Entanglement and sources of magnetic anisotropy in radical pair-based avian magnetoreceptors

Isotope effects on radical pair performance in cryptochrome: A new hypothesis for the evolution of animal migration: The quantum biology of migration

Mechanisms occurring at the atomic level are now known to drive processes essential for life, as revealed by quantum effects on biochemical reactions. Some macroscopic characteristics of organisms may thus show an atomic imprint, which may be transferred across organisms and affect their evolution. This possibility is considered here for the first time, with the aim of elucidating the appearance of an animal innovation with an unclear evolutionary origin: migratory behaviour. This trait may be mediated by a radical pair (RP) mechanism in the retinal flavoprotein cryptochrome, providing essential magnetic orientation for migration. Isotopes may affect the performance of quantum processes through their nuclear spin. Here, we consider a simple model and then apply the standard open quantum system approach to the spin dynamics of cryptochrome RP. We changed the spin quantum number (I) and g-factor of hydrogen and nitrogen isotopes to investigate their effect on RP's yield and magnetic sensitivity. Strong differences arose between isotopes with I = 1 and I = 1/2 in their contribution to cryptochrome magnetic sensitivity, particularly regarding Earth's magnetic field strengths (25-65 µT). In most cases, isotopic substitution improved RP's magnetic sensitivity. Migratory behaviour may thus have been favoured in animals with certain isotopic compositions of cryptochrome.

Diamond surface engineering for molecular sensing with nitrogen-vacancy centers

Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.

Observations about utilitarian coherence in the avian compass

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.

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

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.

How quantum is radical pair magnetoreception?

Semiclassical methods cannot accurately simulate magnetic field effects relevant to avian magnetoreception, which may therefore deserve the label “quantum biology”.

Navigating at night: fundamental limits on the sensitivity of radical pair magnetoreception under dim light

Night-migratory songbirds appear to sense the direction of the Earth's magnetic field via radical pair intermediates formed photochemically in cryptochrome flavoproteins contained in photoreceptor cells in their retinas. It is an open question whether this light-dependent mechanism could be sufficiently sensitive given the low-light levels experienced by nocturnal migrants. The scarcity of available photons results in significant uncertainty in the signal generated by the magnetoreceptors distributed around the retina. Here we use results from Information Theory to obtain a lower bound estimate of the precision with which a bird could orient itself using only geomagnetic cues. Our approach bypasses the current lack of knowledge about magnetic signal transduction and processing in vivo by computing the best-case compass precision under conditions where photons are in short supply. We use this method to assess the performance of three plausible cryptochrome-derived flavin-containing radical pairs as potential magnetoreceptors.

Magnetoreception in birds

Birds can use two kinds of information from the geomagnetic field for navigation: the direction of the field lines as a compass and probably magnetic intensity as a component of the navigational ‘map’. The direction of the magnetic field appears to be sensed via radical pair processes in the eyes, with the crucial radical pairs formed by cryptochrome. It is transmitted by the optic nerve to the brain, where parts of the visual system seem to process the respective information. Magnetic intensity appears to be perceived by magnetite-based receptors in the beak region; the information is transmitted by the ophthalmic branch of the trigeminal nerve to the trigeminal ganglion and the trigeminal brainstem nuclei. Yet in spite of considerable progress in recent years, many details are still unclear, among them details of the radical pair processes and their transformation into a nervous signal, the precise location of the magnetite-based receptors and the centres in the brain where magnetic information is combined with other navigational information for the navigational processes.

Upper bound on the biological effects of 50/60 Hz magnetic fields mediated by radical pairs

Prolonged exposure to weak (~1 μT) extremely-low-frequency (ELF, 50/60 Hz) magnetic fields has been associated with an increased risk of childhood leukaemia. One of the few biophysical mechanisms that might account for this link involves short-lived chemical reaction intermediates known as radical pairs. In this report, we use spin dynamics simulations to derive an upper bound of 10 parts per million on the effect of a 1 μT ELF magnetic field on the yield of a radical pair reaction. By comparing this figure with the corresponding effects of changes in the strength of the Earth’s magnetic field, we conclude that if exposure to such weak 50/60 Hz magnetic fields has any effect on human biology, and results from a radical pair mechanism, then the risk should be no greater than travelling a few kilometres towards or away from the geomagnetic north or south pole.

