Optical projection and spatial separation of spin entangled triplet-pairs from the S1 (21Ag-) state of pi-conjugated systems

The S1 (21Ag-) state is an optically dark state of natural and synthetic pi-conjugated materials that can play a critical role in optoelectronic processes such as, energy harvesting, photoprotection and singlet fission. Despite this widespread importance, direct experimental characterisations of the electronic structure of the S1 (21Ag-) wavefunction have remained scarce and uncertain, although advanced theory predicts it to have a rich multi-excitonic character. Here, studying an archetypal polymer, polydiacetylene, and carotenoids, we experimentally demonstrate that S1 (21Ag-) is a superposition state with strong contributions from spin-entangled pairs of triplet excitons (1(TT)). We further show that optical manipulation of the S1 (21Ag-) wavefunction using triplet absorption transitions allows selective projection of the 1(TT) component into a manifold of spatially separated triplet-pairs with lifetimes enhanced by up to one order of magnitude and whose yield is strongly dependent on the level of inter-chromophore coupling. Our results provide a unified picture of 21Ag-states in pi-conjugated materials and open new routes to exploit their dynamics in singlet fission, photobiology and for the generation of entangled (spin-1) particles for molecular quantum technologies.


Introduction
Electronically conjugated polymers and oligomers are ubiquitous in biological systems, with nature deploying these flexible and chemically tunable systems for a wide variety of advanced optoelectronic functions [1][2][3] . For many photosynthetic organisms they play a vital dual role as both light harvesting antennae and photoprotective molecules that can remove deleterious excess excitations 2,4,5 . In synthetic molecular materials developed for organic electronics they have transformed transistor and lightemitting diode technology [6][7][8] , as well as becoming promising components for next-generation photovoltaic (PV) devices with the potential to overcome the Shockley-Queisser limit via singlet fission (SF). In SF the absorption of a single photon ideally results in the formation of two spatially separated triplet excitons [9][10][11][12] , although a concerted sequence of ultrafast electronic and vibrational dynamics must compete with both radiative and non-radiative losses for this exciton multiplication to be efficient enough for applications [13][14][15][16][17] . Observation, understanding and control of these many-body quantum dynamics is therefore essential for optimisation of conjugated molecules for technologies such as SFenhanced PVs [18][19][20][21] .
However, the nature and understanding of electronic excitations in quasi-1D pi-conjugated polymers is greatly complicated by large system sizes, low dimensionality and very strong Coulombic interactions [22][23][24][25][26][27][28][29][30] . This leads to pronounced and well-studied effects of electronic correlation in these systems, with the key result being that their optical properties are dominated by strongly bound Frenkel excitons (electron-hole pairs) with very large (0.1-1 eV) exchange splittings between the optically excitable singlet excitons and the lowest (dark) triplet excitons. As a result of the low energy of the triplet exciton state (T1), creating a pair of triplet excitations may in fact cost less energy than the excitation of one singlet exciton. In this caseand as two spin-1 particles can possess a total spin of 0, 1, or 2it then becomes possible that the lowest-lying singlet excited state (S1) could be formed from pairs of triplets excitons with zero net spin, i.e. a singlet state. We note here that for a pair of triplet excitations to have zero total spin requires strong quantum correlations between the individual spins of each exciton. Indeed, in the language of quantum information theory, the singlet spin wavefunction for two spin-1 particles is said to be a Bell, or maximally entangled state 31 : if the individual particles could be spatially separated and subjected to independent spin measurements, the results of these measurements would be predicted to violate Bell's inequalities. We shall use the term entanglement henceforth to refer to the potentially long-range (see below) spin correlations between triplet excitons in the materials that we shall study 32 .
In this work we focus on linear pi-conjugated systems with C2h symmetry, which allows us to label the electronic states of the system according to how their wavefunctions transform under the point group symmetry operations. The ground state (S0) is always of Agsymmetry, so is denoted as S0 (1 1 Ag -), and the lowest triplet state is T1 (1 3 Bu + ). Consequently, the product wavefunction of a pair of triplets has an overall Ag symmetry and, as discussed above, it is then possible for S1 to have the same symmetry as the ground state, where it is denoted as the S1 (2 1 Ag -) state 22,[33][34][35][36][37] . The second excited state (S2) is typically of 1 1 Bu + symmetry and one-photon excitation predominantly occurs to this state 38,39 . We note that triplet-pairs are not the only electronic configurations that could contribute to S1 (2 1 Ag -), and some other singly excited configurations are shown in Figure 1. Indeed, what is referred to as the S1 (2 1 Ag -) state is, in general, a complex superposition of single, double and higher-order electronic configurations of overall Ag symmetry and zero spin [39][40][41] .
Electron correlations within S1 (2 1 Ag -) bring its energy below that of S2 (1 1 Bu + ) for sufficiently long carotenoids, with profound consequences. Following one-photon excitation to S2 there is usually rapid and efficient internal conversion to S1; the shared symmetry of S0 and S1 then means that systems become non-fluorescent 39,40,[42][43][44][45][46] . Once formed, these dark states then internally convert (IC) to the ground state, form triplet excitons by intersystem crossing (ISC), orin the case of shorter polyenesmay lead to photoisomerisation events 41,43 . In smaller systems, the former and latter processes are dominant due to the weak spin-orbit coupling for ISC and much stronger vibronic coupling for IC and structural relaxation. However, extended polymers can be large enough to accommodate spatially wellseparated and essentially non-interacting triplet excitations, raising the intriguing possibility of intramolecular-SF from the bound 'triplet-pair' excitations that formally contribute to the S1 (2 1 Ag -) wavefunction (see Figure 1b). Moreover, as rapid and therefore efficient triplet production can only occur via spin-allowed (spin conserving) processes, free triplets formed by intramolecular-SF must be created in entangled singlet spin states.
