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Controlling quantum spins using electric rather than magnetic fields promises significant architectural advantages for developing quantum technologies. In this context, spins in molecular nanomagnets offer tunability of spin-electric couplings (SEC) by rational chemical design. Here we demonstrate systematic control of SECs in a family of Mn(II)-containing molecules via chemical engineering. The trigonal bipyramidal (tbp) molecular structure with C3 symmetry leads to a significant molecular electric dipole moment that is directly connected to its magnetic anisotropy. The interplay between these two features gives rise to significant experimentally observed SECs, which can be rationalised by wavefunction theoretical calculations. Our findings guide strategies for the development of electrically controllable molecular spin qubits for quantum technologies., Comment: 8 pages, 3 figures, 1 table

The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Protocols employing redundancy over multiple physical qubits to encode a single error-protected logical qubit are theoretically effective, but imply a large resource overhead. Alternative, more hardware-efficient, approaches seek to deploy higher-dimensional quantum systems known as qudits. Recently, proposals have emerged for exploiting high-spin magnetic nuclei coupled to condensed matter electron spin qubits to implement fault-tolerant memories. Here, we explore experimentally the simplest of these proposals, a logical qubit encoded on the four states of a I=3/2 nuclear spin hyperfine-coupled to a S=1/2 electron spin qubit; the encoding protects against the dominant decoherence mechanism in such systems, fluctuations of the quantizing magnetic field. We implement the encoding using electron-nuclear double resonance within a subspace of the spin levels in an ensemble of highly coherent manganese defects in zinc oxide. We explore the dynamics of the encoded state both under a controlled application of the fluctuation and under natural decoherence processes. Our results confirm the potential of these proposals for practical, implementable, fault tolerant quantum memories.

The sub-nanometer distance between tip and sample in a scanning tunneling microscope (STM) enables the application of very large electric fields with a strength as high as ~ 1 GV/m. This has allowed for efficient electrical driving of Rabi oscillations of a single spin on a surface at a moderate radio-frequency (RF) voltage of the order of tens of millivolts. Here, we demonstrate the creation of dressed states of a single electron spin localized in the STM tunnel junction by using resonant RF driving voltages. The read-out of these dressed states was achieved all-electrical by a weakly coupled probe spin. Our work highlights the strength of the atomic-scale geometry inherent to the STM that facilitates creation and control of dressed states, which are promising for a design of atomically well-defined single spin quantum devices on surfaces.

We report the development of a continuous-wave and pulsed X-band electron spin resonance (ESR) spectrometer for the study of spins on ordered surfaces down to cryogenic temperatures. The spectrometer operates in ultra-high vacuum and utilizes a half-wavelength microstrip line resonator realized using epitaxially grown copper films on single crystal Al$_2$O$_3$ substrates. The one-dimensional microstrip line resonator exhibits a quality factor of more than 200 at room temperature, close to the upper limit determined by radiation losses. The surface characterizations of the copper strip of the resonator by atomic force microscope, low-energy electron diffraction, and scanning tunneling microscope show that the surface is atomically clean, flat, and single crystalline. Measuring the ESR spectrum at 15 K from a few nm thick molecular film of YPc$_2$, we find a continuous-wave ESR sensitivity of $2.6 \cdot 10^{11}~\text{spins}/\text{G} \cdot \text{Hz}^{1/2}$ indicating that a signal-to-noise ratio of $3.9~\text{G} \cdot \text{Hz}^{1/2}$ is expected from a monolayer of YPc$_2$ molecules. Advanced pulsed ESR experimental capabilities including dynamical decoupling and electron-nuclear double resonance are demonstrated using free radicals diluted in a glassy matrix., Comment: 14 pages, 7 figures

Bulk bismuth has a complex Landau spectrum. The small effective masses and the large g-factors are anisotropic. The chemical potential drifts at high magnetic fields. Moreover, twin boundaries further complexify the interpretation of the data by producing extra anomalies in the extreme quantum limit. Here, we present a study of angle dependence of magnetoresistance up to 65 T in bismuth complemented with Nernst, ultrasound, and magneto-optic data. All observed anomalies can be explained in a single-particle picture of a sample consisting of two twinned crystals tilted by 108$^{\circ}$ and with two adjacent crystals keeping their own chemical potentials despite a shift between chemical potentials as large as 68 meV at 65 T. This implies an energy barrier between adjacent twinned crystals reminiscent of a metal-semiconductor Schottky barrier or a p-n junction. We argue that this barrier is built by accumulating charge carriers of opposite signs across a twin boundary., Comment: 11 pages, 7 figures