Posner qubits: spin dynamics of entangled Ca9(PO4)6 molecules and their role in neural processing

It has been suggested that 31P nuclear spins in Ca9(PO4)6 molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca9(PO4)6 molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical 31P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca9(PO4)6 arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca9(PO4)6 is likely to be much faster than this estimate.

Magnetosensitivity in Dipolarly Coupled Three-Spin Systems

The radical pair mechanism is a canonical model for the magnetosensitivity of chemical reaction processes. The key ingredient of this model is the hyperfine interaction that induces a coherent mixing of singlet and triplet electron spin states in pairs of radicals, thereby facilitating magnetic field effects (MFEs) on reaction yields through spin-selective reaction channels. We show that the hyperfine interaction is not a categorical requirement to realize the sensitivity of radical reactions to weak magnetic fields. We propose that, in systems comprising three instead of two radicals, dipolar interactions provide an alternative pathway for MFEs. By considering the role of symmetries and energy level crossings, we present a model that demonstrates a directional sensitivity to fields weaker than the geomagnetic field and remarkable spikes in the reaction yield as a function of the magnetic field intensity; these effects can moreover be tuned by the exchange interaction. Our results further the current understanding of the effects of weak magnetic fields on chemical reactions, could pave the way to a clearer understanding of the mysteries of magnetoreception and other biological MFEs and motivate the design of quantum sensors. Further still, this phenomenon will affect spin systems used in quantum information processing in the solid state and may also be applicable to spintronics.

The sensitivity of a radical pair compass magnetoreceptor can be significantly amplified by radical scavengers

Birds have a remarkable ability to obtain navigational information from the Earth's magnetic field. The primary detection mechanism of this compass sense is uncertain but appears to involve the quantum spin dynamics of radical pairs formed transiently in cryptochrome proteins. We propose here a new version of the current model in which spin-selective recombination of the radical pair is not essential. One of the two radicals is imagined to react with a paramagnetic scavenger via spin-selective electron transfer. By means of simulations of the spin dynamics of cryptochrome-inspired radical pairs, we show that the new scheme offers two clear and important benefits. The sensitivity to a 50 μT magnetic field is greatly enhanced and, unlike the current model, the radicals can be more than 2 nm apart in the magnetoreceptor protein. The latter means that animal cryptochromes that have a tetrad (rather than a triad) of tryptophan electron donors can still be expected to be viable as magnetic compass sensors. Lifting the restriction on the rate of the spin-selective recombination reaction also means that the detrimental effects of inter-radical exchange and dipolar interactions can be minimised by placing the radicals much further apart than in the current model.

Monolithic OLED-Microwire Devices for Ultrastrong Magnetic Resonant Excitation

Organic light-emitting diodes (OLEDs) make highly sensitive probes to test magnetic resonance phenomena under unconventional conditions since spin precession controls singlet-triplet transitions of electron-hole pairs, which in turn give rise to distinct recombination currents in conductivity. Electron paramagnetic resonance can therefore be detected in the absence of spin polarization. We exploit this characteristic to explore the exotic regime of ultrastrong light-matter coupling, where the Rabi frequency of a charge carrier spin is of the order of the transition frequency of the two-level system. To reach this domain, we have to lower the Zeeman splitting of the spin states, defined by the static magnetic field B₀, and raise the strength of the oscillatory driving field of the resonance, B₁. This is achieved by shrinking the OLED and bringing the source of resonant radio frequency (RF) radiation as close as possible to the organic semiconductor in a monolithic device structure, which incorporates an OLED fabricated directly on top of an RF microwire within one monolithic thin-film device structure. With an RF driving power in the milliwatt range applied to the microwire, the regime of bleaching and inversion of the magnetic resonance signal is reached due to the onset of the spin-Dicke effect. In this example of ultrastrong light-matter coupling, the individual resonant spin transitions of electron-hole pairs become indistinguishable with respect to the driving field, and superradiance of the magnetic dipole transitions sets in.