Unfortunately, probing real-time fission from S1 (2 1 Ag -) states is generally complicated by both fundamental and practical factors. Firstly, the S1 (2 1 Ag -) state is dark and often decays through nonradiative pathways in just a few picoseconds. Secondly, many theoretical properties of correlated 1D electronic systems emerge in the idealised polymer limit of very large and perfectly ordered system sizes 22,33,34,36,37,39 , which in most experimental polymer systems are difficult to realise due to intra-chain disorder, cross-linking and integration into nanostructures such as proteins.
Here, we overcome these limitations by applying ultrafast nonlinear optical techniques to manipulate the S1 (2 1 Ag -) state during its lifetime, thereby altering its dynamical fate in two classes of organic material: (1) disorder-free topochemical polydiacetylene crystals and (2) carotenoids in isolated and aggregated forms. Strikingly, we show that optical pulses centred on well-known triplet-pair-derived absorption transitions can effectively project the S1 (2 1 Ag -) wavefunction into a manifold of spatially separated, quasi-free triplet-pair states. The production of geminate, spin-entangled triplet-pairs is evidenced by their motion-limited recombination to the ground state, giving us additional insight into triplet diffusion and re-binding during relaxation back to 2 1 Ag - (Figure 1b). The results have implications not only for the design of new conjugated molecules for intramolecular-SF, photoreception and photoprotection, but also for exploiting and controlling entangled states, providing the possibility for room temperature quantum circuitry in molecular materials 60 . Figure 1: Energy levels, dynamics and electronic properties of the key excited states of 1D piconjugated polymers of C2h molecular symmetry. a. Schematic of energy levels and dynamics measured in the pump-push-probe experiments detailed in the main text (pumpgreen arrow; push -blue arrow). Because of the 1 (TT) amplitudes in the S1 (2 1 Ag -) wavefunction, this state can be tracked and selectively projected into the triplet-pair manifold by pushing the excited-state absorption transition 1 (TT) -1 (TT)*. The spatially separated triplet-pairs ( 1 [T...T]) appear from relaxation of 1 (TT)* (a Bu symmetry state). b. Some possible electronic configurations of the frontier molecular orbitals that are superposed together by the configuration interaction into the low lying S1 (2 1 Ag -) wavefunction. Red arrows indicate 'hole' excitations, electrons are shown in blue. 1eh indicates an electronic configuration containing one electron-hole pair in an excitonic spin-singlet state. The singlet 1 (TT) configuration is a doubly excited configuration that can be seen as a pair of low energy triplet excitons with anti-aligned spins. c. Illustrative sketch of some possible spatial wavefunctions of electrons and holes for the configurations shown in b. The push pulse is resonant with a transition derived from the single-triplet absorption T1-T* and chiefly acts on the 1 (TT) part of the wavefunction (bottom) and not the 1eh (or 1eh′) amplitudes (top). A mechanism is suggested for the push-induced separation of the triplet-pairs from 1 (TT)*, whereby one of the excited triplets is highly delocalised, promoting relaxation channels that separate the triplets far enough apart to behave as near-free particles. We note that the triplet spins remain correlated (red circles) in this process, as described in the main text.
Topochemically polymerised polydiaceytlene (PDA) chains can take two different geometrical conformations, nominally referred to as the 'red' and 'blue' phases. In the former case the 2 1 Agstate lies above a 'bright' state of 1 1 Bu + symmetry, whereas for the 'blue' phase this arrangement is reversed and chains are non-luminescent. In this work we deal exclusively with the more correlated and SF active 26,55,61 'blue' chains. Uniquely we study chains a few micrometres long, embedded in a crystal of their diacetylene monomer, highly ordered and isolated from one another (~100 nm) 62 . Figure 2b shows the absorption spectrum of a PDA crystal with light polarised parallel, perpendicular and at 27.5° with respect to the long axis of the chain. When light is polarised parallel to the double and triple bond axis, the absorption is maximum with a strong zero-phonon line observed around ~635 nm (1.95 eV), and a vibronic progression out to 530 nm (2.35 eV) 62 . On rotating the polarisation of light, the absorbance is reduced to zero within the resolution of our instrument, evidencing a near perfect orientation of chains (see X-ray diffraction; SI, Figure S1). This near absence of structural disorder extends to the electronic properties highlighted by the high oscillator strength (~10 6 cm -1 ), strong coupling between the monomer units and macroscopic exciton coherence lengths 63,64 . PDA can therefore be considered as an ideal model system to investigate the excited state properties of pi-conjugated polymers and the links between SF and correlated electronic excitations across nm-µm and fs-ps scales.  Femtosecond pump-probe spectrum of 'blue' PDA following photoexcitation with a 10 fs pulse centred at 530 nm (FWHM ~65nm). Three distinct regions can be observed: a sharp positive band centred around ~650 nm corresponding to the stimulated emission (SE), the photoinduced absorption (PIA) of the 2 1 Agstate at ~870 nm and a negative band at ~750 nm resulting from the vibrationally 'hot' ground state ('Hot' GS). The integrated spectra are shown alongside. b. Kinetics (circles) and fits (line) associated with stimulated emission, 'hot' ground state and 2 1 Agstate. The data is obtained following spectral decomposition of the pump-probe response with a genetic algorithm and is normalized for ease of comparison (see SI, Figure S2 for spectra). c. Dependence of the dynamics of the 2 1 Agstate on pump energy (1.8 -3.1 eV, ~200 fs pulse, FWHM ~10 nm). The dynamics are effectively pump energy independent (constant excitation density) with a small variation observed when pumping close to the band edge and at high energies.
