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arXiv:1408.1327 · Physical Review E

State transitions and decoherence in the avian compass

Vishvendra Singh Poonia, Dipankar Saha, Swaroop Ganguly

Published May 21, 2015• 17 citations
arXivHTMLPDF

Abstract

The radical pair model has been successful in explaining behavioral characteristics of the geomagnetic compass believed to underlie the navigation capability of certain avian species. In this study, the spin dynamics of the radical pair model and decoherence therein are interpreted from a microscopic state transition point of view. This helps to elucidate the interplay between the hyperfine and Zeeman interactions that enables the avian compass and clarify the distinctive effects of nuclear and environmental decoherence on it. Three regimes have been identified for the strength of the hyperfine interaction with respect to that of the geomagnetic Zeeman. It is found that the compass is likely to function in the large hyperfine interaction regime. Using a quantum information theoretic quantifier of coherence, we find that nuclear decoherence induces new structure in the spin dynamics for intermediate hyperfine interaction strength. On the other hand, environmental decoherence-modeled by two different noise models-seems to disrupt the compass action.

DOI
10.1103/physreve.91.052709

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The radical pair model has been successful in explaining behavioral characteristics of the geomagnetic compass believed to underlie the navigation capability of certain avian species. In this study, the spin dynamics of the radical pair model and decoherence therein are interpreted from a microscopic state transition point of view. This helps to elucidate the interplay between the hyperfine and Zeeman interactions that enables the avian compass and clarify the distinctive effects of nuclear and environmental decoherence on it. Three regimes have been identified for the strength of the hyperfine interaction with respect to that of the geomagnetic Zeeman. It is found that the compass is likely to function in the large hyperfine interaction regime. Using a quantum information theoretic quantifier of coherence, we find that nuclear decoherence induces new structure in the spin dynamics for intermediate hyperfine interaction strength. On the other hand, environmental decoherence-modeled by two different noise models-seems to disrupt the compass action.
The radical-pair mechanism is one of two distinct mechanisms used to explain the navigation of birds in geomagnetic fields, however little research has been done to explore the role of quantum entanglement in this mechanism. In this paper we study the lifetime of radical-pair entanglement corresponding to the magnitude and direction of magnetic fields to show that the entanglement lasts long enough in birds to be used for navigation. We also find that the birds appear to not be able to orient themselves directly based on radical-pair entanglement due to a lack of orientation sensitivity of the entanglement in the geomagnetic field. To explore the entanglement mechanism further, we propose a model in which the hyperfine interactions are replaced by local magnetic fields of similar strength. The entanglement of the radical pair in this model lasts longer and displays an angular sensitivity in weak magnetic fields, both of which are not present in previous models.
It is hypothesised that the avian compass relies on spin dynamics in a recombining radical pair. Quantum coherence has been suggested as a resource to this process that nature may utilise to achieve increased compass sensitivity. To date, the true functional role of coherence in these natural systems has remained speculative, lacking insights from sufficiently complex models. Here, we investigate realistically large radical pair models with up to 21 nuclear spins, inspired by the putative magnetosensory protein cryptochrome. By varying relative radical orientations, we reveal correlations of several coherence measures with compass fidelity. Whilst electronic coherence is found to be an ineffective predictor of compass sensitivity, a robust correlation of compass sensitivity and a global coherence measure is established. The results demonstrate the importance of realistic models, and appropriate choice of coherence measure, in elucidating the quantum nature of the avian compass.
A radical-pair-based chemical reaction might be used by birds for navigation via the geomagnetic direction. The inherent physical mechanism is that the quantum coherent transition from a singlet state to triplet states of the radical pair could respond to a weak magnetic field and be sensitive to the direction of such a field; this then results in different photopigments to be sensed by the avian eyes. Here, we propose a quantum bionic setup, inspired by the avian compass, as an ultrasensitive probe of a weak magnetic field based on the quantum phase transition of the environments of the two electrons in the radical pair. We prove that the yield of the chemical products via recombination from the singlet state is determined by the Loschmidt echo of the environments with interacting nuclear spins. Thus quantum criticality of environments could enhance the sensitivity of detection of weak magnetic fields.
This work investigates the effect of chirality-induced spin selectivity (CISS) on quantum coherence in the radical-pair (RP) mechanism of avian magnetoreception. Additionally, we examine the correlation of global and local coherence measures with the yield of the signaling state in the RP model. We find that both relative entropy of global coherence and local coherence in the radical pair increase with CISS. However, only global coherence shows a strong correlation with the signaling state yield and thus indicates a plausible utilitarian role for the avian compass. We also analyze the interplay of dipolar and exchange interaction with the CISS and their effect on the coherence of the radical-pair spin. Further, we analyze the effect of environmental decoherence along with CISS. We conclude that a high CISS results in a high correlation of global coherence with signaling state yield. We propose that CISS might play an important role in developing quantum technologies by sustaining coherence in radical-pair-like quantum systems.
The chemical compass model, based on radical pair reactions, is an idea to explain avian magnetoreception. At present, to the best of our knowledge, questions concerning the key ingredients responsible for the high sensitivity of a chemical compass and the possible role of quantum coherence and decoherence remain unsolved. Here, we investigate the optimized hyperfine coupling for a chemical compass in order to achieve the best magnetic field sensitivity. We show that its magnetic sensitivity limit can be further extended by simple quantum control and may benefit from additional decoherence. With this, we clearly demonstrate how quantum coherence can be exploited in the functioning of a chemical compass. The present results also provide routes toward the design of a biomimetic weak magnetic field sensor.
Abstract Quantum sensing enables the ultimate precision attainable in parameter estimation. Circumstantial evidence suggests that certain organisms, most notably migratory songbirds, also harness quantum-enhanced magnetic field sensing via a radical-pair-based chemical compass for the precise detection of the weak geomagnetic field. However, what underpins the acuity of such a compass operating in a noisy biological setting, at physiological temperatures, remains an open question. Here, we address the fundamental limits of inferring geomagnetic field directions from radical-pair spin dynamics. Specifically, we compare the compass precision, as derived from the directional dependence of the radical-pair recombination yield, to the ultimate precision potentially realisable by a quantum measurement on the spin system under steady-state conditions. To this end, we probe the quantum Fisher information and associated Cramér–Rao bound in spin models of realistic complexity, accounting for complex inter-radical interactions, a multitude of hyperfine couplings, and asymmetric recombination kinetics, as characteristic for the magnetosensory protein cryptochrome. We compare several models implicated in cryptochrome magnetoreception and unveil their optimality through the precision of measurements ostensibly accessible to nature. Overall, the comparison provides insight into processes honed by nature to realise optimality whilst constrained to operating with mere reaction yields. Generally, the inference of compass orientation from recombination yields approaches optimality in the limits of complexity, yet levels off short of the theoretical optimal precision bounds by up to one or two orders of magnitude, thus underscoring the potential for improving on design principles inherent to natural systems.