Quantum Beats in Crystalline Tetracene Delayed Fluorescence Due to Triplet Pair Coherences Produced by Direct Singlet Fission

A detailed analysis of the oscillations seen in the delayed fluorescence of crystalline tetracene is presented in order to study the mechanism of singlet fission. Three quantum beat frequencies of 1.06 +/- 0.05, 1.82 +/- 0.05, and 2.92 +/- 0.06 GHz are resolved, which are damped on a time scale of 20 ns. The effects of sample morphology, excitation wavelength, and temperature are 2 examined. A density matrix model for singlet fission is developed. that quantitatively describes the frequencies, amplitudes, and 2 3 4 damping of the oscillations. The model assumes a direct coupling of the initially excited singlet exciton to the triplet: pair manifold. There is no electronic coherence between the singlet and triplet pair states, but the rapid singlet decay time of similar to 200 ps in solution-grown single crystals provides the impulsive population transfer necessary to create a coherent superposition of three zero-field triplet pair states vertical bar xx >, vertical bar yy >, and vertical bar zz > with overall singlet character. This superposition of the three states gives rise to the three quantum beat frequencies seen in the experiment. Damping of the quantum beats results from both population exchange between triplet and singlet manifolds and pure dephasing between the triplet pair states. By lowering the temperature and slowing the SF rate, the visibility of the oscillations decreases. There is no evidence of magnetic dipole-dipole coupling between the product triplets. Our model provides good overall agreement with the data, supporting the conclusion that singlet fission in tetracene proceeds through the "direct" mechanism without strong electronic coupling between the singlet and triplet pair states.