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

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.

Scheme for Detection of Single-Molecule Radical Pair Reaction Using Spin in Diamond

The radical pair reaction underlies the magnetic field sensitivity of chemical reactions and is suggested to play an important role in both chemistry and biology. Current experimental evidence is based on ensemble measurements; however, the ability to probe the radical pair reaction at the single-molecule level would provide valuable information concerning its role in important biological processes. Here, we propose a scheme to detect the charge recombination rate in a radical pair reaction under ambient conditions by using single nitrogen-vacancy center spin in diamond. We demonstrate theoretically that it is possible to detect the effect of the geomagnetic field on the radical pair reaction and propose the present scheme as a possible hybrid model chemical compass.

Quantum information processing in the radical-pair mechanism: Haberkorn's theory violates the Ozawa entropy bound

Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.

The quantum needle of the avian magnetic compass

Migratory birds have a light-dependent magnetic compass, the mechanism of which is thought to involve radical pairs formed photochemically in cryptochrome proteins in the retina. Theoretical descriptions of this compass have thus far been unable to account for the high precision with which birds are able to detect the direction of the Earth's magnetic field. Here we use coherent spin dynamics simulations to explore the behavior of realistic models of cryptochrome-based radical pairs. We show that when the spin coherence persists for longer than a few microseconds, the output of the sensor contains a sharp feature, referred to as a spike. The spike arises from avoided crossings of the quantum mechanical spin energy-levels of radicals formed in cryptochromes. Such a feature could deliver a heading precision sufficient to explain the navigational behavior of migratory birds in the wild. Our results (i) afford new insights into radical pair magnetoreception, (ii) suggest ways in which the performance of the compass could have been optimized by evolution, (iii) may provide the beginnings of an explanation for the magnetic disorientation of migratory birds exposed to anthropogenic electromagnetic noise, and (iv) suggest that radical pair magnetoreception may be more of a quantum biology phenomenon than previously realized.

Sensitive fluorescence-based detection of magnetic field effects in photoreactions of flavins

Magnetic field effect studies have been conducted on a variety of flavin-based radical pair systems chosen to model the magnetosensitivity of the photoinduced radical pairs found in cryptochrome flavoproteins. Cryptochromes are blue-light photoreceptor proteins which are thought to mediate avian magnetoreception, an hypothesis supported by recent in vitro observations of magnetic field-dependent reaction kinetics for a light-induced radical pair in a cryptochrome from the plant Arabidopsis thaliana. Many cryptochromes are difficult to express in large quantities or high concentrations and are easily photodegraded. Magnetic field effects are typically measured by spectroscopic detection of the transient radical (pair) concentrations. Due to its low sensitivity, single-pass transient absorption spectroscopy can be of limited use in such experiments and much recent work has involved development of other methodologies offering improved sensitivity. Here we explore the use of flavin fluorescence as the magnetosensitive probe and demonstrate the exceptional sensitivity of this technique which allows the detection of magnetic field effects in flavin samples at sub-nanomolar concentrations and in cryptochromes.

