Temperature-scanned magnetic resonance and the evidence of two-way transfer of a nitrogen nuclear spin hyperfine interaction in coupled NV-N pairs in diamond

New method for the detection of magnetic resonance signals versus temperature is developed on the basis of the temperature dependence of the spin Hamiltonian parameters of the paramagnetic system under investigation. The implementation of this technique is demonstrated on the nitrogen-vacancy (NV) centers in diamonds. Single NV defects and their ensembles are suggested to be almost inertialess temperature sensors. The hyperfine structure of the ¹⁴N nitrogen nuclei of the nitrogen-vacancy center appears to be resolved in the hyperfine structure characteristic of the hyperfine interaction between NV and an N _s center (substitutional nitrogen impurity) in the optically detected magnetic resonance spectra of the molecular NV-N _s complex. Thus, we show that a direct evidence of the two-way transfer of a nitrogen nuclear spin hyperfine interaction in coupled NV-N _s pairs was observed. It is shown that more than 3-fold enhancement of the NV optically detected magnetic resonance signal can be achieved by using water as a collection optics medium.     

Nuclear spin induced collapse and revival shape of Rabi oscillations of a single electron spin in diamond

A collapse and revival shape of Rabi oscillations in an electron spin of a single nitrogen-vacancy centre has been observed in diamond at room temperature. Because of hyperfine interaction between the host ¹⁴N nuclear spin and the nitrogen-vacancy centre electron spin, different orientations of the ¹⁴N nuclear spins lead to a triplet splitting of the transition between ground state (m_s =0) and excited state (m_s =1). The manipulation of the single electron spin of nitrogen-vacancy centre is achieved by using a combination of selective microwave excitation and optical pumping at 532 nm. Microwaves can excite three transitions equally to induce three independent nutations and the shape of Rabi oscillations is a combination of the three nutations.     

Mechanism of “GSI oscillations” in electron capture by highly charged hydrogen-like atomic ions

We suggest a qualitative explanation of oscillations in electron capture decays of hydrogen-like ¹⁴⁰Pr and ¹⁴²Pm ions observed recently in an ion experimental storage ring (ESR) of Gesellschaft für Schwerionenforschung (GSI) mbH, Darmstadt, Germany. This explanation is based on the electron multiphoton Rabi oscillations between two Zeeman states of the hyperfine ground level with the total angular momentum F = 1/2. The Zeeman splitting is produced by a constant magnetic field in the ESR. Transitions between these states are produced by the second, sufficiently strong alternating magnetic field that approximates realistic fields in the GSI ESR. The Zeeman splitting amounts to only about 10^?5 eV. This allows explaining the observed quantum beats with the period 7 s.     

Rabi Oscillations of Paramagnetic Ions in Solids: Role of Electrostatic Interactions

We study the decay of Rabi oscillations of magnetically coupled impurity ions diluted in the solid. Electrostatic interactions between the ions treated as charged defects shift their g-factors and result in valuable correlations of their Larmor frequencies if the ions are close enough. We find an increase in the decay time of Rabi oscillations in comparison with the case of uncharged defects. The magnitude of the effect depends on the ratio between the impurity and the total defect concentrations, as well as on the type of the electron paramagnetic resonance line broadening mechanism (by random electric fields, electric field gradients, etc.). We present results in the arbitrary order of multipole expansion with respect to valence electron coordinates of the paramagnetic ion. Corresponding corrections to the decay times of Rabi oscillations of Nd³⁺ ions in CaWO₄ crystal are obtained.     

