Transport-Induced Decoherence of the Entangled Triplet Exciton Pair

TL;DR

The paper investigates how exciton transport between two inequivalent lattice sites can cause global decoherence of entangled triplet pairs formed by singlet fission, suppressing fluorescence quantum beats. It builds a Monte Carlo framework that propagates the spin state via a product of time-evolution operators across stochastic configuration changes and derives an effective Hamiltonian in the fast-hopping limit $H_{eff}=\frac{H_{con}^{(AA)}+H_{con}^{(BB)}+2H_{con}^{(AB)}}{4}$. When applied to rubrene, zero-field fast hopping yields multiple beat frequencies, while a moderate magnetic field aligned to symmetry axes restores coherence and reduces the singlet-projection to near $2/9$ (zero field or field along $z$) or $1/9$ otherwise; in slower hopping regimes, decoherence is stronger and beats decay with characteristic timescales exceeding several nanoseconds. The approach provides a general, quantitative framework for predicting quantum-beat suppression due to transport in crystals with two inequivalent sites and is consistent with prior experiments.

Abstract

Decoherence effects for entangled triplet pairs in organic molecular crystals are analyzed for the case when excitons can hop between inequivalent lattice sites. The fluorescence quantum beats caused by quantum interference upon triplet-triplet recombination into an emissive singlet state are predicted as a function of hopping time and magnetic field based on a Monte Carlo analysis. Depending on exciton hopping rates, it is possible to have complete global decoherence and suppression of fluorescence quantum beats in the limit of zero magnetic field, and to have quantum beats that decay at different rates depending on magnetic field strength.

Figures (3)

• Figure 1: Schematic of inequivalent site coordinate systems and global crystal coordinate system in the example of orthorhombic rubrene crystals. The $y_A$ and $y_B$ axes of each site are along the tetracene backbone of the rubrene molecules, and each site's coordinate system is rotated around a shared $z$-axis by the herringbone angle $\pm \theta$. In orthorhombic rubrene crystals, $\theta = 31^\circ$Jurchescu06, with crystal axes labels $a=x,b=y,c=z$ in the convention of Ref. Wolf18Curran24 and $a=z,b=y,c=x$ in the convention of Ref. Jurchescu06
• Figure 2: Time-dependent Singlet Projection Probabilities $P_S(t)$ (Eq. \ref{['UexpVal']}) for the rubrene crystal geometry and for different exciton hopping times and the zero-field parameters of Ref. Curran24. The top row shows quantum beats predicted with no magnetic field for $x$-axis exciton hopping times $\tau_{hop}$ of 5 ps ($a$), 150 ps ($b$), and 10 ns ($c$). The bottom row displays predicted quantum beats for $\tau_{hop} = 150$ ps and an external magnetic field of magnitudes 0 T (d), 0.3 T (e), and 1.0 T (f) and parallel to the global $y$-axis. Transport-induced dephasing effects Curran24 do not occur with this orientation of magnetic field.
• Figure 3: Singlet projection probabilities for each of the nine stationary states for same-type triplet pairs ($AA$/$BB$ configuration, top, red) and mixed-type pairs ($AB$ configuration, bottom, blue), as a function of the strength of a magnetic field applied along the $x$-axis.