Electron spin relaxation in cryptochrome-based magnetoreception

The magnetic compass sense of migratory birds is thought to rely on magnetically sensitive radical pairs formed photochemically in cryptochrome proteins in the retina. An important requirement of this hypothesis is that electron spin relaxation is slow enough for the Earth's magnetic field to have a significant effect on the coherent spin dynamics of the radicals. It is generally assumed that evolutionary pressure has led to protection of the electron spins from irreversible loss of coherence in order that the underlying quantum dynamics can survive in a noisy biological environment. Here, we address this question for a structurally characterized model cryptochrome expected to share many properties with the putative avian receptor protein. To this end we combine all-atom molecular dynamics simulations, Bloch-Redfield relaxation theory and spin dynamics calculations to assess the effects of spin relaxation on the performance of the protein as a compass sensor. Both flavin-tryptophan and flavin-Z˙ radical pairs are studied (Z˙ is a radical with no hyperfine interactions). Relaxation is considered to arise from modulation of hyperfine interactions by librational motions of the radicals and fluctuations in certain dihedral angles. For Arabidopsis thaliana cryptochrome 1 (AtCry1) we find that spin relaxation implies optimal radical pair lifetimes of the order of microseconds, and that flavin-Z˙ pairs are less affected by relaxation than flavin-tryptophan pairs. Our results also demonstrate that spin relaxation in isolated AtCry1 is incompatible with the long coherence times that have been postulated to explain the disruption of the avian magnetic compass sense by weak radiofrequency magnetic fields. We conclude that a cryptochrome sensor in vivo would have to differ dynamically, if not structurally, from isolated AtCry1. Our results clearly mark the limits of the current hypothesis and lead to a better understanding of the operation of radical pair magnetic sensors in noisy biological environments.

Coherent chemical kinetics as quantum walks. II. Radical-pair reactions in Arabidopsis thaliana

We apply the quantum-walk approach proposed in the preceding paper [A. Chia et al., preceding paper, Phys. Rev. E 93, 032407 (2016)] to a radical-pair reaction where realistic estimates for the intermediate transition rates are available. The well-known average hitting time from quantum walks can be adopted as a measure of how quickly the reaction occurs and we calculate this for varying degrees of dephasing in the radical pair. The time for the radical pair to react to a product is found to be independent of the amount of dephasing introduced, even in the limit of no dephasing where the transient population dynamics exhibits strong coherent oscillations. This can be seen to arise from the existence of a rate-limiting step in the reaction and we argue that in such examples, a purely classical model based on rate equations can be used for estimating the time scale of the reaction but not necessarily its population dynamics.

Dark state population determines magnetic sensitivity in radical pair magnetoreception model

What is the real role of the quantum coherence and entanglement in the radical pair (RP) compass, and what determines the singlet yield have not been fully understood. In this paper, we find that the dark states of the two-electron Zeeman energy operator (TEZE) play an important role in the RP compass. We respectively calculate the singlet yields for two initial states in this dark state basis: the coherent state and the same state just removing the dark state coherence. For the later there is neither dark state coherence nor entanglement in the whole dynamical process. Surprisingly we find that in both cases the singlet yields are the same, and based on this result, we believe that the dark state population determines the singlet yield completely, and the dark state coherence and entanglement have little contribution to it. Finally, we also find that the dark state population as well as the singlet yield anisotropy is fragile to the vertical magnetic noise. However, the orientation is robust and is even enhanced by the parallel magnetic noise because the dark states expand a decoherence-free subspace. The dark state population as well as the orientation is more robust to the hyperfine coupling noise.

Synthesis and investigation of donor-porphyrin-acceptor triads with long-lived photo-induced charge-separate states

Two donor-porphyrin-acceptor triads have been synthesized using a versatile Suzuki-coupling route. This synthetic strategy allows the powerful donor tetraalkylphenylenediamine (TAPD) to be introduced into tetraarylporphyrin-based triads without protection. The thermodynamics and kinetics of electron transfer in the new triads are compared with a previously reported octaalkyldiphenyl-porphyrin triad exhibiting a long-lived spin-polarized charge separate state (CSS), from theoretical and experimental perspectives, in both fluid solution and in a frozen solvent glass. We show that the less favorable oxidation potential of the tetraaryl-porphyrin core can be offset by using C60 , as a better electron-acceptor than triptycenenaphthoquinone (TNQ). The C60 -porphyrin-TAPD triad gives a spin-polarized charge-separated state that can be observed by EPR-spectroscopy, with a mean lifetime of 16 ms at 10 K, which is longer than in the previously reported TNQ-porphyrin-TAPD triad, following the predicted trend from calculated charge-recombination rates.

