Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate

Rabi nutations of a single nuclear spin in a solid have been observed. The experiments were carried out on a single electron and a single 13C nuclear spin of a single nitrogen-vacancy defect center in diamond. The system was used for implementation of quantum logical NOT and a conditional two-qubit gate (CROT). Density matrix tomography of the CROT gate shows that the gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms.     

Observation of coherent oscillations in a single electron spin

Rabi nutations and Hahn echo modulation of a single electron spin in a single defect center have been observed. The coherent evolution of the spin quantum state is followed via optical detection of the spin state. Coherence times up to several microseconds at room temperature have been measured. Optical excitation of the spin states leads to decoherence. Quantum beats between electron spin transitions in a single spin Hahn echo experiment are observed. A closer analysis reveals that beats also result from the hyperfine coupling of the electron spin to a single 14N nuclear spin. The results are analyzed in terms of a density matrix approach of an electron spin interacting with two oscillating fields.     

A quantum computer based on NV centers in diamond: Optically detected nutations of single electron and nuclear spins

In an effort to realize a two-bit processor for a quantum computer on the basis of single nitrogen-vacancy defect centers (NV centers) in diamond, the optically detected nutations of the electron spin of a single NV center in the ground state and of the nuclear spin of a ¹³C atom located at a diamond lattice site nearest to the NV center are studied. The photodynamics of NV and NV + ¹³C centers under different temperatures and optical excitation conditions is discussed. A seven-level model of a center excited by radiation from an Ar⁺ laser at room temperature is proposed. On the basis of this model, the experimental spectra of optically detected electron paramagnetic and electron-nuclear double resonances of single NV and NV + ¹³C centers in diamond nanocrystals, as well as experimental data on the optically detected nutations of the electron and nuclear spins of these centers caused by the actions of pulsed microwave and radiofrequency fields, respectively, are interpreted.     

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.     

Shot noises of spin and charge currents in a ferromagnet-quantum-dot-ferromagnet system

We have investigated the shot noises of charge and spin current by considering the spin polarized electron tunneling through a ferromagnet-quantum-dot-ferromagnet system. We have derived the spin polarized current noise matrix, from which we can derive general expressions of shot noises associated with charge and spin currents. The spin and charge currents are intimately related to the polarization angles, and they behave quite differently from each other. The shot noise of charge current is symmetric about the gate voltage whose structure is modified by the Zeeman field considerably. There exists oscillations in spin current shot noise in the absence of source-drain bias at zero temperature, and it is asymmetric in the positive and negative regimes of sourcedrain voltage. The shot noise of spin current behaves quite differently from the shot noise of charge current, since the spin current components I _x ^s , I _y ^s oscillate sinusoidally with the frequency ω_γ in the γth lead, while the I _z ^s component of spin current is independent of time.      

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.     

Interaction of Muons with H2/H3-Centres in Diamond

We report on transverse field muon spin rotation measurements on a nitrogen-rich type Ia diamond, both before and after the conversion of some of the aggregated nitrogen centres to nitrogen-vacancy complexes known as H2/H3-centres. The prompt fractions f and the spin relaxation rates λ were determined for the diamagnetic (μ_d) and the paramagnetic (Mu_T) states in the temperature range 10–300 K. The production of the nitrogen-vacancy complexes had little effect on the parameters of the Mu_T state for which f and λ remained unchanged at approximately 30% and 4 μs⁻¹, respectively. For the μ_d state, on the other hand, the formation of the H2/H3-centres resulted in an increase of the prompt fraction from 10(2)% to 20(3)%, and (for the first time) the spin relaxation rate showed a non-zero value of 0.020(3) μs⁻¹. These results show evidence of strong μ_d interactions with the nitrogen-vacancy complexes in diamond, and suggest a more complex structure for this state than a bare μ⁺. This revised version was published online in September 2006 with corrections to the Cover Date.     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

Zero-field muon spin rotation in monocrystalline chromium

Spin precession of positive muons in chromium in zero applied magnetic field is reported for the first time. The observations cover the temperature range from about 2.5 K to 10 K and thus pertain to the so-called longitudinal spin-density wave (LSDW) state of antiferromagnetic Cr. The conclusions that may be drawn from the existence of one rather sharp spin precession line are discussed, among them the estimateD _μ=2.4·10⁻¹⁴ m² s⁻¹ for the muon diffusivity at 4 K. Considerable evidence exists for a strong interactions of μ⁺ with the charge-density waves that are likely to accompany the LSDWs in Cr.     