Pump-Probe. In Figure 3a we present the pump-probe spectra from our two-pulse pump-probe experiments; unless otherwise stated all experiments are carried with pump, probe (and push) parallel to the long axis of the PDA chains. Following spectral decomposition using a genetic algorithm (see SI, Figure S2), we identify three distinct species in the spectra whose decays can all be fitted with a single exponential ( Figure 3b). Between 650 -800 nm, we observe a rapid (~320 ± 5 fs) decay of the PDA SE from the 1 1 Bu + (S2) state. The SE consists of a vibrational progression of peaks which are slightly red shifted compared to that previously reported [65][66][67] due to some small reabsorption in the crystal; measurements on thinner (~100 nm thick) crystals indicate reabsorption effects play no role in the dynamics reported throughout this study (see SI, Figure S3). Additionally, between 820 -1350 nm there is an energetically broad band that has been previously assigned to the 2 1 Agphotoinduced absorption (PIA) 68 . Vibronic relaxation from 1 1 Bu + to 2 1 Agmeans the growth of the 2 1 Ag -PIA is delayed with respect to that of the SE; 2 1 Agthen decays with an exponential time constant of ~380 ± 5 fs. The results above are fully consistent with previous pump-probe data and state assignments on a range of 'blue' PDAs 65,66,69 .
However, we also note a prominent third species between 675 -750 nm which grows from the 1 1 Bu + and 2 1 Agstates (τrise ~350 ± 10 fs). To the best of our knowledge this latter PIA has not previously been observed or assigned in the spectra of PDA. Comparable features are known in other systems with rapid non-radiative decay such as the polyenes, and they are linked to the deposition of significant electronic energy into highly excited ground-state vibrational modes 51,70-72 . The resulting vibrationally 'hot' ground state is somewhat closer in energy to the optically allowed state and consequently exhibits redshifted absorption. Given the energy of the PIA is higher than that reported or expected for any 1 (TT) or free triplet transition in PDA 49,66 , with the lifetime being also too short, we assign it to a 'hot' ground state (further discussion SI, Figures S4-S7).
Returning to the decay of the PIA associated with the 2 1 Agstate, we find it is largely pump excitation energy and temperature independent (Figure 3c; similar behaviour at 6 K, see SI, Figure S4). These results demonstrate that simply providing the system with increasing amounts of energy does not prolong the 2 1 Aglifetime or significantly change the electronic dynamics, implying rapid dissipation of excess excitation energy. The invariance of the dynamics with pump energy is a crucial point for our pump-push-probe experiments, where the total combined energy provided by pump and push falls within the range of one-photon excitation energies considered in Figure 3c.
Pump-push-probe To directly interrogate and optically control the population of the 2 1 Agstate we extend the pump-probe experiment using a third 'push' pulse 70,73,74 which acts on the photoexcited chains. Here, the same ultrashort pump pulse (10 fs, 550 -650 nm) photoexcites the PDA chains and is subsequently followed by a 200-fs push pulse at a fixed time delay. The push pulse is tuned to be resonant with the excited state absorption of the 2 1 Agstate and promotes a sub-population to higher lying excited states. The resulting signals are then measured in the same way as for pump-probe by a delayed probe pulse. Comparing push 'on' and 'off' signals allows us to extract the push-induced change in differential transmission, Δ(ΔT/T). Using the pulse sequence as shown in Figure 4a enables us to measure the pump-probe, push-probe and pump-push-probe signals within the same experiment.
Recording the push-probe signal separately allows us to ensure that the push fluence is kept sufficiently low, preventing excitation of the ground state via multi-photon absorption. In the pump-push-probe of PDA, negative signals indicate a push-induced increase in the population of a given pump-excited electronic state; positive signals conversely correspond to a depletion of the excited state population by the push pulse. Figure 4b shows the Δ(ΔT/T) response of PDA chains, with the push pulse tuned to 940 nm and delayed to 400 fs after the pump, such that it arrives immediately following the maximum in 2 1 Agpopulation (qualitatively similar results are obtained using pump-push delays of 200 fs and 800 fs in the rise and decay of 2 1 Ag -SI, Figure S9). We observe two negative bands, one centred at 700 nm in the spectral region corresponding to the 'hot' ground state and a second at 870 nm, in line with 2 1 Agexcited state absorption. The Δ(ΔT/T) kinetic of the 'hot' ground state decays at a rate similar to that observed in our pump-probe experiments (τ ~2.3 ± 0.05 ps). Conversely for the 2 1 Agstate, the push pulse suppresses the excited state decay, increasing the lifetime of the population in the spectral region associated with the 2 1 Ag -PIA by one order of magnitude from ~0.38 ps to ~15 ps (Figure 4c,d). Furthermore, although the exact rise time of the push-induced kinetic cannot be resolved in these experiments (IRF ~200 fs), examining the spectra in Figure 4e shows that the 2 1 Agand 'hot' ground state PIAs are present almost instantaneously following the push pulse; this is in stark contrast to the pump-probe spectra where 2 1 Ag -and 'hot' ground state PIAs develop sequentially. The pump-energy dependent measurements ( Figure   3c) show that simply introducing additional energy into the system does not prolong the lifetime of the transitions, hence our observations reflect something other than simple deposition into the electronic state of an additional ~1.3 eVby the push. Additionally, the spectrum of the pushed 2 1 Agstate narrows from ~110 meV to ~60 meV between 700 fs and 7 ps (Figure 4f), as compared to a final linewidth of ~95 meV for the unpushed 'cold' 2 1 Agstate signature.