The implementation of error correction protocols is a central challenge in the development of practical quantum information technologies. Recently, multi-level quantum resources such as harmonic oscillators and qudits have attracted interest in this context because they offer the possibility of additional Hilbert space dimensions in a spatially compact way. Here we propose a quantum memory, implemented on a spin-7/2 nucleus hyperfine-coupled to an electron spin-1/2 qubit, which provides first order $X$, $Y$ and $Z$ error correction using significantly fewer quantum resources than the equivalently effective qubit-based protocols. Our encoding may be efficiently implemented in existing experimentally realised molecular electron-nuclear quantum spin systems. The strategy can be extended to higher-order error protection on higher-spin nuclei.

For the past three decades, nanoscience has widely affected many areas in physics, chemistry, and engineering, and has led to numerous fundamental discoveries as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds a burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this manuscript according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system such as charge, spin, mechanical motion, and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations., Comment: 34 pages, 6 figures, 2 boxes

Alkali-doped fullerides are strongly correlated organic superconductors that exhibit high transition temperatures, exceptionally large critical magnetic fields and a number of other unusual properties. The proximity to a Mott insulating phase is thought to be a crucial ingredient of the underlying physics, and may also affect precursors of superconductivity in the normal state above T$_\text{c}$. We report on the observation of a sizeable magneto-thermoelectric (Nernst) effect in the normal state of K$_3$C$_{60}$, which displays the characteristics of superconducting fluctuations. The anomalous Nernst effect emerges from an ordinary quasiparticle background below a temperature of 80K, far above T$_\text{c}$ = 20K. At the lowest fields and close to T$_\text{c}$, the scaling of the effect is captured by a model based on Gaussian fluctuations. The temperature up to which we observe fluctuations is exceptionally high for a three-dimensional isotropic system, where fluctuation effects are usually suppressed.

Since their discovery three decades ago it has emerged that the physics of high-$T_\mathrm{c}$ cuprate superconductors is characterised by multiple temperature scales, and a phenomenology that deviates significantly from the conventional paradigm of superconductivity. Below the "pseudogap" temperature, $T^*$, a range of experiments indicate a reduction in the density of states. Lower in temperature, $T_\mathrm{c}$ marks the onset of a bulk zero-resistance state. Intermediate between these, numerous other temperature boundaries and cross-overs have been identified, often postulated to be associated with fluctuations of some kind. However, for the most part there is little consensus either over their definitions or the physical mechanisms at play. One of these temperature scales is the Nernst onset temperature, $T_\mathrm{onset}$, below which thermoelectric phenomena characteristic of superconductivity are observed. Depending on the material, the difference between $T_\mathrm{onset}$ and $T_\mathrm{c}$ ranges from almost nothing to over 100K. In this paper, we identify $T_\mathrm{onset}$ from published experimental data according to a consistent definition; this reveals a remarkable consistency of behaviour across the whole high-$T_\mathrm{c}$ family, despite the appreciable variations in other parameters. Our analysis suggests that in the cuprates there is an inherent limit to $T_\mathrm{c} \sim 135$K. We compare this behaviour with other strongly-correlated superconductors and propose a unified picture of superconducting fluctuations close to the Mott state.

Electrical control of spins at the nanoscale offers significant architectural advantages in spintronics, because electric fields can be confined over shorter length scales than magnetic fields. Thus, recent demonstrations of electric-field (E-field) sensitivities in molecular spin materials are tantalising, raising the viability of the quantum analogues of macroscopic magneto-electric devices.However, the E-field sensitivities reported so far are rather weak, prompting the question of how to design molecules with stronger spin-electric couplings. Here we show that one path is to identify an energy scale in the spin spectrum that is associated with a structural degree of freedom with a significant electrical polarisability. We study an example of a molecular nanomagnet in which a small structural distortion establishes clock transitions (i.e. transitions whose energy is to first order independent of magnetic field) in the spin spectrum; the fact that this distortion is associated with an electric dipole allows us to control the clock transition energy to an unprecedented degree. We demonstrate coherent electrical control of the quantum spin state and exploit it to manipulate independently the two magnetically-identical but inversion-related molecules in the unit cell of the crystal. Our findings pave the way for the use of molecular spins in quantum technologies and spintronics.

