Nuclear ground states dressed with rf photons in Mössbauer–Zeeman 57Fe spectroscopy

We have applied the “dressed” state concept, developed in quantum electronics, to the situation in which spin 1/2 ground-state nuclear levels are coupled by rf photons. In particular, we have studied Mössbauer spectroscopy when there is Zeeman splitting of the nuclear levels and a further interaction due to an applied rf-radiation field when the rf frequency is in the neighborhood of the ground-state splitting. The dressed-state approach treats the coupling of the ground nuclear Zeeman levels, due to a radio frequency field, by considering the total system made up of: nucleus, static magnetic field, and rf field as one global quantum system. The energy levels and corresponding eigenstates of the system are calculated as a function of the rf frequency and the magnitude of the rf magnetic flux density. Mössbauer spectra are calculated for the ⁵⁷Fe case in which the source is subjected to both the static and radiation fields while the absorber nuclear levels are unsplit.

     

Raman heterodyne detected magnetic resonance: II. Magnetic transitions of NV centre at level anticrossing region

In the preceding paper [1] we reported both cw and coherent transient measurements carried out in EPR and NMR transitions within the³A ground state of the nitrogen-vacancy centre in diamond using the Raman heterodyne detection technique. In this paper we use these measurements to characterise the nuclear magnetic transitions near a level anticrossing situation. The level anticrossing causes a mixing of the electronic spin and nuclear spin wave functions which results in a greatly enhanced NMR transition moment. The amount of mixing not only affects the dipole moment but, correspondingly, the characteristic relaxation times. In this paper we report the measurement of these parameters in the nitrogen-vacancy centre as a function of applied Zeeman field strength and analyse the results using the spin Hamiltonian formalism. Furthermore, combined with the particular features of the Raman heterodyne technique, such a system represents an ideal testing ground for the nonlinear behaviour of strongly driven transitions. Some results are illustrated, including dynamic Zeeman splitting and gain without inversion.     

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.     

Magnetic field and temperature dependence of the anomalous emission line intensities in LiNbO3:57Co-initial population and relaxation

The magnetic field dependence of the anomalous Fe³⁺ emission line intensities in LiNbO₃:⁵⁷Co cannot be due to a direct spin-lattice relaxation process in the⁶S ground state. Raman and Orbach processes in the ground state are ruled out by the temperature independent behaviour of the spectra. The observed line intensities are proportional to the initial populations of the corresponding Zeeman levels.     

Direct measurement of the nuclear magnetic dipole moment of Ho165 with the atomic beam magnetic resonance method

With an atomic beam magnetic resonance apparatus four rf transitions between different Zeeman levels of the⁴ I _15/2 ground state of Ho¹⁶⁵ have been measured in an external magnetic field of about 3000 Gauss. The interaction between the nuclear magnetic dipole moment and the external field could be deduced from these measurements. Because the magnetic field was measured by calibration transitions in K³⁹, Rb⁸⁵ and Rb⁸⁷, the following value could be determined for the nuclear magnetic dipole moment: μ _I (Ho¹⁶⁵)=4.094(44) μ _n (uncorrected for diamagnetic shielding). Thegj-factor of the ground state of Ho¹⁶⁵ was measured to begj(⁴ I _15/2, Ho¹⁶⁵)=1.1951445(40).     

High-frequency tunable EPR spectroscopy of Tm3+ ions in synthetic forsterite

Paramagnetic centers formed by impurity Tm³⁺ ions in synthetic forsterite Mg₂SiO₄ were studied by high-frequency tunable electron paramagnetic resonance spectroscopy in the frequency range of 150–315 GHz. Crystals were grown from the melt by the Czochralski technique in slightly oxidizing atmosphere. Several centers distinguished by different zero-field splitting between the ground and first excited singlets were found and investigated. Parameters of the effective spin Hamiltonian for these centers describing the dependence of electron-nuclear sublevels on magnetic field were determined.     