We can begin to rationalize these results by first noting that previous studies have identified a strong pump-probe PIA signal at ~1.36 eV (910 nm) that has been unambiguously assigned to excited state absorption from the lowest triplet state 66,68,75,76 . The higher-lying excited triplet state is denoted as T* and has an experimentally determined energy in the region of 2.3-2.4 eV 65,66 . With experimental works placing the energy of the lowest triplet state at around 0.9-1.0 eV 66,68,75 , the energy for creating a free triplet in the lowest state and a free triplet in the T* state from S1 (2 1 Ag -) is 1.35-1.55 eV 66,76 , which matches near perfectly with the position of the 2 1 Ag -PIA , we observe. We therefore consider the possibility that the existence of triplet-pair amplitudes in the 2 1 Agwavefunction (see Figure 1) allow S1 to be projected into an excited manifold consisting of doubly excited configurations involving the coexistence of a low energy triplet and an optically excited triplet. However, due to Coulombic interactions, there will generally be a broad range of physical eigenstates corresponding to such triplet pairs which we denote as 1 (TT)* (Bu symmetry in C2h space group). These states, all of different spatial triplet separations, structure geometries and internal kinetic energies, contribute to the overall broadness of the PIA feature, as does the ultrafast relaxation of the 2 1 Agstate itself. It is important to note that our push pulse does not need to excite the T1-T* transition of an individual triplet, but rather bring 1 (TT) into a higher 1 (TT)* level. The energy for this will be similar but not identical to the excitation of a single triplet into T* 77 . Hence although the 940 nm push pulse used does not precisely match the 2 1 Ag --T + T* energy gap, it is sufficiently resonant with the lower-energy 'tail' of the (cooled) broad 2 1 Ag -PIA to push triplet-pair amplitudes in the superposition to higher 1 (TT)* levels. Even more strikingly, Given the line-narrowing shown in Figure 4f is greater than the original cold 2 1 Ag -PIA (i.e. at 1 ps in Figure 3a), we suggest this to be associated with the freer triplet-pair state as opposed to vibrational cooling. This is further supported by the fact that the long-time species in Figure 4f is slightly redshifted from that on early timescales, whereas vibrational cooling would give rise to a blue-shift. Any excess energy, which likely plays a role in initially separating the bound triplet-pairs, may be rapidly (~200-500 fs) dissipated following the push pulse. These 'near-free' triplet states do not overlap and cannot internally convert as effectively as they do when 'bound' in the 2 1 Agstate, so decay more slowly.
Consequently, the pump-probe kinetic with the push 'on' at ~870 nm will have a longer decay as compared to that with push 'off'. When the two are subtracted this will result in a Δ(ΔT/T) signal with both an enhanced lifetime and rise. The latter will be a convolution of several processes including the time taken to transition between the 1 (TT)* and 1 [T…T] states and the underlying decay of 2 1 Ag -, and as a result the details of the transition from the 1 (TT)* to 1 [T…T] manifold is challenging to ascertain from this data alone. Using a kinetic model (SI, Figure S8) we can quantify the relative amount of 1 [T…T] freed from 2 1 Ag -(branching ratio), obtaining a value of ~29 ± 3 %, though we highlight that no kinetic modelling is needed to establish the qualitative picture above. Eventually the spatially separated triplet-pairs diffuse and recombine resulting in the overall decay of the Δ(ΔT/T) kinetic. Given that no long-lived (µs) signal corresponding to isolated triplet-transitions is observed, the recombination must involve triplet-pairs being annihilated. As we only measure recombination of geminate pairs to the singlet ground state in PDA, the enhanced lifetime we measure implies that the decorrelation time of the triplet spins must be longer than 15 ps at room temperature: any spin-1 pairs would quickly annihilate to leave one triplet in the long-lived T1 state. Given that ISC and the intrinsic spin evolution of geminate SF triplets occurs on nanoseconds time scales in other organic SF systems 79 , we therefore think it highly likely that the triplets remain spin-entangled over the separation, diffusion and recombination process.
The effect of the push pulse can thus be summarised as projecting the 2 1 Agwavefunction into a manifold of spatially separated triplet-pairs by using an optical perturbation that selectively couples the triplet-pair amplitudes of the 2 1 Agwavefunction to the 1 (TT)* excited states, and their decay pathways towards nearly-free entangled triplet-pairs. Not only does this show how triplet-pairs can be harvested with low energy photons from non-luminescent polymers, it also provides a type of analysis of the total triplet character in the many-body 2 1 Agstate, as well as the possibility to study real-time, real-space triplet motion in an organic material. In fact, as ultrafast time-resolved microscopy is rapidly emerging as a viable experimental techniques 80 , it may even become possible in the near future to observe and manipulate the individual triplets in the nearly-free pairs. Push-induced dynamics of PDA with push pulse centred at 940 nm and tpush of 400 fs. The negative signals indicate that the effect of the push is to increase the 'hot' ground state and 2 1 Agpopulations. c. Push-induced response of the 2 1 Agstate when pushing at 400 fs. The 2 1 Aglifetime is increased to 15 ± 0.1 ps in this case. d. Comparison of decay (circles; solid line fit) for spectral region associated with the 2 1 Agstate in pumpprobe measurements, and 2 1 Agand 'hot' ground state in pump-push-probe experiments (tpush = 200 fs; mapped back to single scale where all pulses arrive at t = 0 fs). The PIA associated with 2 1 Agrapidly decays in pump-probe experiments; application of the push however enhances the lifetime of this PIA by at least one order of magnitude. e. Spectral cuts of pump-push-probe spectrum. The 'hot' ground state and 2 1 Ag -PIAs are present almost immediately after the push pulse with the latter being slightly delayed. The data is shown for tpush = 400 fs, with the times in the legends indicating the pump-probe delay. f. Magnification of the spectral region associated with the pushed 2 1 Ag -PIA; the spectra are normalised at 900 nm. Dashed overlay is a fit of two Gaussians to the profile (see SI, Figure S10 for further details) and highlights the narrowing of the spectrum at longer time delays following the push.