Rabi oscillations in two-level semiconductor systems

Rabi oscillations in coherent optical excitations in bulk GaAs and quantum dot two-level systems may be converted into deterministic photocurrents, with the impurities or dots providing the tag for each qubit. Here we perform a theoretical analysis of the damping of Rabi oscillations in two-level semiconductor systems. Present calculations, through optical Bloch equations on excitonic two-level In_xGa_1−xAs quantum-dot systems, are found in good agreement with the corresponding experimental data. Calculated results indicate that the nature underlying the dephasing mechanism associated to the damping of the measured Rabi oscillations, which has previously remained as an open question, may be associated with a field-dependent recombination rate related to the inhomogeneous broadening of the excitonic lines in the In_xGa_1−xAs two-level QD system.     

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).     

A theoretical study of pump–probe experiment in single-layer,bilayer and multilayer graphene

The pump–probe experiment is typically used to study relaxation phenomena in nonlinear optical systems. Here we use it as a tool to study the phenomenon of anomalous Rabi oscillations in graphene that was predicted recently in single-layer graphene. Unlike conventional Rabi oscillations, anomalous Rabi oscillations are unique to graphene (and possibly to surface states of topological insulators (TIs)), attributable to the pseudospin (conventional spin for TI) degree of freedom and Dirac-fermion character of the graphene system. A pump pulse of a finite duration long enough to contain a large number of cycles induces a current density that oscillates with the frequency of the pump pulse. The amplitude associated with these fast oscillations is seen to exhibit much slower oscillations with a frequency given by \({ 2 \omega ^2_{\mathrm {R}} }/{ \omega } \) – the anomalous Rabi frequency, where ω _R is the conventional Rabi frequency and ω is the frequency of the external pump field. This effect is easily probed by a probe pulse subsequent to the pump, where it manifests itself as periodic oscillations of the probe susceptibility as a function of pump duration at each probe frequency. Alternatively, it is also seen as an oscillatory function of the pump–probe delay with other variables remaining fixed. This period corresponds to the anomalous Rabi frequency. An analysis of the previously reported experimental data confirms the presence of anomalous Rabi oscillations in graphene.     

Transition dipole moment measurements for the ν2 band of NH3 with molecular beam laser Stark spectroscopy

Rabi oscillations were observed in the ASR(110), ΔM = 0 and ASQ(222), ΔM = 0 transitions of the ν₂ band of ¹⁴NH₃ in a molecular beam crossed by a CO₂ laser beam. The frequency (in terms of the laser field amplitude) of the oscillations was used to determine the transition dipole moment of the ν₂ band, yielding μ_s←a = 0.261 ± 0.006 D. The hyperfine structure due to the electric quadrupole interaction of the nitrogen nucleus was clearly resolved.     

Phase-locked light sources with low-phase noise for manipulating terahertz-separated metastable states in 40Ca+

We report the development of phase-locked light sources for manipulating terahertz-separated metastable states in ⁴⁰Ca⁺. Two Ti:sapphire lasers with frequencies separated by 1.82 THz are phase-locked using an optical comb generator. The obtained phase noise is 49.8 mrad when the phase-locked loop is closed. Using the developed light sources, we excite Rabi oscillations between the terahertz-separated 3²D_3/2 and 3²D_5/2 states in ⁴⁰Ca⁺. We discuss the phase noises of the light sources and their effect on excitation of Rabi oscillations.     

Decay of rabi oscillations induced by magnetic dipole interactions in dilute paramagnetic solids

Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid matrix and coupled by magnetic dipole interactions is theoretically studied. It is shown that these interactions result in random shifts of spin transient nutation frequencies and thus lead to the decay of the transient signal. Averaging over random spatial distribution of spins within the solid and over their spectral positions within magnetic resonance line, we obtain analytical expressions for the decay of Rabi oscillations. The rate of the decay in the case when the half-width of magnetic resonance line exceeds Rabi frequency is found to depend on the intensity of resonant microwave field and on the spin concentration. The results are compared with the literature data for E′₁ centers in glassy silica and [AlO₄]⁰ centers in quartz.     

