroscopic states: (i) a dark, non-emissive state with Nd³⁺ ions occupying their ground energy level and (ii) an avalanching, luminescent state with Nd³⁺ ions populated predominantly in their first-excited energy level. At low 1,064 nm pump intensities (Fig. 1b, P_low), the dark state (Fig. 1b, (1)) is stabilized from moderate increases in pump power by the suppression of non-resonant GSA in the low-phonon-energy KPb₂Cl₅ host at low temperatures. MPR also stabilizes the dark state by quenching the few excited Nd³⁺ ions before they can achieve the intermediate ⁴I_11/2 populations necessary for avalanching. The bright state (Fig. 1b, (3))—established at high intensities (P_high)—is stable because the positive feedback of the avalanching process maintains PI. Even when the pump power is reduced below the PA threshold, avalanching persists because the intermediate ⁴I_11/2 population has already been seeded and is not readily quenched due to suppressed MPR in the low-phonon-energy host. Owing to the giant nonlinearity of PA, only a small amount of ESA from this ⁴I_11/2 level is necessary to sustain the cascade of CR back to the same level and counteract its depopulation by MPR. As a result, both bright and dark states are stable at moderate pump intensities (Fig. 1b, (2), P_med).

To reiterate, this IOB is a direct consequence of the low phonon energy of KPb₂Cl₅ and the positive feedback of PA in Nd³⁺ dopants. These driving forces create a potential energy barrier (that is, instability region) that separates the two states in the bistable regime (the potential energy surface is shown in Fig. 1b). This barrier ultimately gives rise to the latching hysteresis and history dependence that characterizes the bistable luminescence of KPb₂Cl₅:Nd³⁺ ANPs.

Temporal modulation of IOB

After establishing that IOB in KPb₂Cl₅:Nd³⁺ ANPs is realized through a PA mechanism, we hypothesized that the dynamics of this positive feedback could be manipulated by modulating the excitation power over time, potentially influencing the IOB behaviour. To test this hypothesis, we performed power dependence studies with a 1,064 nm pump modulated at various pulse frequencies and duty cycles. We find that modulating the laser selectively inhibits or induces IOB in ANPs and allows for control over luminescence hysteresis (Fig. 4 and Supplementary Figs. 16 and 17). Slow pulsing (<170 Hz, 40% duty cycle) of the excitation laser eliminates the hysteresis observed with continuous-wave (CW) 1,064 nm excitation and decreases the PA nonlinearity (s = 40 at 140 Hz; Fig. 4a). In contrast, at higher pulsing frequencies the hysteresis widens (Fig. 4b), and the PA threshold shifts to higher average powers (Fig. 4c). At a 1,000 Hz pump frequency, the hysteresis width reached 4.5 kW cm^–2 (Fig. 4) and 24 kW cm^–2 (Supplementary Fig. 18) for 40% and 10% pulse duty cycle, respectively, considerably wider than that under CW excitation (1.6 kW cm^–2).

Fig. 4: Temporal modulation of luminescence hysteresis.

a, Pump power dependence of Nd³⁺ emission in KPb₂Cl₅:Nd³⁺ ANPs at 77 K under 1,064 nm CW and pulsed pump excitation (40% duty cycle). cps, counts per second; PD, power density. b,c, Hysteresis width (b) and PA switch-on threshold versus pump pulse frequency (40% duty cycle) (c). The corresponding dependence on the temporal separation between pulses is also shown. The respective values under the CW pump are shown as squares. Emission scaling in a is derived from a linear fit of the log[light–light] curves. Data in b and c are shown as the mean values ± one standard deviation (n = 3).

We rationalize this dynamic control over IOB by considering the pulse duration and period between pulses. The greater switch-on power thresholds at higher frequencies arise due to the decreased probability of GSA with decreasing pulse energies (25 nJ at 100 Hz versus 3.6 nJ at 1,000 Hz). Similarly, IOB emerges at high pulsing frequencies because the time period between pulses is short enough to sustain the positive feedback of CR + ESA in KPb₂Cl₅:Nd³⁺ ANPs. We also examined the notable difference in hysteresis characteristics between CW and high-frequency pulsed excitation of ANPs. The widening of hysteresis and higher average switch-on powers observed in the 500–1,000 Hz range are not observed at pulse frequencies higher than 4,000 Hz because such closely spaced pulses become analogous to quasi-CW excitation (Supplementary Figs. 19 and 20). On the basis of the frequencies at which ANPs begin to exhibit luminescence hysteresis (180 Hz and 300 Hz at 40% and 10% duty cycle, respectively), we estimate that the PI in ANPs lasts up to 3 ms, which is probably related to the lifetime of the ⁴I_11/2 excited energy level of Nd³⁺ ions in KPb₂Cl₅ matrix (2.3 ms at room temperature³⁵). The duration of PI also dictates the photoactivation kinetics of the KPb₂Cl₅:Nd³⁺ ANPs. With high-frequency pulsing, we measure short rise times for emitting energy levels populated directly by ESA (for example, ⁴F_3/2 is populated in 305 µs). In contrast, PI is lost between low-frequency excitation pulses, resulting in millisecond rise times from the initially slow GSA followed by PA, similar to KPb₂Cl₅:Nd³⁺ ANPs at room temperature²⁴ (Supplementary Note 3).