We show that strong electron-electron interactions in cavity-coupled quantum materials can enable collectively enhanced light-matter interactions with ultrastrong effective coupling strengths. As a paradigmatic example we consider a Fermi-Hubbard model coupled to a single-mode cavity and find that resonant electron-cavity interactions result in the formation of a quasi-continuum of polariton branches. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and scales with $g_{\text{eff}}\propto\sqrt{2L}$, where $L$ is the number of electronic sites, and the maximal achievable value for $g_{\text{eff}}$ is determined by the volume of the unit cell of the crystal. We find that $g_{\text{eff}}$ for existing quantum materials can by far exceed the width of the first excited Hubbard band. This effect can be experimentally observed via measurements of the optical conductivity and does not require ultra-strong coupling on the single-electron level. Quantum correlations in the electronic ground state as well as the microscopic nature of the light-matter interaction enhance the collective light-matter interaction compared to an ensemble of independent two-level atoms interacting with a cavity mode., Comment: 11 pages, 4 figures. arXiv admin note: text overlap with arXiv:1806.06752

We show that the macroscopic magnetic and electronic properties of strongly correlated electron systems can be manipulated by coupling them to a cavity mode. As a paradigmatic example we consider the Fermi-Hubbard model and find that the electron-cavity coupling enhances the magnetic interaction between the electron spins in the ground-state manifold. At half filling this effect can be observed by a change in the magnetic susceptibility. At less than half filling, the cavity introduces a next-nearest neighbour hopping and mediates a long-range electron-electron interaction between distant sites. We study the ground state properties with Tensor Network methods and find that the cavity coupling can induce a new phase characterized by a momentum-space pairing effect for electrons., Comment: 10 pages, 5 figures

Coherent control of individual molecular spins in nano-devices is a pivotal prerequisite for fulfilling the potential promised by molecular spintronics. By applying electric field pulses during time-resolved electron spin resonance measurements, we measure the sensitivity of the spin in several antiferromagnetic molecular nanomagnets to external electric fields. We find a linear electric field dependence of the spin states in Cr$_7$Mn, an antiferromagnetic ring with a ground-state spin of $S=1$, and in a frustrated Cu$_3$ triangle, both with coefficients of about $2~\mathrm{rad}\, \mathrm{s}^{-1} / \mathrm{V} \mathrm{m}^{-1}$. Conversely, the antiferromagnetic ring Cr$_7$Ni, isomorphic with Cr$_7$Mn but with $S=1/2$, does not exhibit a detectable effect. We propose that the spin-electric field coupling may be used for selectively controlling individual molecules embedded in nanodevices., Comment: 6 pages, 3 figures

We report quantum interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry-Perot interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry-Perot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.

Proposals for systems embodying condensed matter spin qubits cover a very wide range of length scales, from atomic defects in semiconductors all the way to micron-sized lithographically-defined structures. Intermediate scale molecular components exhibit advantages of both limits: like atomic defects, large numbers of identical components can be fabricated; as for lithographically defined structures, each component can be tailored to optimize properties such as quantum coherence. Here, we demonstrate what is perhaps the most potent advantage of molecular spin qubits, the scalability of quantum information processing structures using bottom-up chemical self-assembly. Using Cr7Ni spin qubit building blocks, we have constructed several families of two-qubit molecular structures with a range of linking strategies. For each family, long coherence times are preserved, and we demonstrate control over the inter-qubit quantum interactions that can be used to mediate two-qubit quantum gates., Comment: Manuscript: 20 pages. Supplementary Information: 16 pages. npj Quantum Information, in press

We report room-temperature Coulomb blockade in a single layer graphene three-terminal single-electron transistor (SET) fabricated using feedback-controlled electroburning. The small separation between the side gate electrode and the graphene quantum dot results in a gate coupling up to 3 times larger compared to the value found for the back gate electrode. This allows for an effective tuning between the conductive and Coulomb blocked state using a small side gate voltage of about 1V. The technique can potentially be used in the future to fabricate all-graphene based room temperature single-electron transistors or three terminal single molecule transistors with enhanced gate coupling.

