Spin-selective low temperature spectroscopy on single molecules with a triplet-triplet optical transition: Application to the NV defect center in diamond

The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T ₀–T ₁, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g ⁽²⁾(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T ₁→S→T ₀ to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T ₀) state sublevels can be obtained from the spectra and g ⁽²⁾(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet ³ A-³ E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m _S =0 sublevel of the excited ³ E state to the singlet ¹ A state (~1 kHz) is much slower than the rates from the m _S =±1 substates, while the rates of ISC transitions to different m _S substates of the ground ³ A state are close to each other (~1 Hz). As a result, only the optical transition between m _S =0 sublevels in the ³ A-³ E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g ⁽²⁾(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T ₀(m _S )=0) transition and (ii) the S→T ⁰(m _S =±1) transitions followed by the slow spin-lattice relaxation T ₀(m _S =±1)→T ₀(m _S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.     

TheSU(3) structure of the 3−/2 baryons

TheSU(3) structure of the 3^?/2 baryonsN ^*(1525),Ξ ^*(1820),Y ₁ ^* (1660),Y ₁ ^* (1715),Y ₀ ^* (1520) andY ₀ ^* (1700) is investigated on the hypothesis that they form a decupletoctet-singlet combination. Their branching ratios seem to be consistent with this picture. Mixing angles are determined, andΞ ^*(1820) is deduced to be mainly decuplet.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Photon distribution functions of the fluorescence photons from a single nanoparticle in various photon counting methods

Simple expressions have been derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. In contrast to the previously derived expressions represented in the form of N multiple integrals, the new expressions contain only single or double integrals of Poisson functions, which makes it possible to easily perform the numerical calculation of the photon distribution. The simplest photon counting method corresponds to the lengthiest function w _N ^M (T); on the contrary, the simplest function w _N ^O (T) corresponds to the most complex photon counting method. The functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) are noticeably different in short time intervals T; however, the distributions calculated using these functions are almost indistinguishable from each other in long T intervals. This circumstance makes it possible to use the simplest function w _N ^O (T) to consider the photon statistics measured by the simplest method. This possibility is particularly important for investigating the fluorescence photon statistics, where the intensity fluctuates.     

Zeitliches Abklingen und Anisotropie von p-Terphenyl- undp-Terphenyl-Anthrazen-Mischkristallen bei Beschuß mit α-Teilchen

The time dependence of scintillation intensity from single crystals ofp-terphenyl and mixed crystals ofp-terphenyl and anthracene after bombarding with α-particles was investigated at the two temperaturesT=296 °K andT=92 °K. For the crystals ofp-terphenyl the time dependence of the scintillation anisotropy was also measured. Using the formulas given byKing andVoltz the decay curves ofp-terphenyl were decomposed into two components. Good agreement between experiment and theory was found. The ratio of the prompt intensity to the delayed intensity was determined to be 1∶2 atT=296 °K and 1∶3 atT=92 °K. The diffusion constants for triplet excitons were calculated to beD _T(296 °K)≈10^?5 cm² sec^?1 andD _T(92 °K)≈ 2×10^?6 cm² sec^?1, and the triplet-triplet interaction rate constantsχ _tt(296 °K)≈ 2.5×10^?11 cm³ sec^?1 andχ _tt(92 °K)≈0.5×10^?11 cm³ sec^?1.     

Einfluß der Pion-Pion-Wechselwirkung auf Pion-Nukleon-Streuphasen

The isospin dependent part of theS-wave pion-nucleon amplitude is calculated according to the CGLN approach, but recoil and projection on the partial waves are treated exactly. Then the difference against the experimental data is approximately a constant up to 100 MeV and amounts to 1/3 of the total value. It is shown, that at low energies the main corrections of the CGLN equations are taken into account by a subtraction of theπ+π→?+\(\overline \Re \),J=I=1 amplitudesf _± ¹ (t) as proposed byMandelstam andFrazer. Calculations have been done forS, P andD pion-nucleon amplitudes. The main result is a prediction of theS-wave amplitude obtained without adjusting free parameters up to 100 MeV. The relations of this method to the equations derived byBowcock, Cottingham andLurié according to the Cini-Fubini approach are discussed.     

Effect of the orbital structure and symmetry of electronic states on nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing: Dibenzofuran

The nonradiative S-T intersystem crossing S ₁(ππ*) ? T ₁(ππ*) in dibenzofuran (DB(O)) molecules has been theoretically investigated within the model of vibronically induced spin-orbit (VISO) coupling of electronic states, where the vibronic perturbation takes into account all out-of-plane vibrational modes of a molecule. It is established that the S-T intersystem crossing S ₁(¹ A ₁) ? T ₁(³ B ₂) involves also the intermediate (T _m )T ₂(³ A ₁) and T ₃(³ B ₂) triplet states. The calculated rate constant K _ST = (4.5–4.7) × 10⁷s^?1 of the nonradiative transition is in agreement with the known experimental data. The manifestation of approximate (belonging to the D _2h group) symmetry of singlet and triplet molecular states in VISO couplings has been studied. An effect of the heavy (oxygen) atom of a DB(O) molecule on K _ST is established.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.     