The 2 1 Agmanifold is energetically broad, so we also examined the effect of varying the push energy (SI, Figure S10) at a constant tpush of 400 fs. When tuning our push pulse to be resonant with either the high-or low-energy side of the 2 1 Ag -PIA at 860 nm and 1100 nm respectively we observe no change in the dynamics as compared to a 940 nm push, with the same push-induced population change and aforementioned lifetime enhancement. However, when we centre our push pulse at 1350 nm in the tail of the 2 1 Agstate no push-induced signal is observed. Based on the absorption cross-section at 1350 nm, obtained from the ΔT/T signal in Figure 3, and relative push power used at 1350 nm compared to 940 nm we would expect a maximum Δ(ΔT/T) of ~4 × 10 -4 , well above our noise floor of ~2 × 10 -5 . This suggests that the 1350 nm push does not extract separated triplets from the 2 1 Agsuperposition. We note that the total energy provided via the 1350 nm push is ~2.32 eV (2 1 Agat ~1.4 eV 62 + 0.92 eV from push), which is significantly higher than the expected energy for 2 triplet (T) excitons at ~1.8 -2.0 eV 62 . Given that the energy difference between the 1100 nm and 1350 nm push pulses is only ~200 meV, it suggests that in both instances a 'hot' 2 1 Agstate will be formed, but only for the (860 -) 1100 nm push is there sufficient energy to access 1 (TT)* states. Hence, contrary to the original model proposed in the literature 39 , a 'hot' 2 1 Agstate is not a sufficient condition to extract spatially separated triplets from the mixed 2 1 Agwavefunction, and in addition projection of the wavefunction via excitation into the triplet-pair manifold is required. More interestingly given that regardless of the push energy (and time delay) only the lifetime of 1 (TT) contribution can be greatly enhanced, the results indicate that not all components of the 2 1 Agsuperposition (e.g. CT or localized exciton) can likely be addressed. There are likely to be several contributing factors. These other amplitudes (Figure 1b) constitute a relatively small fraction of the 2 1 Agwavefunction and consequently would contribute only weakly to the total excited-state absorption 81 . Indeed, the similarity of the PIA lineshape to that expected of triplet-pairs also suggests the triplet-like character dominates the transition 81 . Moreover, unlike the transition cross into and/or net entropic gain on transition, hence would only contribute to the sub-400 fs depletion signals observed in the pump-push-probe spectra (Figure 4d).
We further highlight the unexpected observation that the push photon energy does not appear to alter the degree of 1 [T…T] separation (SI, Figure S10). This result indicates that formation of near-free triplet-pairs occurs from the lowest energy 1 (TT)* state. Any excess energy in the push pulse beyond the 1 (TT)* threshold is rapidly (sub-200 fs) lost as heat/vibration as the 'hot' 1 (TT)* relaxes, making the subsequent dynamics independent of the initial photon energy. This makes a surprising contrast with conventional acene thin-film systems, where 1 (TT) separation is known to be thermally activated 82  for vibrational relaxation within this state to have any effect on the dynamics. Based on this preliminary scan of push energy, the crucial parameter that determines the likelihood of 1 [T…T] is thus not the degree of vibrational excitation or 'heat'as found to be the case in many intermolecular singlet fission systems 14,84-86but the underlying nature of the upper 1 (TT)* state. We suggest that this highly electronically excited state is more delocalized than 2 1 Ag -, a common phenomenon in conjugated polymers 87 , resulting in a greater average T-T separation and enabling relaxation into the more localized Figure 5: Pump-probe and pump-push-probe spectroscopy of a carotenoid (astaxanathin, AXT) monomer and weakly coupled H-aggregate. a. Differential transmission map following excitation of isolated AXT at 515 nm (~200 fs time resolution). The PIA bands centred at 620 nm and 1220 nm are assigned to the S1 state, which in the AXT monomer is 2 1 Agin character. b. Pump-probe spectrum of H-aggregated AXT. The PIA bands at 620 and 1220 nm correspond to S1, which on the timescales considered (0.3 -10 ps) have a characteristic of the strongly bound 2 1 Agstates seen in the monomer. In both the monomer and aggregate the 1220 nm S1 PIA is ~10 times weaker and strongly overlapped at early times (sub-200 fs) with S2, but normalisation of the kinetics shows it follows the same decay as the PIA at 620 nm (SI, Figure S13). c. Pump-push-probe spectrum of isolated AXT following a push pulse at 1220 nm and tpush = 500 fs where the S1 population is at a maximum. Only depletion of S1 is observed (positive Δ(ΔT/T) response 600 -700 nm). d. Push-induced response of AXT aggregates following 1220 nm push pulse at 200 fs. Initially there is a depletion of the population at 620 nm; this decays into a negative 'enhancement' that is still increasing at the end of the measurement window (40 ps).