Surface acoustic wave (SAW) devices based on thin films of ZnO are a well established technology. However, SAW devices on bulk ZnO crystals are not practical at room temperature due to the significant damping caused by finite electrical conductivity of the crystal. Here, by operating at low temperatures, we demonstrate effective SAW devices on the (0001) surface of bulk ZnO crystals, including a delay line operating at SAW wavelengths of {\lambda} = 4 and 6 {\mu}m and a one-port resonator at a wavelength of {\lambda} = 1.6 {\mu}m. We find that the SAW velocity is temperature dependent, reaching $v \simeq 2.68$ km/s at 10mK. Our resonator reaches a maximum quality factor of $Q_i \simeq 1.5\times 10^5$, demonstrating that bulk ZnO is highly viable for low temperature SAW applications. The performance of the devices is strongly correlated with the bulk conductivity, which quenches SAW transmission above about 200 K., Comment: 4 pages, 3 figures

Among the factors determining the quantum coherence of the spin in molecular magnets is the presence and the nature of nuclear spins in the molecule. We have explored modifying the nuclear spin environment in Cr$_7$Ni-based molecular nanomagnets by replacing hydrogen atoms with deuterium or the halogen atoms, fluorine or chlorine. We find that the spin coherence, studied at low temperatures by pulsed electron spin resonance, is modified by a range of factors, including nuclear spin and magnetic moment, changes in dynamics owing to nuclear mass, and molecular morphology changes., Comment: 8 pages, 5 figures, including supplemental material

Unconventional superconductivity typically occurs in materials in which a small change of a parameter such as bandwidth or doping leads to antiferromagnetic or Mott insulating phases. As such competing phases are approached, the properties of the superconductor often become increasingly exotic. For example, in organic superconductors and underdoped high-$T_\mathrm{c}$ cuprate superconductors a fluctuating superconducting state persists to temperatures significantly above $T_\mathrm{c}$. By studying alloys of quasi-two-dimensional organic molecular metals in the $\kappa$-(BEDT-TTF)$_2$X family, we reveal how the Nernst effect, a sensitive probe of superconducting phase fluctuations, evolves in the regime of extreme Mott criticality. We find strong evidence that, as the phase diagram is traversed through superconductivity towards the Mott state, the temperature scale for superconducting fluctuations increases dramatically, eventually approaching the temperature at which quasiparticles become identifiable at all., Comment: 19 pages, 4 figures, 1 table

High-spin paramagnetic manganese defects in polar piezoelectric zinc oxide exhibit a simple almost axial anisotropy and phase coherence times of the order of a millisecond at low temperatures. The anisotropy energy is tunable using an externally applied electric field. This can be used to control electrically the phase of spin superpositions and to drive spin transitions with resonant microwave electric fields.

We demonstrate the strong coupling between an electron spin ensemble and a three-dimensional cavity in a reflection geometry. We also find that an anticrossing in the cavity/spin spectrum can be observed under conditions that the collective coupling strength $g_c$ is smaller than the spin linewidth $\gamma_s$ or the cavity linewidth. We identify a ratio of $g_c$ to $\gamma_s$ ($g_c/\gamma_s >$ 0.64) as a condition to observe a splitting in the cavity frequency. Finally, we confirm that $g_c$ scales with $\sqrt{N}$, where $N$ is the number of polarized spins., Comment: To appear in Appl. Phys. Lett

Electron spin qubits in molecular systems offer high reproducibility and the ability to self assemble into larger architectures. However, interactions between neighbouring qubits are 'always-on' and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both controllably turn on/off dipolar interactions between neighbouring spins and benefit from the long nuclear spin decoherence times (T2n). We transfer qubit states between the electron and 15N nuclear spin in 15N@C60 with a two-way process fidelity of 88%, using a series of tuned microwave and radiofrequency pulses and measure a nuclear spin coherence lifetime of over 100 ms., Comment: 5 pages, 3 figures with supplementary material (8 pages)

