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The Journal of Chemical Physics

Time dependent correlations of entangled states with nondegenerate branches and possible experimental realization using singlet fission

Christopher J. Bardeen

Published Sep 27, 2019• 29 citations

Abstract

The spin-entangled exciton states produced by singlet fission provide an experimental route to generate entangled states with nondegenerate branches. Nondegenerate entangled pair states possess an internal "clock" that leads to quantum beating in various detected quantities. The implications of this internal clock for Bell's inequality measurements and correlated particle detection are analyzed using two- and three-state spin models. In a Bell's inequality experiment, we find that the choice of detection times can determine whether quantum or classical correlations are observed. The conditions under which the detection events could be time- or spacelike separated are analyzed in order to clarify how the temporal evolution of one particle can influence the time-dependent detection probability of the other. Possible routes to the detection of individual correlated triplet excitons are discussed, emphasizing both physical questions concerning the separation and propagation of triplet excitons over macroscopic distances and experimental challenges concerning decoherence, detection, and interpretation of the signals. We argue that spin-entangled triplet exciton states produced by singlet fission could provide a new way to probe entangled state detection and collapse, complementing schemes based on polarization-entangled photon states.

DOI: 10.1063/1.5117155

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The spin-entangled exciton states produced by singlet fission provide an experimental route to generate entangled states with nondegenerate branches. Nondegenerate entangled pair states possess an internal "clock" that leads to quantum beating in various detected quantities. The implications of this internal clock for Bell's inequality measurements and correlated particle detection are analyzed using two- and three-state spin models. In a Bell's inequality experiment, we find that the choice of detection times can determine whether quantum or classical correlations are observed. The conditions under which the detection events could be time- or spacelike separated are analyzed in order to clarify how the temporal evolution of one particle can influence the time-dependent detection probability of the other. Possible routes to the detection of individual correlated triplet excitons are discussed, emphasizing both physical questions concerning the separation and propagation of triplet excitons over macroscopic distances and experimental challenges concerning decoherence, detection, and interpretation of the signals. We argue that spin-entangled triplet exciton states produced by singlet fission could provide a new way to probe entangled state detection and collapse, complementing schemes based on polarization-entangled photon states.

Singlet fission is a photoconversion process that generates a doubly excited, maximally spin entangled pair state. This state has applications to quantum information and computing that are only beginning to be realized. In this article, we construct and analyze a spin-exciton hamiltonian to describe the dynamics of the two-triplet state. We find the selection rules that connect the doubly excited, spin-singlet state to the manifold of quintet states and comment on the mechanism and conditions for the transition into formally independent triplets. For adjacent dimers that are oriented and immobilized in an inert host, singlet fission can be strongly state-selective. We make predictions for electron paramagnetic resonance experiments and analyze experimental data from recent literature. Our results give conditions for which magnetic resonance pulses can drive transitions between optically polarized magnetic sublevels of the two-exciton states, making it possible to realize quantum gates at room temperature in these systems.

Polarization-entangled photons provide intriguing insight into the fundamentals of quantum physics, and are vital technology for large scale quantum computing with linear optics, and extending the distance over which a quantum key can be shared. However, those entangled photon sources that have been implemented so far are typically probed using time-averaged measurements, thus obscuring any quantum correlations that evolve over the lifetime of the state. Here we measure the evolution of quantum correlations over the lifetime of a photon pair state, generated by an optically excited quantum dot at ~10K. Time-dependent oscillations of the entanglement fidelity are observed, and attributed to the spin-dependent phase acquired in the intermediate, non-degenerate, exciton-photon state.

Singlet fission is commonly defined to involve a process by which an overall singlet state with local triplet structure spin decoheres into two triplet states, thereby completing the fission process. This process, often defined in loose terms involving the multiplicity of the overall state, is investigated here using a uniform Heisenberg spin chain subject to a dephasing environmental interaction. We introduce results from quantum information theory which enables the quantification of coherence and entanglement in a bi- and multipartite system. The calculated measures of these quantum effects can be linked to observables, such as magnetization and total spin, with simulations of the model and using theoretical methods. We demonstrate that these observables can act as a proxy for the coherence and entanglement measures. The decay of both of these between the two local triplets can be monitored, enabling a clear definition of the spin-decoherence process in singlet fission.

Bell-state experiments with pairs of polarization-entangled photons are interpreted without any hinge on non-local mechanisms. The presented model rests on a careful analysis of published experimental findings. These foundations are implemented into a standard quantum mechanical treatment that obeys the purely local nature of each polarization preparation in the course of a measurement process. Polarization entanglement is ascribed to the generation of indiscernible photon pairs while undistorted propagation maintains this interrelation. Thus, the proposed approach assigns the essential characteristics of polarization entanglement to each constituent of an entangled pair. Accordingly, space-time separated polarization preparations lead to consistent probabilities of joint detection events. The obtained results agree with those of previous non-local models and thus reproduce the experimentally required violations of the Bell inequality. Since the presented approach lacks any non-local phenomenon, hidden variables are rendered superfluous, too.

Bell-type experiments that test correlated observables typically involve measurements of spin or polarization on multi-particle systems in singlet states. These observables are all non-commuting and satisfy an uncertainty relation. Theoretically, the non-commuting nature should be independent of whether the singlet state consists of multiple particles or a single particle. In addition, if Bell-type inequalities can be found for experiments involving spin and polarization, the same should be true for experiments involving other non-commuting observables such as position and momentum. In fact the original EPR paper used position and momentum, though in a different experimental situation. As such, an experiment is proposed to measure (quantum mechanically) position and momentum for a single oscillator as a means for deriving a Bell-type inequality for these correlated observables. The experiment, if realizable, would shed light on the basic nature of matter, perhaps pointing to some form of self-entanglement, and would also help to further elucidate a possible mechanism behind the Heisenberg uncertainty principle. Violation of these inequalities would, in fact, offer yet another confirmation of the principle.