Effect of lattice relaxation on spin density of nitrogen-vacancy centers in diamond and oscillator strength calculations

Using a generalized Hubbard Hamiltonian, many-electron wavefunctions of negatively charged (NV⁻) and neutral nitrogen-vacancy (NV⁰) centers in diamond were calculated. We report the effect of symmetric relaxation of surrounding atoms on the spin density, calculated from the many electron wavefunctions in the ground and excited states. We evaluated the error, that, arises in estimation of spin density when lattice relaxation effect is neglected in Electron Paramagnetic Resonance experiment and showed that the ground state spin density distribution is accessible in outward relaxations. The computed oscillator strengths give a higher efficiency for the 1.945 eV photoluminescence (PL) line of NV⁻ with respect to 2.156 eV PL line of NV⁰ which agrees well with experiment. This result is explained based on the largest the ground state spin among available values for the NV⁻ with respect to NV⁰. The transition probability between degenerate ground and excited states slightly depends on the S _z value. Finally, we report on the electronic configurations which contribute to the ground and excited states and discuss the population variation of electronic configurations with relaxation.     

Towards T 1-limited magnetic resonance imaging using Rabi beats

Two proof-of-principle experiments toward T ₁-limited magnetic resonance imaging with NV centers in diamond are demonstrated. First, a large number of Rabi oscillations is measured and it is demonstrated that the hyperfine interaction due to the NV??s ¹⁴N can be extracted from the beating oscillations. Second, the Rabi beats under V-type microwave excitation of the three hyperfine manifolds is studied experimentally and described theoretically.     

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.     

Strong coupling of a spin ensemble to a superconducting resonator

We report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are nitrogen-vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the nitrogen-vacancy center electron spin resonance.     

Double-quantum nutations in a two-level spin system

We report experimental results of the oscillatory response of a two-level spin system (E'₁ centres in glassy silica) excited by a step-modulated radiation tuned to the double-quantum (DQ) resonance. On the basis of a semiclassical calculation of the transient regime, the observed oscillations are ascribed to the nutations of the DQ transitions.     

InAs量子点中自旋-轨道相互作用下电子自旋弛豫的参量特征

本文在处理InAs单电子量子点哈密顿模型时,将自旋-轨道(SO)相互作用作为微扰项,计算在Fock-Darwin本征函数下SO相互作用的矩阵元,利用其对能级和波函数的二阶修正,并且考虑新的能级对g因子和有效质量m^*的影响,计算得到在声子协助下电子的自旋弛豫率Γ的表达式.给出了InAs量子点中声子协助的电子自旋弛豫率Γ对于限制势频率ω₀、温度T、纵向高度z_{0关键词： 自旋弛豫率 自旋-轨道(SO)相互作用 InAs量子点 Fock-Darwin本征函数}     

Observation and reaction control of a singlet born radical pair formed photochemically in an SDS micelle by pulsed microwave irradiation

The photochemical reaction of tetraphenylhydrazine in an SDS micellar solution is studied using a transient absorption detected magnetic resonance (ADMR) method. This system is photo-dissociated via the singlet excited state and forms a transient radical pair. Strong microwave irradiation of this system under an × band EPR magnetic field provides an ADMR spectrum of the singlet born radical pair as the optical absorbance change of the diphenylaminyl radical. The employment of a short duration microwave pulse that efficiently flips the electron spin quantum (Δm _s = 1) controls the reaction of the radical pair, and the reaction rate constant of this system is determined. Furthermore, changing the microwave duration shows the quantum beat of this system induced by the electromagnetic field. This beat signal carries both a single beat that corresponds to the Rabi frequency and a double-frequency beat that is due to simultaneous two-spin controlling.     

Nuclear spin lattice relaxation of191mIr in Fe

Thermal cycling of the lattice temperature was used to determine the nuclear spin lattice relaxation of^191m IrFe in polarizing fields of 0.05 to 1.3 T. At low temperatures, the relaxation time is not very much shorter than the lifetime of^191m Ir. In the first part of the paper, the master equation formalism is extended to include a finite lifetime. Our result for the reduced relaxation constant, ² C _K =(1.48±0.11)·10¹⁴ K s^–1 T^–2 (high field limit) is in serious disagreement with that of a spin echo measurement of¹⁹³IrFe, but fits much better into the general systematics. A comparison of relaxation rates for 3d-, 4d-, and 5d-impurities in Fe is given. As a by-product, a Kapitza conductivity constant ofl _K =1.5 mW cm^–2 K^–4±30% was found between Fe and dilute³He/⁴He.     

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.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.