Fictitious magnetic resonance by quasielectrostatic field

We propose a new kind of spin manipulation method using a fictitious magnetic field generated by a quasielectrostatic field. The method can be applicable to every atom with electron spins and has distinct advantages of small photon scattering rate and local addressability. By using a CO₂ laser as a quasielectrostatic field, we have experimentally demonstrated the proposed method by observing the Rabi oscillation of the ground state hyperfine spin F=1 of the cold ⁸⁷Rb atoms and the Bose–Einstein condensate.     

Quantum-chemical modeling of structural,electronic, and spin characteristics of NV centers in nanostructured diamond: Surface effect

The effect of the surface of diamond on atomic, electronic, and spin properties of diamond nanocrystals containing single nitrogen-vacancy defects ([NV]⁻ centers) is studied. The surface was modeled with clusters C₃₃H₃₀[NV]⁻, C₆₆H₇₂[NV]⁻, which were constructed based on bulk clusters C₃₃H₃₆[NV]⁻ and C₆₉H₈₄[NV]⁻, respectively. In all cases, clusters in the triplet state S = 1 are considered with the cluster charge being −1. The geometric structure of clusters is optimized using the principle of minimization of the total energy of the system; then, the electronic and spin characteristics of clusters are calculated by the density functional theory. The isotropic and anisotropic hyperfine interaction constants of the electron spin of the NV center with the nuclear spin of the nitrogen atom and ¹³C atoms located at different sites in the cluster are calculated. It is found that, in contrast to bulk clusters with [NV]-centers in which the spin density is mainly localized at the three carbon atoms that are the nearest neighbors of the vacancy of the center, upon arrangement of the NV center in the immediate proximity to the surface, the spin density is redistributed such that it is mainly localized at the three carbon atoms that are the nearest neighbors of the nitrogen atom of the center and at C atoms that form the first atomic layer of the (111) surface of the nanocrystal.     

The magnetic properties of the MgZn ferrite system by Mössbauer spectroscopy

Samples of the magnetism-zinc ferrite series Zn_xMg_1?xFe₂O₄ (x = 0.0 to 1.0) have been studied by the Mössbauer effect technique at 77 K. Mössbauer spectra for x = 0.0 to 0.6 suggest the existence of two hyperfine fields, one due to the Fe³⁺ tetrahedral ions (A-sites) and the other due to the Fe³⁺ octachedral ions (B-sites), while for x=0.7 it shows relaxation behaviour and for x?0.8 it exhibits a paramagnetic quadrupole doublet. The variation of nuclear magnetic fields at the A and B sites is explained on the basis of the AB and BB supertransferred hyperfine interactions. Analysis of the average Mössbauer line width as a function of zinc concentration suggests that the relaxation spectrum observed at x=0.7 (77 K) is possibly due to domain wall oscillations.     

Hyperfine Interactions in Pb<Superscript>3+</Superscript>F<Stack><Subscript>8</Subscript><Superscript>−</Superscript></Stack>F<Stack><Subscript>a</Subscript><Superscript>−</Superscript></Stack> clusters in fluorite crystals

The parameters of hyperfine interactions in Pb³⁺F ₈ ^? F _a ^? tetragonal clusters of MeF₂ crystals (Me=Ca, Sr, Ba) are interpreted. The contributions of the spin polarization to the parameters of the proper hyperfine interaction and additional (ligand) hyperfine interactions are calculated in the approximation of weak binding between a charge-compensating ion F _a ^? and a cubic fragment in the tetragonal cluster. It is demonstrated that correct inclusion of the contributions from the spin polarization to the ligand isotropic hyperfine interaction for the F _a ^? ion leads to anomalously large parameters of this interaction for MeF₂ crystals. These results are in agreement with experimental data.     

