Abstract |
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. These pairs of biomolecular ions are recently shown to be biological open
quantum systems. We show that the coupling of the radical-pair spin degrees of freedom to its decohering
vibrational reservoir leads to a phononic Lamb shift of the radical-pair magnetic energy levels. The Lamb
shift Hamiltonian is diagonal in the singlet-triplet basis, and results in a singlet-triplet energy splitting
physically indistinguishable from an exchange interaction. This could have significant implications for
understanding the energy level structure and the dynamics of photosynthetic reaction centers, which are
intimately connected with the remarkable efficiency of photosynthesis [Eur. Phys. J. Plus 129, 187 (2014)].
Moreover, we address radical-pair reactions from the perspective of quantum metrology and parameter
estimation. Since the coherent spin-motion of radical pairs is affected 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. 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. Hence, this work opens the
application of well-advanced quantum metrology methods to biological systems [Phys. Rev. A 95, 032129
(2017)].
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