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arXiv:0804.3503

Quantum Zeno Effect in Radical-Ion-Pair Recombination Reactions

Iannis K. Kominis

Published Apr 22, 2008• 2 citations
arXivHTMLPDF

Abstract

Radical-ion pairs are ubiquitous in a wide range of biochemical reactions, ranging from photosynthesis to magnetic sensitive chemical reactions underlying avian magnetic navigation. We here show that the charge recombination of a radical-ion-pair is a continuous quantum measurement process that interrogates the spin state of the pair. This naturally leads to the appearance of the quantum Zeno effect, explaining a large amount of data on unusually long-lived radical-ion-pairs.

DOI
10.48550/arxiv.0804.3503

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Radical-ion pairs are ubiquitous in a wide range of biochemical reactions, ranging from photosynthesis to magnetic sensitive chemical reactions underlying avian magnetic navigation. We here show that the charge recombination of a radical-ion-pair is a continuous quantum measurement process that interrogates the spin state of the pair. This naturally leads to the appearance of the quantum Zeno effect, explaining a large amount of data on unusually long-lived radical-ion-pairs.
Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion-pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70s cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density-matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high magnetic-field radical-ion-pair reactions.
A new paradigm emerging in the description of magnetic-sensitive radical-ion-pair recombination reactions is presented. This paradigm is founded on the realization that the recombination process of radical-ion pairs is a continuous quantum measurement. In the regime of low magnetic fields we describe the appearance of purely quantum phenomena, that fade away as the magnetic field increases. We will analyze the magnetic sensitivity of these reactions under this perspective and bridge the new full quantum theory with the existing classical reaction theory applicable at high magnetic fields. Based on the quantum theory of recombination we will then explain experimental observations incompatible with classical reaction theory, in particular the effect of deuteration on the magnetic sensitivity of radical-ion pair recombination yields.
Radical-ion pair reactions are currently understood to underlie the biochemical magnetic compass of migratory birds. It was recently shown that radical-ion pair reactions form a rich playground for the application of quantum-information-science concepts and effects. We will show here that the intricate interplay between the quantum Zeno effect and the coherent excitation of radical-ion pairs leads to an exquisite angular sensitivity of the reaction yields. This results in a significant and previously unanticipated suppression of the avian compass heading error, opening the way to quantum engineering precision biological sensors.
It has been recently shown that radical-ion pairs and their reactions are a paradigm biological system manifesting non-trivial quantum effects, so far invisible due to the phenomenological description of radical-ion-pair reactions used until now. We here use the quantum-mechanically consistent master equation describing magnetic-sensitive radical-ion-pair reactions to explain experimental data [C. R. Timmel and K. B. Henbest, Phil. Trans. R. Soc. Lond. A {\bf 362}, 2573 (2004); C. T. Rodgers, S. A. Norman, K. B. Henbest, C. R. Timmel and P. J. Hore, J. Am. Chem. Soc. {\bf 129} 6746 (2007)] on the effect of deuteration on the reaction yields. Anomalous behavior of radical-ion-pair reactions after deuteration, i.e. data inconsistent with the predictions of the phenomenological theory used so far, has been observed since the 70's and has remained unexplained until now.
Manifestations of the chemical Zeno effect (slowing down of the quantum evolution of radical pairs as a result of spin-selective recombination of exchange-bounded radical pairs) are considered. In radical pairs created in singlet and random spin states, the chemical kinetics is described by the sum of kinetic evolution (exponential) and oscillatory functions. The kinetic function is a superposition of two exponential functions. Recombination monotonically decreases the amplitude of quantum beats in singlet radical pairs. The dependence of the amplitude of quantum beats in noncorrelated radical pairs on the recombination rate constant is not monotonic.
Radical-ion pairs and their reactions have triggered the study of quantum effects in biological systems. This is because they exhibit a number of effects best understood within quantum information science, and at the same time are central in understanding the avian magnetic compass and the spin transport dynamics in photosynthetic reaction centers. Here we address radical-pair reactions from the perspective of quantum metrology. Since the coherent spin motion of radical pairs is effected by an external magnetic field, these spin-dependent reactions essentially realize a biochemical magnetometer. Using the quantum Fisher information, we find the fundamental quantum limits to the magnetic sensitivity of radical-pair magnetometers, arriving at a sensitivity $\ensuremath{\delta}B=2\phantom{\rule{0.16em}{0ex}}\mathrm{pT}/\ensuremath{\tau}[1\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\text{s}]\sqrt{{\ensuremath{\nu}}_{0}[{10}^{12}]}$, given in terms of radical-pair lifetime $\ensuremath{\tau}$ and number of radical pairs ${\ensuremath{\nu}}_{0}$. We then explore how well the usual measurement scheme considered in radical-pair reactions, the measurement of reaction yields, approaches the fundamental limits. In doing so, we find the optimal hyperfine interaction Hamiltonian that leads to the best magnetic sensitivity as obtained from reaction yields. This is still an order of magnitude smaller than the absolute quantum limit. Finally, we demonstrate that with a realistic quantum reaction control reminding one of Ramsey interferometry, here presented as a quantum circuit involving the spin-exchange interaction and a recently proposed molecular switch, we can approach the fundamental quantum limit within a factor of 2. This work opens the application of well-advanced quantum metrology methods to biological systems.