© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2607.20546

Influence of Oscillating Magnetic Fields on the Electric Dipole Moment of Radical Pairs in Cryptochrome Based Magnetoreception

Ali Soltanmanesh, Mahboobe Sehati, Sareh Rostami, Abolfazl Bahrampour, Alireza Bahrampour

physics.bio-phquant-phSubmitted Jul 13, 2026• Announced Jul 14, 2026

Abstract

Radical pairs induced by light-driven reduction of cryptochrome protein constitute a spin dependent mechanism that is accompanied by an electric dipole moment and is found to be sensitive to external magnetic fields. In this research, to investigate for the further proof of such model, the simultaneous effect of the Earth's static magnetic field and the time-dependent magnetic field noise on the electric dipole moment of the radical pair has been studied within the quantum mechanical framework. The effect of the external magnetic field discussed in different angles regarding the Earth magnetic field within various frequencies and magnitudes. The sensitivity of the system behavior to the external magnetic field frequencies and magnitudes, vastly differs among the changes in the magnetic field angle to the Earth's static field. Furthermore, the sensitivity studied under the effect of the environmental noise. The relative spatial orientation of the two magnetic field components plays an important role in the time evolution of the electric dipole moment. Also, deeper discussions on specific relative orientations of the external magnetic fields, such as 24 degree, shows that the quantum model of radical pairs which is based on dipole moment, is in agreement with the results of the birds behavorial studies. These findings provide new insights into the sensitivity of the radical pair model to the combination of magnetic fields and may contribute to a comprehensive understanding of the phenomenon of magnetoreception and the advancement of bioinspired magnetic sensors.

Related papers

Geometric Protection of Spin-Correlated Radical Pairs: A Relational Model for Cryptochrome Magnetoreception Lifetimes

Daphne Garrido

Migratory birds detect the Earth’s magnetic field with remarkable precision using a quantum process in retinal cryptochrome proteins. We review the observational and experimental evidence supporting the radical-pair mechanism and propose a simple dynamical model that augments the standard radical-pair Hamiltonian with a minimal geometric protection term. This term is modulated by consecutive Fibonacci numbers whose ratios converge to the golden ratio ϕ = (1 + √5)/2 ≈ 1.618. Numerical integration and analytical fixed-point analysis show that the protection term naturally stabilizes singlet–triplet coherence lifetimes and optimizes magnetic sensitivity at geomagnetic field strengths and inclinations observed in nature. The model is fully classical, self-contained, and provides a new quantitative explanation for the robustness of avian magnetoreception. It offers the first empirical hint of a universal geometric principle governing quantum coherence in biological systems.

•May 7, 2026•0 citations

An open quantum system approach to the radical pair mechanism

Betony Adams, Ilya Sinayskiy, Francesco Petruccione

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.

Scientific Reports•Oct 18, 2018•26 citations

Quantum coherence and entanglement in the avian compass

James A. Pauls, Yiteng Zhang, G. P. Berman +1 more

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.

arXiv:1211.4255•Physical Review E•Jun 11, 2013•64 citations

A precise measure of avian magnetoreception based on quantum metrology

Li-Sha Guo, Bao-Ming Xu, Jian Zou +1 more

The radical pair (RP) mechanism, which describes the quantum dynamics of a spatially separated electron pair, is considered as one of the principal models of avian magnetoreception. Different from the conventional phenomenological approach where the sensitivity of avian magnetoreception is characterized by the singlet yield $Φ_{S}$, we introduce the quantum Fisher information (QFI), which represents the maximum information about the magnetic field's direction extracted from the RP state, to give a precise measure of sensitivity of avian compass essentially. The consistency between our results and experimental observations suggests that QFI plays a decisive role in avian magnetoreception. Besides, within the framework of quantum metrology, we can judge the feasibility of any possible measurement scheme for avian magnetoreception, and shed light on an intrinsic relevance between the singlet yield and a concrete measurement scheme of our approach. The present work allows us to understand many things about avian magnetoreception from a fully new perspective of quantum metrology, and provide a new route to establish a direct connection between quantum information and many other biological functions.

arXiv:1612.00557•Dec 2, 2016•0 citations

Quantifying Magnetic Sensitivity of Radical Pair Based Compass by Quantum Fisher Information

Li-Sha Guo, Bao-Ming Xu, Jian Zou +1 more

The radical pair (RP) based compass is considered as one of the principal models of avian magnetoreception. Different from the conventional approach where the sensitivity of RP based compass is described by the singlet yield, we introduce the quantum Fisher information (QFI), which represents the maximum information about the magnetic field's direction extracted from the RP state, to quantify the sensitivity of RP based compass. The consistency between our results and experimental observations suggests that the QFI may serve as a measure to describe the sensitivity of RP based compass. Besides, within the framework of quantum metrology, we give two specific possible measurement schemes and find that the conventional singlet yield is corresponding to the measurement of total angular momentum. Moreover, we show that the measurement of fluctuation of the total magnetic moment is much more accurate than the singlet yield measurement, and is close to the optimal measurement scheme. Finally, the effects of entanglement and decoherence are also discussed in the spirit of our approach.