We present an electron paramagnetic resonance (EPR) study of ErSc2N@C80 fullerene in which there are two Er3+ sites corresponding to two different configurations of the ErSc2N cluster inside the C80 cage. For each configuration, the EPR spectrum is characterized by a strong anisotropy of the g factors (gx,y = 2.9, gz = 13.0 and gx,y = 5.3, gz = 10.9). Illumination within the cage absorption range (<600 nm) induces a rearrangement of the ErSc2N cluster inside the cage. We follow the temporal dependence of this rearrangement phenomenologically under various conditions., Comment: 7 pages, 7 figures

Endohedral fullerenes encapsulating a spin-active atom or ion within a carbon cage offer a route to self-assembled arrays such as spin chains. In the case of metallofullerenes the charge transfer between the atom and the fullerene cage has been thought to limit the electron spin phase coherence time (T2) to the order of a few microseconds. We study electron spin relaxation in several species of metallofullerene as a function of temperature and solvent environment, yielding a maximum T2 in deuterated o-terphenyl greater than 200 microseconds for Y, Sc and La@C82. The mechanisms governing relaxation (T1, T2) arise from metal-cage vibrational modes, spin-orbit coupling and the nuclear spin environment. The T2 times are over 2 orders of magnitude longer than previously reported and consequently make metallofullerenes of interest in areas such as spin-labelling, spintronics and quantum computing., Comment: 5 pages, 4 figures

We analyze pulsar fluxes at 1400 MHz ($S_{1400}$) and distances ($d$) extracted from the Parkes Multibeam Survey. Under the assumption that distribution of pulsar luminosities is distance-independent, we find that either (a) pulsar fluxes diminish with distance according to a non-standard power law, due, we suggest, to the presence of a component with $S_{1400} \propto 1/d$, or (b) that there are very significant (i.e. order of magnitude) errors in the dispersion-measure method for estimating pulsar distances. The former conclusion (a) supports a model for pulsar emission that has also successfully explained the frequency spectrum of the Crab and 8 other pulsars over 16 orders of magnitude of frequency, whilst alternative (b) would necessitate a radical re-evaluation of both the dispersion-measure method and current ideas about the distribution of free electrons within our Galaxy.

Molecular nanostructures may constitute the fabric of future quantum technologies, if their degrees of freedom can be fully harnessed. Ideally one might use nuclear spins as low-decoherence qubits and optical excitations for fast controllable interactions. Here, we present a method for entangling two nuclear spins through their mutual coupling to a transient optically-excited electron spin, and investigate its feasibility through density functional theory and experiments on a test molecule. From our calculations we identify the specific molecular properties that permit high entangling power gates under simple optical and microwave pulses; synthesis of such molecules is possible with established techniques.

There is a fundamental difference between the classical expression for the retarded electromagnetic potential and the corresponding retarded solution of the wave equation that governs the electromagnetic field. While the boundary contribution to the retarded solution for the {\em potential} can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation governing the {\em field} may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a source whose distribution pattern both rotates and travels faster than light {\em in vacuo}, as realized in recent experiments, the boundary term in the retarded solution governing the field is by a factor of the order of $R^{1/2}$ {\em larger} than the source term of this solution in the limit that the distance $R$ of the boundary from the source tends to infinity. This result is consistent with the prediction of the retarded potential that part of the radiation field generated by a rotating superluminal source decays as $R^{-1/2}$, instead of $R^{-1}$, a prediction that is confirmed experimentally. More importantly, it pinpoints the reason why an argument based on a solution of the wave equation governing the field in which the boundary term is neglected (such as appears in the published literature) misses the nonspherical decay of the field.