Coherent nonlinear electromagnetic response in twisted bilayer and few-layer graphene

The phenomenon of Rabi oscillations far from resonance is described in bilayer and few-layer graphene. These oscillations in the population and polarization at the Dirac point in n-layer graphene are seen in the nth harmonic term in the external driving frequency. The underlying reason behind these oscillations is attributable to the pseudospin degree of freedom possessed by all these systems. Conventional Rabi oscillations, which occur only near resonance, are seen in multiple harmonics in multilayer graphene. However, the experimentally measurable current density exhibits anomalous behaviour only in the first harmonic in all the graphene systems. A fully numerical solution of the optical Bloch equations is in complete agreement with the analytical results, thereby justifying the approximation schemes used in the latter. The same phenomena are also described in twisted bilayer graphene with and without an electric potential difference between the layers. It is found that the anomalous Rabi frequency is strongly dependent on twist angle for weak applied fields – a feature absent in single-layer graphene, whereas the conventional Rabi frequency is relatively independent of the twist angle.     

Effect of the Bloch-Siegert shift on the frequency responses of Rabi oscillations in the case of nutation resonance

The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω_rf is close to the Rabi frequency ω₁ in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ? are accompanied by higher-frequency oscillations at frequencies nω_rf and nω_rf ± ?, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ? on the sign of the detuning ω₁ ? ω_rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω_rf + ? increases, while the amplitude at the difference frequency ω_rf ? ? decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E′₁ centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.     

Optical resolution of the hyperfine structure of the Na D lines by atomic beam absorption from a cw tunable dye laser

An optical spectroscopic experiment, allowing a resolution of at least 20 MHz, is described. A cw tunable dye laser with very high frequency stability is used in conjunction with a Rabi type sodium atomic beam. The experimental linewidth was only limited by the natural width of the sodium resonance lines. The hyperfine structure of the 3²P_{$\text{3}\text{2}$} state of sodium has been resolved, for the first time with a purely optical technique.     

Mossbauer study of the Cu-Cd ferrite system

The magnetic properties of the Cd_xCu_1?xFe₂O₄ ferrite system (x = 0 to 1) have been investigated by means of Mossbauer Spectroscopy. Mossbauer Spectra for x = 0.0 to 0.6 suggest the existence of two hyperfine fields, one due to the Fe³⁺ tetrahedral ions (A-sites) and the other due to Fe³⁺ octahedral ions (B-sites), while for x = 0.7 it shows relaxation behaviour and for x ? 0.8 it exhibits a paramagnetic quadrupole doublet. The systematic dependence of the isomer shift, quadrupole interactions and nuclear fields of ⁵⁷Fe³⁺ ions in both A- and B-sites has been determined as a function of cadmium content. The variation of nuclear magnetic fields at the A- and B-sites are explained on the basis of A-B and B-B supertransferred hyperfine interactions. Analysis of the relaxation spectrum observed at x = 0.7 (300 K) suggests that the relaxation mechanism is due to domain wall oscillations. It has been found here that the QS increases from CuFe₂O₄ as the cadmium concentration is increased.     

Confirmation of the giant hyperfine anomaly of the system184W2+-183W g by new spin-echo experiments with183WFe and remarks on possible explanations

Spin-echo measurements on¹⁸³W were performed with dilute alloys of W (0.1, 0.25, 0.5 and 1 at %) in Fe. The result for the hyperfine field:B _4.2K ^hf =(?)62 · 54 (3) T agrees with the old data of Kontani and Itoh, but the accuracy is much better. The giant hyperfine anomaly of¹⁸³W with respect to¹⁸⁴W₂₊ observed by Alzner et al. is thus confirmed and the errors are reduced to:¹⁸⁴W₂₊Δ¹⁸³W_g=+0.150(31). This is the first case of a very large hyperfine anomaly in electronic hyperfine fields which is not caused by the pathological cancellation of orbital and spin magnetism in jackknifep _1/2 ord _3/2 single proton configurations. A detailed discussion shows that the large hyperfine anomaly may be related to the anomalously small magnetic dipole moment of¹⁸³W. Our result should stimulate further theoretical work with the aim to understand this magnetic moment as well as the giant hyperfine anomaly.