Scientific Reports•Jul 13, 2017•10 citations

The arrangement of anisotropic spin couplings can optimize sensitivity of the cryptochrome radical pair to the direction of geomagnetic field

Victor Bezchastnov, Tatiana Domratcheva

Sensing of the geomagnetic field direction by many living organisms is commonly thought to involve radical pairs, such as those formed photochemically between the flavin and tryptophan radicals in the cryptochrome proteins. Previous theoretical studies have shown that strongly axial hyperfine couplings in the cryptochrome radicals greatly enhance the formation of a signaling state of the protein when the magnetic field is directed perpendicular to the hyperfine axis of either of the radicals. However, further analysis led to the conclusion that sharpness of detecting those magnetic directions is strongly suppressed by the inter-radical electron spin coupling. Here, we perform theoretical simulations of the compass function for a set of arrangements of the intra- and inter-radical spin couplings in the idealized cryptochrome radical pair, and find certain arrangements that preserve the sharpness in detecting the direction of the geomagnetic field. One particular arrangement, with the hyperfine axes of the radicals orthogonal to the symmetry axis of inter-radical coupling, provides even sharper field-direction sensitivity than that contributed solely by the anisotropy of the hyperfine coupling.

physics.bio-phCross-listedarXiv:2602.18480•Feb 11, 2026

Radical pairs induced by light-driven reduction of cryptochrome protein constitute a spin dependent mechanism that is accompanied by an electric dipole moment and is found to be sensitive to external magnetic fields. In this research, to investigate for the further proof of such model, the simultaneous effect of the Earth's static magnetic field and the time-dependent magnetic field noise on the electric dipole moment of the radical pair has been studied within the quantum mechanical framework. The effect of the external magnetic field discussed in different angles regarding the Earth magnetic field within various frequencies and magnitudes. The sensitivity of the system behavior to the external magnetic field frequencies and magnitudes, vastly differs among the changes in the magnetic field angle to the Earth's static field. Furthermore, the sensitivity studied under the effect of the environmental noise. The relative spatial orientation of the two magnetic field components plays an important role in the time evolution of the electric dipole moment. Also, deeper discussions on specific relative orientations of the external magnetic fields, such as 24 degree, shows that the quantum model of radical pairs which is based on dipole moment, is in agreement with the results of the birds behavorial studies. These findings provide new insights into the sensitivity of the radical pair model to the combination of magnetic fields and may contribute to a comprehensive understanding of the phenomenon of magnetoreception and the advancement of bioinspired magnetic sensors.

Migratory birds detect the Earth’s magnetic field with remarkable precision using a quantum process in retinal cryptochrome proteins. We review the observational and experimental evidence supporting the radical-pair mechanism and propose a simple dynamical model that augments the standard radical-pair Hamiltonian with a minimal geometric protection term. This term is modulated by consecutive Fibonacci numbers whose ratios converge to the golden ratio ϕ = (1 + √5)/2 ≈ 1.618. Numerical integration and analytical fixed-point analysis show that the protection term naturally stabilizes singlet–triplet coherence lifetimes and optimizes magnetic sensitivity at geomagnetic field strengths and inclinations observed in nature. The model is fully classical, self-contained, and provides a new quantitative explanation for the robustness of avian magnetoreception. It offers the first empirical hint of a universal geometric principle governing quantum coherence in biological systems.

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.

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.

The radical pair (RP) mechanism, which describes the quantum dynamics of a spatially separated electron pair, is considered as one of the principal models of avian magnetoreception. Different from the conventional phenomenological approach where the sensitivity of avian magnetoreception is characterized by the singlet yield

Φ_{S}

, we introduce the quantum Fisher information (QFI), which represents the maximum information about the magnetic field's direction extracted from the RP state, to give a precise measure of sensitivity of avian compass essentially. The consistency between our results and experimental observations suggests that QFI plays a decisive role in avian magnetoreception. Besides, within the framework of quantum metrology, we can judge the feasibility of any possible measurement scheme for avian magnetoreception, and shed light on an intrinsic relevance between the singlet yield and a concrete measurement scheme of our approach. The present work allows us to understand many things about avian magnetoreception from a fully new perspective of quantum metrology, and provide a new route to establish a direct connection between quantum information and many other biological functions.

The radical pair (RP) based compass is considered as one of the principal models of avian magnetoreception. Different from the conventional approach where the sensitivity of RP based compass is described by the singlet yield, we introduce the quantum Fisher information (QFI), which represents the maximum information about the magnetic field's direction extracted from the RP state, to quantify the sensitivity of RP based compass. The consistency between our results and experimental observations suggests that the QFI may serve as a measure to describe the sensitivity of RP based compass. Besides, within the framework of quantum metrology, we give two specific possible measurement schemes and find that the conventional singlet yield is corresponding to the measurement of total angular momentum. Moreover, we show that the measurement of fluctuation of the total magnetic moment is much more accurate than the singlet yield measurement, and is close to the optimal measurement scheme. Finally, the effects of entanglement and decoherence are also discussed in the spirit of our approach.

Sensing of the geomagnetic field direction by many living organisms is commonly thought to involve radical pairs, such as those formed photochemically between the flavin and tryptophan radicals in the cryptochrome proteins. Previous theoretical studies have shown that strongly axial hyperfine couplings in the cryptochrome radicals greatly enhance the formation of a signaling state of the protein when the magnetic field is directed perpendicular to the hyperfine axis of either of the radicals. However, further analysis led to the conclusion that sharpness of detecting those magnetic directions is strongly suppressed by the inter-radical electron spin coupling. Here, we perform theoretical simulations of the compass function for a set of arrangements of the intra- and inter-radical spin couplings in the idealized cryptochrome radical pair, and find certain arrangements that preserve the sharpness in detecting the direction of the geomagnetic field. One particular arrangement, with the hyperfine axes of the radicals orthogonal to the symmetry axis of inter-radical coupling, provides even sharper field-direction sensitivity than that contributed solely by the anisotropy of the hyperfine coupling.