Environment-induced anisotropy and sensitivity of the radical pair mechanism in the avian compass

Several experiments over the years have shown that the earth's magnetic field is essential for orientation in birds' migration. The most promising explanation for this orientation is the photo-stimulated radical pair (RP) mechanism. In order to define a reference frame for the orientation task radicals must have an intrinsic anisotropy. We show that this kind of anisotropy and consequently the entanglement in the model are not necessary for the proper functioning of the compass. Classically correlated initial conditions for the RP, subjected to a fast decoherence process, are able to provide the anisotropy required. Even a dephasing environment can provide the necessary frame for the compass to work and also implies fast decay of any quantum correlation in the system without damaging the orientation ability. This fact significantly expands the range of applicability of the RP mechanism providing more elements for experimental search.

Photoactivated biological processes as quantum measurements

We outline a framework for describing photoactivated biological reactions as generalized quantum measurements of external fields, for which the biological system takes on the role of a quantum meter. By using general arguments regarding the Hamiltonian that describes the measurement interaction, we identify the cases where it is essential for a complex chemical or biological system to exhibit nonequilibrium quantum coherent dynamics in order to achieve the requisite functionality. We illustrate the analysis by considering measurement of the solar radiation field in photosynthesis and measurement of the earth's magnetic field in avian magnetoreception.

Probing a chemical compass: novel variants of low-frequency reaction yield detected magnetic resonance

We present a study of a carotenoid-porphyrin-fullerene triad previously shown to function as a chemical compass: the photogenerated carotenoid-fullerene radical pair recombines at a rate sensitive to the orientation of an applied magnetic field. To characterize the system we develop a time-resolved Low-Frequency Reaction Yield Detected Magnetic Resonance (tr-LF-RYDMR) technique; the effect of varying the relative orientation of applied static and 36 MHz oscillating magnetic fields is shown to be strongly dependent on the strength of the oscillating magnetic field. RYDMR is a diagnostic test for involvement of the radical pair mechanism in the magnetic field sensitivity of reaction rates or yields, and has previously been applied in animal behavioural experiments to verify the involvement of radical-pair-based intermediates in the magnetic compass sense of migratory birds. The spectroscopic selection rules governing RYDMR are well understood at microwave frequencies for which the so-called 'high-field approximation' is valid, but at lower frequencies different models are required. For example, the breakdown of the rotating frame approximation has recently been investigated, but less attention has so far been given to orientation effects. Here we gain physical insights into the interplay of the different magnetic interactions affecting low-frequency RYDMR experiments performed in the challenging regime in which static and oscillating applied magnetic fields as well as internal electron-nuclear hyperfine interactions are of comparable magnitude. Our observations aid the interpretation of existing RYDMR-based animal behavioural studies and will inform future applications of the technique to verify and characterize further the biological receptors involved in avian magnetoreception.

Sensitivity and entanglement in the avian chemical compass

The radical pair mechanism can help to explain avian orientation and navigation. Some evidence indicates that the intensity of external magnetic fields plays an important role in avian navigation. In this paper, using a two-stage model, we demonstrate that birds could reasonably detect the directions of geomagnetic fields and gradients of these fields using a yield-based chemical compass that is sensitive enough for navigation. Also, we find that the lifetime of entanglement in this proposed compass is angle dependent and long enough to allow adequate electron transfer between molecules.

Effect of radio frequency fields on the radical pair magnetoreception model

Although the radical pair (RP) model is widely accepted for birds' orientation, the physical mechanism of it is still not fully understood. In this paper we consider the RP model in the total angular-momentum representation and clearly show a detailed mechanism for orientation. When only the vertical hyperfine (HF) coupling component is considered, analytical expressions of singlet yield angular profiles are obtained with and without considering the radio frequency field, and when the horizontal HF coupling components are considered, a numerical calculation of the singlet yield is given. Based on these analytical and numerical results we present a detailed account of the following issues: how the HF coupling induces the singlet-triplet conversion; why the vertical radio frequency field can disorient the birds, while the parallel one cannot; and why the birds are able to "train" to different field strengths. Finally, we consider a multinuclei RP model.

