The avian compass can be sensitive even without sustained electron spin coherence

Abstract

Theoretical studies indicating the presence of long-lived coherence in the radical pair system have engendered questions about its utilitarian role in the avian compass. In this paper, we investigate the role of electron spin coherence in a multinuclear radical pair system including its impact on compass sensitivity. We find that sustenance of long-lived electron spin coherence is unlikely in a multinuclear hyperfine environment. After probing the role of the hyperfine interactions in the compass, we affirm the hyperfine anisotropy to be an essential parameter for the necessary sensitivity required for the compass action. Thereby, we identify a parameter regime where the compass would exhibit good sensitivity even without sustained electron spin coherence.

Observations about utilitarian coherence in the avian compass

“…Surprisingly, an anti-correlation with respect to µ[ Ci ] is observed that is present in both the UD and ST basis, but larger in the former. Specifically, ∆ S is found to anti-correlate with µ[ CE,UD r ], which is based on the same coherence measure as used by Jain et al 32 , giving rise to a remarkable correlation coefficient of R = −0.927. In contrast, a positive (but weaker) correlation is observed with respect to the ∆[ CE,ST r ] measure.…”

“…Large spin system electronic coherence. Previous studies on coherence in the avian compass typically use systems with a modest number of nuclear spins (only one or 5-6) and often randomly assumed hyperfine interactions 28,29,32,38,41 . Under the assumptions as laid out above, we have been able to overcome this limitation and evaluate fidelities and coherence measures for flavintryptophan and flavin-tyrosine radical pairs with up to 21 nuclear spins and judiciously chosen hyperfine parameters, as summarized in the Supplementary Information (SI).…”

“…Various measures to quantify coherence have been developed [11][12][13] . Several such measures have previously been used in the context of the avian compass 28,29,32,38,39 . One canonical measure to quantify coherence is the relative entropy of coherence, which, in terms of the normalized density operator ρ and a chosen basis, {|n } d n=1 , of the d-dimensional Hilbert space, is defined as…”

“…To distinguish these choices, we will henceforth index the coherence labels with G (global, based on ρ), E (electronic, based on σ, and ST (singlet-triplet basis) and UD (up-down basis). For example, C E,UD r corresponds to the electronic coherence assessed via the relative entropy quantifier in the up-down basis, which is the measure used by Jain et al 32 . Note that, for all definitions used above, the non-trace preserving density matrix characteristic of recombining radical pair systems must be renormalized (by Tr [ρ]; which here simply yields the k = 0 result).…”

“…This is a parameter which could have been subject to evolutionary optimisation in the protein cryptochrome and is more likely to reflect any potential quantum advantage that is exercisable in the well-defined biological system, if it exists. Specifically, considering more realistic modelling conditions, we analyse whether the relative orientations of optimal compass fidelity are correlated with the electronic coherence (as anticipated based on investigations 22,28,29 ) or not (as advocated in a recent study by Jain et al 32 ). Our results question the effectiveness of coherence, measured by electronic coherence quantifiers, as the sole driver of magnetoreception and explanation of increased compass sensitivity.…”