Carotenoids Carotenoids are arguably some of the most important naturally occurring photoactive organic molecules. Commonly found bound to the proteins of photosynthetic organisms they play a key role in light-harvesting and photoprotection in plants and bacteria, as well as giving rise to the characteristic colours of many crustaceans and fish 88 . The electronic structure of carotenoids (and their aggregates) is remarkably similar to that of 'blue' PDA as shown in Figure 1a. Additionally, weakly (both structurally and electronically) bound carotenoid aggregates have been shown to undergo efficient interchain singlet fission with triplet yields up to 200% 52,53 , and the introduction of comparable polyene character is increasingly suggested as a design strategy for intramolecular singlet fission 18,26,45,55,78,89,90 .
We use the carotenoid astaxanthin (AXT) to probe the analogy with the PDA 2 1 Agstate, both in isolated small molecules and aggregates.
In Figure 5a,b we present the pump-probe characterization of monomeric AXT and its weakly coupled H-aggregate, excited at 515 nm (pulse duration ~200 fs). In agreement with previous reports on AXT 52 and similar carotenoids 91 we assign the prominent excited-state absorption band at 600 -850 nm and the markedly weaker tail 1200 -1350 nm in the monomer to the S1 (i.e. 2 1 Ag -) state, which is formed from the initial S2 (SE at ~550 nm) in <300 fs. The aggregate presents similar, albeit slightly shifted features, where once again the initial S2 state, which has a weak PIA in the 850 -1100 nm region, is depleted within 300 fs. The long-lived PIA peak at ~600 nm has previously been assigned to tripletpairs formed through singlet fission 52 . Here we highlight that on intermediate timescales (0.3-10 ps) the spectrum is broadened and red-shifted and exhibits substantial rapid decay (SI, Figures S11-S13). These features are characteristic of the strongly bound 2 1 Agstates observed in monomeric AXT and 'blue' PDA, and we thus propose the state on these timescales is best represented by a superposition as in Figure 1b with primarily triplet-pair character and similarly denote it as S1. In both aggregated and monomeric AXT the S1 PIA also has contributions in the near-infrared (1200 -1350 nm) 52 . Here the PIA is ~10 times weaker than in the visible and at early times overlapped with the strong and rapidly decaying S2 PIA; normalizing the kinetic at 620 nm and 1220 nm however shows the two bands decay at the same rate (SI, Figure S13). Depending on the number of conjugated double bonds several other states have been shown to sit in the S2-S1 gap of carotenoids 92 . In AXT for instance, another triplet-pair state 1 1 Buis predicted to lie below the 1 1 Bu + (S2) transition, albeit with more covalent character and lower oscillator strength especially in the solution phase 40,93 . The role of this and other intermediate states has been intensely debated [94][95][96] , however given the ~200 fs pulse duration, we presume rapid decay from these states to have occurred within our resolution and before arrival of the push pulse (tpush > 200 fs in both monomeric and aggregated AXT). Consequently, we base our observations on a three state model considering only 1 1 Ag -(S0), 2 1 Ag -(S1) and 1 1 Bu + (S2) 94,97,98 (further discussion is provided in SI, Figure S12).
To probe the superpositions contained within the S1 state, pump-push-probe experiments were performed on both samples with a push pulse centred at 620 nm and 1220 nm; the tpush was chosen to overlap with the maximum in the rise of the respective PIAs (the behavior is approximately independent of the precise tpush values further emphasizing the role of any rapidly decaying intermediate states to be minimal, SI, Figure S14, or the choice of push wavelength within the indicated bands, SI, Figure S15). Figure 5c shows the push-induced signal following a push at 1220 nm of isolated AXT. Pushing the S1 (2 1 Ag -) PIA band results in a positive push-induced Δ(ΔT/T) signal indicating population has been driven out of S1 to higher lying states, with the depletion signal decaying over ~5 ± 0.05 ps, in accord the with the intrinsic S1 lifetime. In this case no (long-lived) enhancement can be observed which suggests that on a single chain there is insufficient space for triplet-pairs to separate from the 2 1 Agsuperposition. In the case of the aggregates the behavior is markedly different as shown in Figure 5d.
Immediately following the push pulse there is a depletion of S1, resulting in a positive Δ(ΔT/T) signal that decays (τ~4.2 ± 0.05 ps) to yield a slightly blue shifted negative Δ(ΔT/T) 'enhancement' signal, that grows to the end of the measurement window (SI, Figure S13). As with PDA, this growth in the negative Δ(ΔT/T) signal indicates that the push slows the decay of the S1 state, i.e. the population is able to reach a new, more stable part of the configuration space. We note at the pump and push fluences used here, the transition between 2 1 Agand the higher excited state follows a strict one-photon dependence in both monomers and aggregates (SI, Figures S16-S17). This is in contrast to other studies which have shown access to the triplet state manifold via 3-4 photon excitation from the 1 1 Agground state of monomeric carotenoids 99,100 .