Frequency (field) dependent NMR relaxation rate in the interrupted metallic strand model

We calculate the nuclear magnetic resonance rate T^?1₁ arising from the electron-nuclear hyperfine contact interaction, within the interrupted metallic strand model. The electron levels are assumed to have an energy half width Γ and a mean spacing Δ₀ and it is assumed that all segments have the same nuclear spin temperature. In the limit Γ ? Δ₀, T^?1₁ has nearly the same behaviour for kT ? Δ₀ and kT?Δ₀. It is proportional to temperature but has a Lorentzian magnetic field dependence with halfwidth H= Γ/μ_B. At low fields it is enhanced over the value for a normal metal by the factor Δ₀/Γ.This anomalous behaviour arises from the suppression of electron spin flip processes by a magnetic field and should always occur when electronic states are localised, that is when there is a locally discrete electron energy spectrum. Therefore it may be relevant not only to certain linear chain conductors but to other cases of electron localisation.The present model provides an additional possible source of frequency dependence of T₁ in linear chain materials. In certain materials especially those containing defects, it may be more appropriate than the currently accepted mechanism which involves electron spin diffusion in one dimension.     

19F nuclear spin relaxation and spin diffusion effects in the single-ion magnet LiYF4:Ho3+

Temperature and magnetic field dependences of the ¹⁹F nuclear spin-lattice relaxation in a single crystal of LiYF₄ doped with holmium are described by an approach based on a detailed consideration of the magnetic dipole-dipole interactions between nuclei and impurity paramagnetic ions and nuclear spin diffusion processes. The observed non-exponential long time recovery of the nuclear magnetization after saturation at intermediate temperatures is in agreement with predictions of the spin-diffusion theory in a case of the diffusion limited relaxation. At avoided level crossings in the spectrum of electron-nuclear states of Ho^{3 +} ions, rates of nuclear spin-lattice relaxation increase due to quasi-resonant energy exchange between nuclei and paramagnetic ions in contrast to the predominant role played by electronic cross-relaxation processes in the low-frequency ac-susceptibility.     

Spontaneous emission of an ensemble of 57Fe nuclei interacting with a coherent radiation field coupling the Zeeman sublevels of a nuclear excited 3/2 state

The concept “dressed nucleus” is introduced to describe the interaction of a nucleus (in a static magnetic field) with a coherent radiation field at resonance with the Zeeman sublevels. The idea is to consider the global system as a one quantum system in the Schrödinger representation. It is shown that it is possible to associate to each nuclear Zeeman substate an infinite number of equidistant energy levels, each of them having a four-fold degeneracy when any interaction with the coherent field is neglected. This periodic energy scheme, which is the same for any nuclear Zeeman substate, is a consequence of the resonance condition and of the specific form of the coherent state of the radiation field. When the interaction is included the energy degeneracy is lifted and each level splits into (2I+1)² equidistant levels, where I is the spin of the free nuclear state. The energy difference between two adjacent levels is proportional to the square root of the mean photon number in the coherent state. When the global system decays spontaneously to a possible ground state a \gamma-photon is produced. Taking into account the selection rules 24 different \gamma-energies are possible for a nuclear M1 3/2→1/2 transition.     

Calculation of emission spectra in terms of a stochastic relaxation model: Fe3+ in LiNbO3

Mössbauer emission spectra of LiNbO₃:⁵⁷Co single crystals at 100 K in a magnetic field of 4 T show Fe³⁺ line intensities corresponding to a nearly Boltzmann population of the⁶A_1g Zeeman sublevels. Supposing that this is due to a spin-lattice relaxation in the ground state, no relaxation matrix can reproduce the shape of the spectrum. We conclude that the initial populations are temperature dependent due to spin-lattice relaxation within the \(\Gamma _6 ^T \) excited doublet.     

Hyperfine interactions and lattice dynamics of the two dimeric forms of [FeCp(CO)2]2

The concept “dressed nucleus” is introduced to describe the interaction of a nucleus (in a static magnetic field) with a coherent radiation field at resonance with the Zeeman sublevels. The idea is to consider the global system as a one quantum system in the Schrödinger representation. It is shown that it is possible to associate to each nuclear Zeeman substate an infinite number of equidistant energy levels, each of them having a four-fold degeneracy when any interaction with the coherent field is neglected. This periodic energy scheme, which is the same for any nuclear Zeeman substate, is a consequence of the resonance condition and of the specific form of the coherent state of the radiation field. When the interaction is included the energy degeneracy is lifted and each level splits into (2I+1)² equidistant levels, where I is the spin of the free nuclear state. The energy difference between two adjacent levels is proportional to the square root of the mean photon number in the coherent state. When the global system decays spontaneously to a possible ground state a \gamma-photon is produced. Taking into account the selection rules 24 different \gamma-energies are possible for a nuclear M1 3/2→1/2 transition.     

