FIGURE: Quantum beats measured in a rubrene crystal in the first 20 ns after photoexcitation for magnetic field directions that differ by a few degrees. The data is superimposed on an image of a mm-sized rubrene crystal and the fluorescence it emits. (See Persistence of Spin Coherence in a Crystalline Environment at Phys. Rev. Lett. for details)
Photon absorption in some organic molecular semiconductor crystals can create a photoexcited state that spontaneously splits into a pair of mobile, spin-entangled triplet excitons, where each quasiparticle has an electronic spin of 1 but the pair has a total spin of zero. The triplet excitons (spin-1 excitons) in this system are a condensed matter equivalent of the entangled photons created by parametric down conversion in nonlinear optical crystals.
While the existence and persistence of the entanglement of photon pairs is generally studied by detecting the spin of individual photons and studying the correlation between those measurements, for this solid-state system the entanglement can be seen from the quantum interference that occurs on the occasion of a re-encounter of the two excitons in a pair, after they have independently traveled for significant distances (hundreds of nanometers) since separation (See here for how the diffusion of triplet excitons can be seen).
Upon meeting again, the excitons can combine to form a single emissive spin-0 state (a singlet exciton) again, leading to the release of a fluorescence photon.
The probability of the two excitons undergoing a fusion process depends on the projection of the spin-wavefunction of the pair, which is a linear combination of stationary states with slightly different energies (two of them in the presence of a magnetic field) onto the required zero-spin state. This projection oscillates in time, leading to quantum beats after impulsive photoexcitation of a population of triplet exciton pairs.
But these quantum beats do not always appear. We have shown that in certain materials the global spin-coherence of an entangled exciton-pair population can be destroyed even though the entanglement of individual exciton pairs is maintained indefinitely. This decoherence is caused by exciton transport: the excitons hopping between inequivalent sites in the crystal lattice. However, we have also shown that decoherence can be eliminated when applying a magnetic field along specific symmetric directions of the crystal. This enables an all-optical method to characterize exciton transport and obtain information on triplet-exciton localization on inequivalent molecular sites. The exciton hopping time can be derived from how quickly decoherence manifests itself again when slightly changing the direction of the magnetic field. Given the typical energy differences between different spin orientations in molecular crystals, one can in this way determine hopping times of the order of a few 100 picoseconds.
The decoherence effect is shown in the above figure. By changing the direction of the magnetic field by just a few degrees one can tune the global decoherence of the exciton-pair population, leading to a faster and faster decay of the quantum beats.
Acknowledgement. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award No. DE-SC0020981.
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Ivan Biaggio
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More information:
- Gerald Curran III, Zachary Rex, Casper Xallan Wilson, Luke J. Weaver, Ivan Biaggio, Ivan Biaggio, “Persistence of spin coherence in a crystalline environment,” Phys. Rev. Lett. 133, 056901 (2024).
- Eric A. Wolf, Ivan Biaggio, “Geminate exciton fusion fluorescence as a probe of triplet exciton transport after singlet fission,” Phys. Rev. B Letters 103 (20), L201201 (2021).
- Eric A. Wolf, Drew M. Finton, Vincent Zoutenbier, Ivan Biaggio, “Quantum beats of a multiexciton state in rubrene single crystals,” Appl. Phys. Lett. 112, 083301 (2018).