Retrodictive derivation of the radical-ion-pair master equation and Monte Carlo simulation with single-molecule quantum trajectories

Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.

Sensing magnetic directions in birds: radical pair processes involving cryptochrome

Birds can use the geomagnetic field for compass orientation. Behavioral experiments, mostly with migrating passerines, revealed three characteristics of the avian magnetic compass: (1) it works spontaneously only in a narrow functional window around the intensity of the ambient magnetic field, but can adapt to other intensities, (2) it is an “inclination compass”, not based on the polarity of the magnetic field, but the axial course of the field lines, and (3) it requires short-wavelength light from UV to 565 nm Green. The Radical Pair-Model of magnetoreception can explain these properties by proposing spin-chemical processes in photopigments as underlying mechanism. Applying radio frequency fields, a diagnostic tool for radical pair processes, supports an involvement of a radical pair mechanism in avian magnetoreception: added to the geomagnetic field, they disrupted orientation, presumably by interfering with the receptive processes. Cryptochromes have been suggested as receptor molecules. Cry1a is found in the eyes of birds, where it is located at the membranes of the disks in the outer segments of the UV-cones in chickens and robins. Immuno-histochemical studies show that it is activated by the wavelengths of light that allow magnetic compass orientation in birds.

Approaches to measuring entanglement in chemical magnetometers

Chemical magnetometers are radical pair systems such as solutions of pyrene and N,N-dimethylaniline (Py–DMA) that show magnetic field effects in their spin dynamics and their fluorescence. We investigate the existence and decay of quantum entanglement in free geminate Py–DMA radical pairs and discuss how entanglement can be assessed in these systems. We provide an entanglement witness and propose possible observables for experimentally estimating entanglement in radical pair systems with isotropic hyperfine couplings. As an application, we analyze how the field dependence of the entanglement lifetime in Py–DMA could in principle be used for magnetometry and illustrate the propagation of measurement errors in this approach.

Chemical compass model for avian magnetoreception as a quantum coherent device

It is known that more than 50 species use the Earth's magnetic field for orientation and navigation. Intensive studies, particularly behavior experiments with birds, provide support for a chemical compass based on magnetically sensitive free radical reactions as a source of this sense. However, the fundamental question of how quantum coherence plays an essential role in such a chemical compass model of avian magnetoreception yet remains controversial. Here, we show that the essence of the chemical compass model can be understood in analogy to a quantum interferometer exploiting global quantum coherence rather than any subsystem coherence. Within the framework of quantum metrology, we quantify global quantum coherence and correlate it with the function of chemical magnetoreception. Our results allow us to understand and predict how various factors can affect the performance of a chemical compass from the unique perspective of quantum coherence assisted metrology. This represents a crucial step to affirm a direct connection between quantum coherence and the function of a chemical compass.

Estimating the hyperfine coupling parameters of the avian compass by comprehensively considering the available experimental results

Migratory birds can utilize the geomagnetic field for orientation and navigation through a widely accepted radical-pair mechanism. Although many theoretical works have been done, the available experimental results have not been fully considered, especially the temporary disorientation induced by the field which is increased by 30% of the geomagnetic field and the disorientation of the very weak resonant field of 15 nT. In this paper, we consider the monotonicity of the singlet yield angular profile as the prerequisite of direction sensitivity, and find that for some optimal values of the hyperfine coupling parameters (that is, the order of 10^{-7}∼10^{-6} meV) the experimental results available so far can be satisfied. We also investigate the effects of two decoherence environments and demonstrate that, in order to satisfy the available experimental results, the decoherence rate should be lower than the recombination rate. Finally, we investigate the effects of the fluctuating magnetic noises and find that the vertical noise destroys the monotonicity of the profile completely, but the parallel noise preserves the monotonicity perfectly and even can enhance the direction sensitivity.

