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arXiv:physics/0602016 · Journal of Physics B Atomic Molecular and Optical Physics

Time evolution of the spin state of the radical ion pair in the microwave field: an analytical solution

S V Anishchik, V N Verkhovlyuk, V A Bagryansky

Published Apr 24, 2006• 1 citation
arXivHTMLPDF

Abstract

The paper reports an exact solution for the problem of spin evolution of radical ion pair in static magnetic and resonant microwave field taking into account Zeeman and hyperfine interactions and spin relaxation. The values of parameters that provide one of the four possible types of solution are analysed. It is demonstrated that in the absence of spin relaxation, besides the zero field invariant an invariant at large amplitudes of the resonant microwave field can be found. The two invariants open the possibility for simple calculation of microwave pulses to control quantum state of the radical pair. The effect of relaxation on the invariants is analysed and it is shown that changes in the high field invariant are induced by phase relaxation.

DOI
10.1088/0953-4075/39/9/010

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The paper reports an exact solution for the problem of spin evolution of radical ion pair in static magnetic and resonant microwave field taking into account Zeeman and hyperfine interactions and spin relaxation. The values of parameters that provide one of the four possible types of solution are analysed. It is demonstrated that in the absence of spin relaxation, besides the zero field invariant an invariant at large amplitudes of the resonant microwave field can be found. The two invariants open the possibility for simple calculation of microwave pulses to control quantum state of the radical pair. The effect of relaxation on the invariants is analysed and it is shown that changes in the high field invariant are induced by phase relaxation.
Abstract. The paper reports an exact solution for the problem of spin evolution of radical ion pair in static magnetic and resonant microwave field taking into account Zeeman and hyperfine interactions and spin relaxation. The values of parameters that provide one of the four possible types of solution are analysed. It is demonstrated that in the absence of spin relaxation, besides the zero field invariant an invariant at large amplitudes of the resonant microwave field can be found. The two invariants open the possibility for simple calculation of microwave pulses to control quantum state of the radical pair. The effect of relaxation on the invariants is analysed and it is shown that changes in the high field invariant are induced by phase relaxation. PACS numbers: 03.65.Db, 33.35.+r Submitted to: J. Phys. B: At. Mol. Opt. Phys. Time evolution of spin state of radical ion pair in microwave field 2
The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.
Radical pairs and the dynamics they undergo are prevalent in many chemical and biological systems. Specifically, it has been proposed that the radical-pair mechanism results from a relatively strong hyperfine interaction with its intrinsic nuclear spin environment. While the existence of this mechanism is undisputed, the nanoscale details remain to be experimentally shown. Here, we analyze the role of a quantum sensor in detecting the spin dynamics (non-Markovian) of individual radical pairs in the presence of a weak magnetic field. We show how quantum control methods can be used to set apart the dynamics of the radical-pair mechanism at various stages of the evolution. We expect these findings to have implications to the understanding of the physical mechanism in magnetoreception and other biochemical processes with a microscopic detail.
The spin-chemical radical pair mechanism (RPM) has emerged as a leading theory for explaining the biological effects of low-intensity magnetic fields. These intriguing effects occur when the quantum system of radicals is well isolated from the disturbing influence of the environment. In other words, these effects are closely related to the spin coherence relaxation time τ, but an explicit relationship has not yet been established. In our study, we found an analytical solution to the Liouville-Neumann equation for an open system made up of two electrons and one nucleus, considering minimal interactions while concentrating on spin relaxation and chemical kinetics. This solution, supported by numerical integration, highlights the crucial role of quantum coherence. A straightforward expression is proposed that describes the RPM effect as a function of τ, within the ranges of magnetic field strength H and rate κ of chemical kinetics relevant to magnetobiology. Our findings reveal that RPM effects become significant only when fundamental relation γHτ>1+κτ holds: it controls the magnitude of the effects, and it is consistent with the principles of spin chemistry. Additionally, by comparing our results with existing experimental data, we estimate that the plausible spin decoherence times in magnetosensitive radical pairs within cryptochromelike proteins range from units to tens of nanoseconds. The effects of radio-frequency magnetic fields at the nT level were also examined, taking into account decoherence. These effects turned out to be negligible and incapable of disrupting the RPM patterns. The role of the quantum Zeno effect in magnetobiology is inspected from the perspective of the τ dependence of the RPM effect.
Identification of the external electromagnetic fields and internal hyperfine parameters which optimize the quantum singlet-triplet yield of simplified radical pairs modeled by Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms are analyzed. A method that combines sensitivity analysis with Tikhonov regularization is implemented. Numerical results demonstrate that the quantum singlet-triplet yield of the radical pair system can be significantly reduced if optimization is pursued simultaneously for both external magnetic fields and internal hyperfine parameters. The results may contribute towards understanding the structure-function relationship of a putative magnetoreceptor to manipulate and enhance quantum coherences at room temperature and leveraging biofidelic function to inspire novel quantum devices.