Electron and nuclear spins have good coherence times and an ensemble of spins is a promising candidate for a quantum memory. By employing holographic techniques via field gradients a single ensemble may be used to store many bits of information. Here we present a coherent memory using a pulsed magnetic field gradient, and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds., Comment: Corrected reference and typos

Measurement devices could benefit from entangled correlations to yield a measurement sensitivity approaching the physical Heisenberg limit. Building upon previous magnetometric work using pseudo-entangled spin states in solution-state NMR, we present two conceptual advancements to better prepare and interpret the pseudo-entanglement resource as well as the use of a 13-spin cat state to measure the local magnetic field with a sensitivity beyond the standard quantum limit., Comment: 6 pages, 5 figures; v2: corrected figure 3, expanded conclusion, simplified explanation of equation 2; v3: accepted version

Observational data imply the presence of superluminal electric currents in pulsar magnetospheres. Such sources are not inconsistent with special relativity; they have already been created in the laboratory. Here we describe the distinctive features of the radiation beam that is generated by a rotating superluminal source and show that (i) it consists of subbeams that are narrower the farther the observer is from the source: subbeams whose intensities decay as 1/R instead of 1/R^2 with distance (R), (ii) the fields of its subbeams are characterized by three concurrent polarization modes: two modes that are 'orthogonal' and a third mode whose position angle swings across the subbeam bridging those of the other two, (iii) its overall beam consists of an incoherent superposition of such coherent subbeams and has an intensity profile that reflects the azimuthal distribution of the contributing part of the source (the part of the source that approaches the observer with the speed of light and zero acceleration), (iv) its spectrum (the superluminal counterpart of synchrotron spectrum) is broader than that of any other known emission and entails oscillations whose spacings and amplitudes respectively increase and decrease algebraically with increasing frequency, and (v) the degree of its mean polarization and the fraction of its linear polarization both increase with frequency beyond the frequency for which the observer falls within the Fresnel zone. We also compare these features with those of the radiation received from the Crab pulsar., Comment: 8 pages, 8 figures

The concept of entanglement, in which coherent quantum states become inextricably correlated, has evolved from one of the most startling and controversial outcomes of quantum mechanics to the enabling principle of emerging technologies such as quantum computation and quantum sensors. The use of entangled particles in measurement permits the transcendence of the standard quantum limit in sensitivity, which scales as N^1/2 for N particles, to the Heisenberg limit, which scales as N. This approach has been applied to optical interferometry using entangled photons and spin pairs for the measurement of magnetic fields and improvements on atomic clocks. Here, we demonstrate experimentally an 9.4-fold increase in sensitivity to an external magnetic field of a 10-spin entangled state, compared with an isolated spin, using nuclear spins in a highly symmetric molecule. This approach scales in a favourable way compared to systems where qubit loss is prevalent, and paves the way for enhanced precision in magnetic field sensing, Comment: 5 pages, 3 figures

There is a fundamental difference between the classical expression for the retarded electromagnetic potential and the corresponding retarded solution of the wave equation that governs the electromagnetic field. While the boundary contribution to the retarded solution for the potential can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation governing the field may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a source whose distribution pattern rotates superluminally (i.e., faster than the speed of light in vacuo), the boundary term in the retarded solution governing the field is by a factor of the order of R^(1/2) larger than the source term of this solution in the limit where the distance R of the boundary from the source tends to infinity. This result is consistent with the prediction of the retarded potential that the radiation field generated by a rotating superluminal source decays as 1/R^(1/2), instead of 1/R. It also explains why an argument based on the solution of the wave equation governing the field in which the boundary term is neglected, such as Hannay presents in his Comment, misses the nonspherical decay of the field.

The fact that the formula used by Hannay in his Comment is "from a standard text on electrodynamics" neither warrants that it is universally applicable, nor that it is unequivocally correct. We have explicitly shown [J. Opt. Soc. Am. A 25, 543 (2008)] that,since it does not include the boundary contribution toward the value of the field, the formula in question is not applicable when the source is extended and has a distribution pattern that rotates faster than light in vacuo. The neglected boundary term in the retarded solution to the wave equation governing the electromagnetic field forms the basis of diffraction theory. If this term were identically zero, for the reasons given by Hannay, the iffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible. If this term were identically zero, for the reasons given by Hannay, the diffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible.