In other monomeric carotenoids long-lived signatures of population depletion, similar to those seen in Figure 5c, have been observed following application of a push-pulse to the 2 1 Ag -PIA 101,102 . However, to the best of our knowledge, in none of these systems has there been evidence for an enhancement in the lifetime of the triplet-pair like (or other) contributions or branching into a particular dark-state. In monomeric β-carotene it has been reported that excitation from the ground state with significant excess photon energy can result in a longer-lived PIA band, blue-shifted from the S1-Sn transition 102 , and the same effect is evident in several other carotenoids 103 . This bears superficial resemblance to our pushinduced effects in that an enhancement signal is also observed in 530 -570 nm range in Figure 5d, but caution should be taken in comparing spectra between different carotenoids. Recent work by Ostroumov et al. has shown that long-lived features in the transient absorption spectra of carotenoids such as βcarotene can be explained by population impurities arising from cis-isomers in the sample 97 . Following rigorous purification, these long-lived features are removed and the entire transient absorption spectrum after 1 ps can be explained by single S1-Sn transition 97,98 . Hence, care must be taken in interpreting results on these materials, especiallsy given such cis-isomers can be generated transiently at highexcitation densities and pump energies 104 . It is for this reason we specifically chose to excite towards the lower energy band-edge of AXT at 515 nm (2.4 eV) as opposed to at 400 nm (3.1 eV) as is more commonly used in the literature. In addition to these precautions, our control measurements on monomeric AXT (Figure 5a,c) reveal no long-lived features demonstrate that the push pulse does not access any other electronic pathways. Likewise, control measurements on monomeric β-carotene (SI, Figure S18) reveal only depletion of the S1/2 1 Agstate with no longer-lived features. Pathways involving multiple dark states, as reported by Larsen et al. applying a similar total excitation energy to monomeric β-carotene 102 in the ground electronic state, do not appear to be active in our systems following selective stimulation of the S1-Sn transition.
Introducing an increasing number of conjugated oxygen atoms into the carotenoid backbone has also been shown to make these molecules more robust to conformational effects 88 , which guided our choice of AXT as a model carotenoid. Performing absorption measurements after each pump-push-probe scan further confirms there are no structural changes in the molecule during measurements (SI, Figure S12).
The high-energy edge of the S1-Sn PIA (550 -570 nm feature in Figure 5b) has been assigned to both a dark S* state and cis-isomer impurities in some monomeric carotenoids and protein complexes with isolated carotenoids 102,103,105,106 , but these have not been found to contribute significantly to the spectrum of AXT. Nonetheless, it is possible that the early-time (<1 ps) negative Δ(ΔT/T) feature we detect in Figure 5d reflects a slight enhancement of the lifetime or population of such dark/impurity states.
However, this feature exhibits rapid decay which is not matched by corresponding growth in the band at 600 nm assigned to the 2 1 Ag -/ 1 (TT) state in carotenoid aggregates 52,77 (SI, Figure S13). Any pushinduced effects in possible dark/impurity states thus have no connection to the 'freeing' of triplet-pairs.
In light of this, the conformational robustness of AXT, the control experiments detailed in the supporting information (SI, Figure S12 -S15) and the similarity of push-induced effects between AXT aggregates and PDA, where we expect no such isomerization effects, we are confident that our results are not related to population impurities.
In the study of monomeric carotenoids, comparable PIA features are also frequently analysed in terms of other dark states such as 1 1 Bu -, which are also predicted to lie below the bright 1 1 Bu + state for sufficiently long molecules 39,40 . Such states are invoked both to mediate internal conversion into 2 1 Agand to explain long-lived features in the transient spectra, though their assignment remains highly controversial 92,102 , and the demonstration of a conical intersection between 1 1 Bu + and 2 1 Agsuggests no intervening states are present 94 . In the present work, the limited temporal resolution of the push experiment means that only the terminal 2 1 Agis detectable, and we cannot comment directly on the presence of other dark states within the relaxation pathway from high-lying Sn. Within the aggregates, it has previously been suggested that 1 1 Bumight play a role in the SF process 52 , as it is also expected to carry triplet-pair character 39,40 . It is certainly possible that the 1 [T…T] we observe is related to 1 1 Bu -, though it is beyond the scope of this work to determine the exact symmetry of the state. Moreover, we note that these symmetry labels are strictly defined only for polyacetylene. The electronic coupling within multi-chromophoric aggregates must alter the symmetry of the system, such that it is unlikely that precisely the same states can be used to describe monomer and aggregate electronic structure. This being the case, we consider it most appropriate to focus in this work on the relevant diabatic contributions to the overall states, e.g. 1 (TT) and 1 [T…T].
The remarkable similarity in behavior to PDA suggests that in AXT aggregates, optical stimulation of S1 (which has some 2 1 Agsuperposition state contribution on early timescales) separates and delocalizes the bound triplet-pairs over multiple chains to a greater degree than occurs naturally within the aggregates. Using a kinetic model complementary to that shown for PDA (SI, Figure S8) we find the amount of 1 [T…T] optically liberated from 2 1 Agin AXT aggregates to be significantly less, 3 ± 1 %, in line with the weak interchromophore coupling. We do remark however this to be a qualitative upper bound estimate as care must be taken in modelling the photophysics of carotenoids with transient absorption data due to alternate branching pathways introduced by numerous 'dark' or charge transfer states which would serve to reduce this number further. Although AXT is chemically different to PDA, the likeness in photophysical response suggests that the possibility for extraction of the 1 [T…T] state from a 2 1 Agsuperposition, via an optical pulse, is widespread. The range of energetic orderings, numerous 'dark' states and potential for conformational changes on photoexcitation means further investigation is required to show these observations hold for all carotenoid systems. Figure 6: Schematic of the spatial separation of triplet-pairs from the 2 1 Agstate in pi-conjugated molecular systems. The bound triplet-pair excitons (dashed boxes on blue background) separate along the conjugated molecular backbone into a spatially free triplet-pair state where there is maximum spin entanglement but minimum spatial entanglement. After a given time, the spins recombine to give rise to the observation of an overall lifetime enhancement in 2 1 Ag -.