The fact that this IOB occurs via photophysical interactions between dopant ions (that is, non-thermally) allows us to actively control the switch-on power threshold, hysteresis width and nonlinearity of bistable ANPs, underscoring their utility in photonic applications^36,37,38.

Optical switching via instability crossing

With the ability to induce and control IOB in KPb₂Cl₅:Nd³⁺ ANPs, we sought to demonstrate how their bistable response can be used for switching logic and memory. In principle, a bistable ANP can be treated as a bit whose dark state (assigned a value of 0) may be flipped by increasing the pump intensity to activate the ANP’s bright (1) state. The bright bit can then be maintained at lower pump intensities. However, this single-laser approach may be impractical as it requires varying the pump intensity and requires a dedicated laser beam to address each bit independently.

To overcome these challenges, we hypothesized that bistable ANPs could be manipulated using laser pumps at two different wavelengths, mimicking a transistor (Fig. 5a). We developed an approach that uses an 808 nm control laser pulse to set an ANP in its bright state and a constant 1,064 nm laser as a bias to maintain this state. The advantage of this two-laser approach is that the 1,064 nm bias laser, in principle, can be spread diffusely to maintain the state of many bits simultaneously, allowing the control laser to raster freely and flip individual bits. Furthermore, the 808 nm control pulse enables the fast switching of ANPs from their dark to a bright state because it is resonant with GSA (⁴I_9/2 → ⁴F_3/2) in Nd³⁺ ions. This resonant excitation of the ANP bright states at 808 nm bypasses, or crosses, the instability barrier that normally exists when exciting ANPs non-resonantly at 1,064 nm (Fig. 5b). Such ‘instability crossing’ simplifies bit operations because it eliminates the need to vary the 1,064 nm laser power.

Fig. 5: Photoswitching of ANPs via instability crossing.

a, Schematic of the transistor-like addressing of KPb₂Cl₅:Nd³⁺ nanocrystals with 808 nm control input (7 W cm^–2) under a constant 1,064 nm pump bias (4.7 kW cm^–2). b, Pump power dependence of KPb₂Cl₅:Nd³⁺ nanocrystals used for photoswitching experiments. The bistability region (grey) and instability crossing (orange arrow) are shown. The 1,064 nm bias for the experiment in c was applied at three different power densities: a dark state outside the bistability region (cross), within the bistability region (circle) and a bright state outside the bistability region (square). c, Time recording of emission at 880 nm of KPb₂Cl₅:Nd³⁺ ANPs before and after 808 nm control pulse when biased at 1,064 nm pump. The symbols in c indicate the 1,064 nm bias power densities for each trace as defined by the placement of those symbols in b.

When we implemented this two-laser scheme on a film of ANPs, we observed that their 880 nm (⁴F_3/2 → ⁴I_9/2) luminescence flips from a dark (0) to a bright (1) state after an ~1 s pulse of the 808 nm laser and is maintained as long as a 1,064 nm bias laser (4.7 kW cm^–2) is present (Fig. 5c). In particular, the switching between the two stable states is achieved at an extremely low 808 nm power density (7 W cm^–2, corresponding to 75 nW power). We note that the latching of the bright state via instability crossing would not occur with thermally activated avalanching and is enabled by the PA-driven IOB in KPb₂Cl₅:Nd³⁺ ANPs.

To determine whether photoswitching occurs only when ANPs are biased within the bistable region, we performed control experiments by applying the 1,064 nm laser bias outside the bistable region and observed no change in ANP luminescence before or after the 808 nm input (Fig. 5c). Furthermore, we demonstrate the instability crossing using a pulsed 1,064 nm laser to exploit larger hysteresis (Supplementary Fig. 22) and using control lasers with wavelengths resonant with different GSA transitions of Nd³⁺ ions (875 nm for ⁴I_9/2 → ⁴F_3/2 GSA and 745 nm for ⁴I_9/2 → ⁴F_7/2 GSA; Supplementary Fig. 23). These findings demonstrate the versatility of bistable ANPs and establish the foundation for their use as nanoscale optical transistors and volatile optical memory³⁹.