The transfer of information between different physical forms is a central theme in communication and computation, for example between processing entities and memory. Nowhere is this more crucial than in quantum computation, where great effort must be taken to protect the integrity of a fragile quantum bit. Nuclear spins are known to benefit from long coherence times compared to electron spins, but are slow to manipulate and suffer from weak thermal polarisation. A powerful model for quantum computation is thus one in which electron spins are used for processing and readout while nuclear spins are used for storage. Here we demonstrate the coherent transfer of a superposition state in an electron spin 'processing' qubit to a nuclear spin 'memory' qubit, using a combination of microwave and radiofrequency pulses applied to 31P donors in an isotopically pure 28Si crystal. The electron spin state can be stored in the nuclear spin on a timescale that is long compared with the electron decoherence time and then coherently transferred back to the electron spin, thus demonstrating the 31P nuclear spin as a solid-state quantum memory. The overall store/readout fidelity is about 90%, attributed to systematic imperfections in radiofrequency pulses which can be improved through the use of composite pulses. We apply dynamic decoupling to protect the nuclear spin quantum memory element from sources of decoherence. The coherence lifetime of the quantum memory element is found to exceed one second at 5.5K., Comment: v2: Tomography added and storage of general initial states

Systems exhibiting both spin and orbital degrees of freedom, of which Er3+ is one, can offer mechanisms for manipulating and measuring spin states via optical excitations. Motivated by the possibility of observing photoluminescence and electron paramagnetic resonance from the same species located within a fullerene molecule, we initiated an EPR study of Er3+ in ErSc2N@C80. Two orientations of the ErSc2N rotor within the C80 fullerene are observed in EPR, consistent with earlier studies using photoluminescence excitation (PLE) spectroscopy. For some crystal field orientations, electron spin relaxation is driven by an Orbach process via the first excited electronic state of the 4I_15/2 multiplet. We observe a change in the relative populations of the two ErSc2N configurations upon the application of 532 nm illuminations, and are thus able to switch the majority cage symmetry. This photoisomerisation, observable by both EPR and PLE, is metastable, lasting many hours at 20 K., Comment: 4 pages, 4 figures

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (mu) that is by a factor of order mu^(2/3) slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: it, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: the focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density proportional to mu^alpha) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4.

We calculate the gradient of the radiation field generated by a polarization current with a superluminally rotating distribution pattern and show that the absolute value of this gradient increases as R^(7/2) with distance R within the sharply focused subbeams constituting the overall radiation beam. This result not only supports the earlier finding that the azimuthal and polar widths of these subbeams narrow with distance (as R^(-3) and R^(-1), respectively), but also implies that the boundary contribution to the solution of the wave equation governing the radiation field does not always vanish in the limit where the boundary tends to infinity. There is a fundamental difference between the classical expressions for the retarded potential and field: while the boundary contribution for the potential can always be made zero via a gauge transformation preserving the Lorenz condition, that for the field may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a rotating superluminal source, however, the boundary term in the retarded solution for the field is by a factor of order R^(1/2) larger than the source term of this solution in the limit, which explains why an argument based on the solution of the wave equation governing the field that neglects the boundary term (such as that presented by J. H. Hannay) misses the nonspherical decay of the field. Given that the distribution of the radiation field of an accelerated superluminal source in the far zone is not known a priori, the only way to calculate the free-space radiation field of such sources is via the retarded solution for the potential. Finally, we apply these findings to pulsar observational data: the more distant a pulsar, the narrower and brighter its giant pulses should be.

By applying a new technique for dynamic nuclear polarization involving simultaneous excitation of electronic and nuclear transitions, we have enhanced the nuclear polarization of the nitrogen nuclei in 15N@C60 by a factor of 1000 at a fixed temperature of 3 K and a magnetic field of 8.6 T, more than twice the maximum enhancement reported to date. This methodology will allow the initialization of the nuclear qubit in schemes exploiting N@C60 molecules as components of a quantum information processing device., Comment: 9 pages, 5 figures

We have studied the interlayer resistivity of the prototypical quasi-two-dimensional organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ as a function of temperature, current and magnetic field, within the superconducting state. We find a region of non-zero resistivity whose properties are strongly dependent on magnetic field and current density. There is a crossover to non-Ohmic conduction below a temperature that coincides with the 2D vortex solid -- vortex liquid transition. We interpret the behaviour in terms of a model of current- and thermally-driven phase slips caused by the diffusive motion of the pancake vortices which are weakly-coupled in adjacent layers, giving rise to a finite interlayer resistance., Comment: Four pages, three figures