Subsecond spin relaxation times in quantum dots at zero applied magnetic field due to a strong electron-nuclear interaction

A key to ultralong electron spin memory in quantum dots (QDs) at zero magnetic field is the polarization of the nuclei, such that the electron spin is stabilized along the average nuclear magnetic field. We demonstrate that spin-polarized electrons in n-doped (In,Ga)As/GaAs QDs align the nuclear field via the hyperfine interaction. A feedback onto the electrons occurs, leading to stabilization of their polarization due to formation of a nuclear spin polaron [I. A. Merkulov, Phys. Solid State 40, 930 (1998)]. Spin depolarization of both systems is consequently greatly reduced, and spin memory of the coupled electron-nuclear spin system is retained over 0.3 sec at temperature of 2 K.     

Zeeman effect of the 6011 Å line of Pr3+: LaCl3 using the fluorescence line-narrowing technique

The Zeeman effect of the 6011 Å resonance line of Pr³⁺ in a LaCl₃ crystal has been studied by means of the fluorescence line-narrowing technique using a cw single-mode tunable laser. The experiments have confirmed the assumptions made previously to interpret the spectra in zero magnetic field. They have led to accurate values of the hyperfine structure constant and of the spectroscopic splitting g-factor of the ground level.     

Charge and spin currents tunnelling through a toroidal carbon nanotube side-coupled with a quantum dot

We have investigated the mesoscopic transport through the system with a quantum dot (QD) side-coupled to a toroidal carbon nanotube (TCN) in the presence of spin-flip effect. The coupled QD contributes to the mesoscopic transport significantly through adjusting the gate voltage and Zeeman field applied to the QD. The compound TCN-QD microstructure is related to the separate subsystems, the applied external magnetic fields, as well as the combination of subsystems. The spin current component I_z^s is independent on time, while the spin current components I_x^s and I_y^s evolve with time sinusoidally. The rotating magnetic field induces novel levels due to the spin splitting and photon absorption procedures. The suppression and enhancement of resonant peaks, and semiconductor-metal phase transition are observed by studying the differential conductance through tuning the source-drain bias and photon energy. The magnetic flux induces Aharonov-Bohm oscillation, and it controls the tunnelling behavior due to adjusting the flux. The Fano type of multi-resonant behaviors are displayed in the conductance structures by adjusting the gate voltage V_g and the Zeeman field applied to the QD.     

Zeeman effect and stark splitting of the electronic states of the rare-earth ion in the paramagnetic terbium garnets Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> and Tb<Subscript>3</Subscript>Al<Subscript>5</Subscript>O<Subscript>12</Subscript>

The Zeeman effect in the ⁷ F ₆ → ⁵ D ₄ absorption band of the Tb³⁺ ion in the paramagnetic garnets Tb₃Ga₅O₁₂ and Tb₃Al₅O₁₂ was studied. The field dependences of the Zeeman splitting of some absorption lines are found to exhibit unusual behavior: as the magnetic field increases, the band splitting decreases rather than increases. Symmetry analysis relates these lines to 4f → 4f electron transitions of the doublet-quasi-doublet or quasi-doublet-doublet type, for which the field dependences of the splitting differ radically from the well-known field dependences of the Zeeman splitting for quasi-doublet-quasi-doublet or quasi-doublet-singlet transitions in a longitudinal magnetic field.     

The transient EPR spectra and spin dynamics of coupled three-spin systems in photosynthetic reaction centres

