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Quantum Compass of Migratory Birds

times, i.e., t = 0.08 μs and t = 0.71 μs. Both magnetic feld efect traces follow the expected behavior, with

the application of both low and high felds afecting changes in radical concentration of opposite signs.

Following the discussion by Lewis et al. (2018), weak magnetic felds mainly enhance the S–T0 inter­

conversion efciency, which results in an increase in radical concentration at early times afer laser

excitation (the initially predominantly singlet population is driven by radical concentration at late times

when formed triplet radical pairs can return more efciently to singlet radical pairs, which might sub­

sequently recombine).

In contrast, higher felds afect the radical recombination via the Zeeman efect, energetically isolat­

ing the S/T0 manifold from the T+/T levels, therefore impeding efcient singlet-triplet (S-T) mixing.

–

Following the arguments above, this results in a decrease in radical concentration at early times afer

the laser pulse and a corresponding increase on longer timescales.

It is, at frst sight, perhaps surprising that the magnetic feld efect data obtained at intermediate

times, namely, 0.28 μs afer the laser pulse, do not exhibit a sign inversion of the magnetic feld efect.

Tis fnding is, however, in agreement with the results of Lewis et al. (2018), in which it was demon­

strated that the feld efects on the populations of T0 and T+/T are not only in opposite directions but

–

evolve at diferent timescales. While the initially positive low feld efect has, at 0.28 μs, already changed

sign, the high feld efect lags about 0.2 μs behind in its evolution.

Barnes and Greenebaum (2015, 2016) made some theoretical considerations on the weak magnetic

feld efects on radical pair reactions as follows. Radicals are produced during many biological reactions,

including the mitochondrial metabolic processes. Te vector representations of the components of the

electron spin, electron angular momentum, and the nuclear spin with respect to the applied magnetic

feld are shown by Barnes and Greenebaum (2015). Here, a radical pair forms either a singlet state, where

the spins are aligned with electron spins with opposite spins, or a triplet state, with the spins parallel

(Barnes and Greenebaum, 2015).

In the singlet state, these pairs recombine with typical lifetimes between 10⁻⁶ and 10⁻¹⁰ s. In the trip­

let state, they are not allowed to recombine, and the opportunity for them to difuse away increases so

that they can react with other molecules (Barnes and Greenebaum, 2016). Te coupling between the

unpaired electrons and the nuclei in each fragment of the radical pair is diferent and, typically, can be

described by magnetic felds in the range 10 μT–3 mT (Brocklehurst and McLauchlan, 1996). Barnes and

Greenebaum (2016) proposed a schematic diagram of the evolution of spins of two members of a radical

pair, one with only an electron spin and the other with both an electron and a nonzero nuclear spin,

illustrating changes between relative S and T states under two sets of conditions. Here, (1) Precession of

spins in an external magnetic feld. (2) Stimulated transition by absorption of a photon of energy cor­

responding to the energy diference between levels in one radical. A photon must also carry angular

momentum corresponding to the diference between levels.

For many radicals, this is stronger than the GMF (∼50 μT) so that the quantum numbers describing

the state of each fragment are determined by the sum F of the electron angular momentum and electron

spin J and the nuclear spin I (Barnes and Greenebaum, 2016). Te unpaired electrons in the outer orbit

of each of the radical pair fragments can be thought of as rotating about their nuclei at diferent rates, so

the net magnetic moments for the two fragments switch from an S to a T state and back (Brocklehurst

and McLauchlan, 1996). Te rate at which this happens is perturbed by the external magnetic feld. Te

energy levels in each fragment are shifed by diferent amounts by the external magnetic felds (Barnes

and Greenebaum, 2016).

Changes in the applied magnetic feld shif the size of the energy barrier for the recombination and

the recombination rate (Barnes and Greenebaum, 2015, 2016). Nuclear magnetic spectra may have very

narrow absorption lines with bandwidths of a few cycles with corresponding lifetimes for excited states

of seconds or longer (Barnes and Greenebaum, 2015, 2016). Te energies of D2 molecule states as a func­

tion of the magnetic feld with low feld (F, m) and high feld (J, mJ, I, mI) are estimated by Barnes and

Greenebaum (2015). Here, quantum number labels mJ and mI are the projections of the electron angular

moment and nuclear spin on the external magnetic felds. Note the linearity of curves in the low feld