Conclusion
We have provided experimental evidence that the 2 1 Agstate in polydiacetylene and a carotenoid aggregate can be a superposition state with significant 1 (TT) character. We demonstrated that optical excitation addressing the triplet-pair amplitudes of the 2 1 Agwavefunction, can be used to project the 2 1 Agwavefunction into a manifold of spatially separated triplet-pair states. The resulting lifetime enhancements observed in the 2 1 Agexcited state absorption (PIA) is due to long-range spatial distribution of the spin-entangled triplet-pairs along a PDA polymer chain or between carotenoid molecules in weakly coupled aggregates ( Figure 6). The degree of electronic coupling between the individual monomer chromophores dictates the time taken for spatial separation of these pairs and the overall yield liberated from 2 1 Ag -. In the strongly coupled, highly ordered PDA, stimulated separation into 1 [T…T] takes ~200 fs with a yield of ~29%, whereas in the weakly bound carotenoid aggregates the spatial separation happens over ~5 ps and only ~3% are freed. In small monomers of the carotenoid AXT there is no evidence for extraction of 1 [T…T] by the one-photon push pulse due to the strong spatial confinement. Our results indicate that it is possible not only to 'control' but enhance and quantify the 1 (TT) character of the 2 1 Agwavefunction providing an all-optical approach to steering the singletfission reaction towards the desired triplet photoproduct over internal conversion. Furthermore, the indirect evidence present for the near-free triplet pairs remaining entangled over their entire lifetime (S1 lifetime enhancement decays only via recombination of geminate pairs to the S0) willwe hopeinspire future experiments that tackle the challenging task of measuring such quantum correlations in organic materials 32 .
Given the prevalence of 2 1 Agstates in molecular systems we expect our results to be applicable to a wide range of other technologically relevant systems such as polyacenes, iso-indingo-based polymers and other singlet fission materials. Further studies should aim to address the universality of our observations potentially using techniques such as 2D electronic spectroscopy which may be sensitive to 'dark state' signatures in carotenoid systems 58,107 . In fact, it may be possible to develop a quantitative tool based on the general idea of optically projecting out certain contributions to a complex wavefunction, For example, by quantifying the degree of 1 (TT) character in materials possessing a S1 (2 1 Ag -) state, it could become possible to rationally design new polymers for singlet fission and photoprotection by identifying structures that optimise the 1 (TT) contribution to 2 1 Ag -. Even more widely, given the ubiquity of 'hybrid' states in organic materials, particularly those mixing charge transfer and excitonic characters, projecting out the individual components will provide a powerful tool to explore and manipulate electronic states in many other molecular systems.

Polydiacetylene
The 3BCMU (3-methyl-n-butoxy-carbonylmethyl-urethane) diacetylene molecules were synthetized in-house using the method previously outlined by Se et al. and references therein 108  all measurements were performed under standard ambient conditions. The spectra were measured simultaneously with the solvent to correct for its absorbance in case of the carotenoids.
X-Ray diffraction X-Ray diffraction (XRD) was performed using a Bruker X-Ray D8 Advance diffractometer with Cu Kα1,2 radiation (λ = 1.541 Å). To prevent sample damage from X-Rays, measurements were carried out at 12 K using an Oxford Cyrosytem PheniX stage. Spectra were collected with an angular range of 1 < 2θ < 56° and θ = 0.0051° over 60 minutes. Measurements were made on a flat crystal mounted in a non-specific orientation. The Bruker Topas software was used to carry out Le Bail analysis over an angular range of 8.75 < 2θ < 26.7°. Backgrounds were fit with a Chebyshev polynomial function and the peak shape modelled with a pseudo-Voigt function.
Femtosecond pump-probe and pump-push-probe spectroscopy The fs-TA experiments were performed using a Yb-based amplified system (PHAROS, Light Conversion) providing 14.5 W at 1030 nm and 38 kHz repetition rate. The probe beam was generated by focusing a portion of the fundamental in a 4 mm YAG substrate and spanned from 520 nm to 1400 nm. The pump pulses were generated in home-built noncollinear optical parametric amplifiers (NOPAs), as previously outlined by Liebel et al. 109 . The NOPAs output (∼4 to 5 mW) was centred typically between 520 and 560 nm (FWHM ~65-80 nm) depending on the exact experiment, and pulses were compressed using a chirped mirror and wedge prism (Layerterc) combination to a temporal duration of ~9 fs. Compression was determined by second-harmonic generation frequency-resolved optical gating (SHG-FROG; upper limit) and further confirmed by reference measurements on acetonitrile where the 2200 cm -1 mode could be resolved (see SI, Figure S7). The probe white light was delayed using a computer-controlled piezoelectric translation stage (Physik Instrumente), and a sequence of probe pulses with and without pump was generated using a chopper wheel (Thorlabs) on the pump beam. The pump irradiance was set to a maximum of 30 μJ/cm 2 . After the sample, the probe pulse was split with a 950 nm dichroic mirror (Thorlabs). The visible part (520-950 nm) was then imaged with a Silicon photodiode array camera (Entwicklunsbüro Stresing; visible monochromator 550 nm blazed grating). The near infrared part was imaged using an InGaAs photodiode array camera (Sensors Unlimited; 1200 nm blazed grating). Measurements were carried out with a time step size of 4 fs out to 2 ps to minimize the exposure time of the sample to the beam. Unless otherwise stated, all measurements were carried out with the probe polarisation set parallel with respect to that of the pump (using a half-waveplate; Eksma) and along the PDA chains. The absorption spectrum of samples was measured after each pump-probe sweep to account for any sample degradation.
For the pump-push-probe spectroscopy, an additional third pulse was added to the above configuration, and spatially and temporally overlapped in the sample through a boxcar geometry. The pump-push delay of the push was controlled by a DC servo delay stage (Thorlabs). For the source of the push pulse