The concept of introducing an additional, stable paramagnetic species into photosynthetic reaction centres to increase the information content of their spin polarized transient EPR spectra is investigated theoretically. The light-induced electron transfer in such systems generates a series of coupled three-spin states consisting of sequential photoinduced radical pairs coupled to the stable spin which acts as an “observer”. The spin polarized transient EPR spectra are investigated using the coupled three-spin system P⁺I⁻Q⁻ _A in pre-reduced bacterial reaction centres as a specific example which has been studied experimentally. The evolution of the spin system and the spin polarized EPR spectra of P⁺I⁻Q⁻ _A and Q⁻ _A following recombination of the radical pair (P = primary donor, I = primary acceptor, Q_A = quinone acceptor) are calculated numerically by solving the equations of motion for the density matrix. The net polarization of the observer spin is also calculated analytically by perturbation theory for the case of a single, short-lived, charge-separated state. The result bears a close resemblance to the chemically induced nuclear polarization (CIDNP) generated in photolysis reactions in which a nuclear spin plays the role of the observer interacting with the radical pair intermediates. However, because the Zeeman frequencies of the three electron spins involved are usually quite similar, the polarization of the electron observer spin in strong magnetic fields can reflect features of the CIDNP effect in both, high and low magnetic fields. The dependence of the quinone spin polarization on the exchange couplings in the three-spin system is investigated by numerical simulations, and it is shown that the observed emissive polarization pattern is compatible with either sign, positive or negative, for a range of exchange couplings, J_PI, in the primary pair. The microwave frequency and orientation dependence of the spectra are discussed as two of several possible criteria for determining the sign of J_PI.     

Ultrahigh-frequency NMR of Tm3+ ions in single crystals of thulium ethylsulfate in high magnetic fields

Resonant transitions predicted earlier between low-lying electron-nuclear sublevels of the Tm³⁺ ground state were observed at frequencies up to 700 MHz in a dielectric Van Vleck paramagnet—thulium ethylsulfate single crystal. It is shown that, due to the distortion of the 4f-electron shell of a rare-earth ion in an applied magnetic field, the parameters of electron-nuclear interaction become field-dependent.     

Präzisionsmessung der Kerndipolmomente von Ba135 und Ba137 mit optischem Pumpen

The nuclear Zeeman levels of the ground state of Barium (6s^{2 1}S₀, F=I=3/2) were polarized by means of optical pumping with the resonance line (6s^{2 1}S₀?6s 6p¹P₁, λ=5535 Å). The magnetic field was calibrated by means of optical pumping of sodium. The magnetic moments, calculated from the nuclear Hf-Zeeman-transitions at 228 Gauss are μ₁₃₅=0,83651 (6) μ_N μ₁₃₇=0,93573 (6) μ_N (with diamagnetic correction). With the results of nuclear induction in BaCl₂ we calculate the chemical shift to be (8.6±1.0)·10^?4. The ratio of the nuclear moments is μ₁₃₇/μ₁₃₅=1.11862 (3) in agreement with the measurements in BaCl₂.     

Optical pumping and population transfer of nuclear-spin states of caesium atoms in high magnetic fields

Nuclear-spin states of gaseous-state Cs atoms in the ground state are optically manipulated using a Ti:sapphire laser in a magnetic field of 1.516T, in which optical coupling of the nuclear-spin states is achieved through hyperfine interactions between electrons and nuclei. The steady-state population distribution in the hyperfine Zeeman sublevels of the ground state is detected by using a tunable diode laser. Furthermore, the state population transfer among the hyperfine Zeeman sublevels, which results from the collision-induced modification \delta a(\bm S \cdot \bm I) of the hyperfine interaction of Cs in the ground state due to stochastic collisions between Cs atoms and buffer-gas molecules, is studied at different buffer-gas pressures. The experimental results show that high-field optical pumping and the small change \delta a(\bm S \cdot \bm I) of the hyperfine interaction can strongly cause the state population transfer and spin-state interchange among the hyperfine Zeeman sublevels. The calculated results maybe explain the steady-state population in hyperfine Zeeman sublevels in terms of rates of optical-pumping, electron-spin flip, nuclear spin flip, and electron-nuclear spin flip-flop transitions among the hyperfine Zeeman sublevels of the ground state of Cs atoms. This method may be applied to the nuclear-spin-based solid-state quantum computation.     

MAGNETIC FIELD EFFECT OF THE EUROPIUM a8S7/2-z6P7/2 LINES

The magnetic field effect of a⁸S_7/2-z⁶P_7/2 lines of ¹⁵¹Eu and ¹⁵³Eu in magnetic fields up to 66.7 mT has been studied by using laser atomic beam spectroscopy. The Zeeman level structures of the europium a⁸S_7/2 and z⁶P_7/2 states in magnetic fields were discussed. The location and intensity of the measured Zeeman transition lines were found in good agreement with the theoretical results.