Magnetoreception: activated cryptochrome 1a concurs with magnetic orientation in birds

The radical pair model proposes that the avian magnetic compass is based on radical pair processes in the eye, with cryptochrome, a flavoprotein, suggested as receptor molecule. Cryptochrome 1a (Cry1a) is localized at the discs of the outer segments of the UV/violet cones of European robins and chickens. Here, we show the activation characteristics of a bird cryptochrome in vivo under natural conditions. We exposed chickens for 30 min to different light regimes and analysed the amount of Cry1a labelled with an antiserum against an epitope at the C-terminus of this protein. The staining after exposure to sunlight and to darkness indicated that the antiserum labels only an illuminated, activated form of Cry1a. Exposure to narrow-bandwidth lights of various wavelengths revealed activated Cry1a at UV, blue and turquoise light. With green and yellow, the amount of activated Cry1a was reduced, and with red, as in the dark, no activated Cry1a was labelled. Activated Cry1a is thus found at all those wavelengths at which birds can orient using their magnetic inclination compass, supporting the role of Cry1a as receptor molecule. The observation that activated Cry1a and well-oriented behaviour occur at 565 nm green light, a wavelength not absorbed by the fully oxidized form of cryptochrome, suggests that a state other than the previously suggested Trp^•/FAD^• radical pair formed during photoreduction is crucial for detecting magnetic directions.

Quantum coherence and entanglement in the avian compass

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.

Avian magnetic compass can be tuned to anomalously low magnetic intensities

The avian magnetic compass works in a fairly narrow functional window around the intensity of the local geomagnetic field, but adjusts to intensities outside this range when birds experience these new intensities for a certain time. In the past, the geomagnetic field has often been much weaker than at present. To find out whether birds can obtain directional information from a weak magnetic field, we studied spontaneous orientation preferences of migratory robins in a 4 µT field (i.e. a field of less than 10 per cent of the local intensity of 47 µT). Birds can adjust to this low intensity: they turned out to be disoriented under 4 µT after a pre-exposure time of 8 h to 4 µT, but were able to orient in this field after a total exposure time of 17 h. This demonstrates a considerable plasticity of the avian magnetic compass. Orientation in the 4 µT field was not affected by local anaesthesia of the upper beak, but was disrupted by a radiofrequency magnetic field of 1.315 MHz, 480 nT, suggesting that a radical-pair mechanism still provides the directional information in the low magnetic field. This is in agreement with the idea that the avian magnetic compass may have developed already in the Mesozoic in the common ancestor of modern birds.

Magnetoreception in laboratory mice: sensitivity to extremely low-frequency fields exceeds 33 nT at 30 Hz

Magnetoreception in the animal kingdom has focused primarily on behavioural responses to the static geomagnetic field and the slow changes in its magnitude and direction as animals navigate/migrate. There has been relatively little attention given to the possibility that weak extremely low-frequency magnetic fields (wELFMF) may affect animal behaviour. Previously, we showed that changes in nociception under an ambient magnetic field-shielded environment may be a good alternative biological endpoint to orientation measurements for investigations into magnetoreception. Here we show that nociception in mice is altered by a 30 Hz field with a peak amplitude more than 1000 times weaker than the static component of the geomagnetic field. When mice are exposed to an ambient magnetic field-shielded environment 1 h a day for five consecutive days, a strong analgesic (i.e. antinociception) response is induced by day 5. Introduction of a static field with an average magnitude of 44 µT (spatial variability of ±3 µT) marginally affects this response, whereas introduction of a 30 Hz time-varying field as weak as 33 nT has a strong effect, reducing the analgesic effect by 60 per cent. Such sensitivity is surprisingly high. Any purported detection mechanisms being considered will need to explain effects at such wELFMF.