A nonradiative intersystem crossing <Emphasis Type="Italic">S</Emphasis>(ππ*) ↝ <Emphasis Type="Italic">T</Emphasis>(ππ*) transition in dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxin

The probability of the nonradiative S-T intersystem crossing in dibenzo-p-dioxin is theoretically studied using a model for the vibronically induced spin-orbit coupling between electronic states and taking into account all out-of-plane vibrational modes. Several symmetry variants for the lowest S ₁(ππ*) singlet state are considered. In the case of g symmetry of this state, a provision is made for the possibility of its vibronic coupling with the nearest dipole-active singlet ¹ B _2u ππ* state. The rate constants K _ST of the S ₁ ? T(ππ*) transitions to the T ₁(³ B _3g ) state are estimated taking into account several intermediate triplet T _m (ππ*) states of g and u symmetry. For different symmetry types of the S ₁ state, the effect of K _ST on the fluorescence quantum yield ?_fl is discussed. The ¹ B _3g symmetry state is found to be the lowest S ₁ state. It is found that the main contribution to K _ST is made by the S ₁(¹ B _3g ) ? T ₄(³ A _g ) transition.     

Polarization of phosphorescence transitions and probabilities of intramolecular nonradiative deactivation of the lowest triplet state of aromatic molecules

This study continues the experimental testing of the validity of the inductive resonance theory of dipole-dipole energy transfer from the T ₁→S ₀ transition dipole to stretching vibrations of intramolecular CH bonds of naphthalene and its hydroxy derivatives. To this end, in the series of compounds under study, the range of variation of the geometrical parameter [Φ(CH)]² of the Förster theory, which accounts for the mutual orientation of the energy donor and acceptor, is estimated. Preliminarily, the angles between the transition dipole moments of the radiative and absorptive electronic transitions (T ₁→S ₀ and S ₀→S ₁; T ₁→S ₀ and S ₀→S ₂; S ₁→S ₀ and S ₀ →S ₁; and S ₁→S ₀ and S ₀→S ₂) are measured at 77 K by the method of polarization photoselection. From the polarization measurements, the angles between the phosphorescence transition dipole moment and the plane of a molecule are determined. It was found that, upon passage from naphthalene to its β derivatives, the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule markedly changes, with the in-plane component of the dipole moment being increased by an order of magnitude. The experimentally determined rate constants of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system, k _nr(CH), are compared with the rate constants [Φ(CH)]² of the inductive resonance energy transfer from the dipole of the T ₁→S ₀ transition to the dipole of the CH vibrations polarized in the plane of a molecule, calculated with regard to the orientational factor [Φ(CH)]². This comparison showed that, in the series of compounds under study, a change in the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule does not affect the rate of the nonradiative T ₁?S ₀ transition. This inference is confirmed by the absence of a correlation between the rate constants k _dd(CH) calculated by us (with regard to [Φ(CH)]²) and the well-known rate constants k _nr(CH) of individual sublevels of the T ₁ state measured at T≤1.35 K for a number of organic molecules. The possible sources of discrepancy between the experimental data that k _nr(CH) is independent of [Φ(CH)]² and the predictions of the theory are considered. A conclusion is made that the electronic-vibrational energy transfer between electric dipoles is the most probable mechanism of the T ₁?S ₀ transitions, but the rate constant of the dipole-dipole energy transfer upon interaction of the electronic and vibrational dipoles in a molecule does not depend on their orientations.     

Anomalous thermopower in heavy-fermion compounds CeB<Subscript>6</Subscript>, CeAl<Subscript>3</Subscript>, and CeCu<Subscript>6 − <Emphasis Type="Italic">x</Emphasis></Subscript>Au<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

High-precision measurements of thermopower have been performed in a wide temperature range (2–300 K) for a series of cerium-based heavy-fermion compounds, including CeB₆, CeAl₃, CeCu₆, and substitutional solid solutions of the CeCu_{6 ? x} Au _x system (x = 0.1, 0.2). All compounds exhibit an unusual (logarithmic) asymptotic behavior of the temperature dependence of the Seebeck coefficient: S ∝ ?lnT. In the case of cerium hexaboride, this anomalous behavior of S(T) is accompanied by the appearance of weak-carrier-localization-mode asymptotics in the conductivity (σ(T) ∝ T ^0.39), while the paramagnetic susceptibility χ(T) and the effective mass of charge carriers m _eff(T) vary according to a power law (χ(T), m _eff(T) ∝ T ^?0.8) in the temperature interval T = 10–80 K. This behavior corresponds to renormalization of the density of states at the Fermi level. The observed anomalous behavior of thermopower in CeB₆ and other cerium-based intermetallic compounds is attributed to the formation of heavy fermions (many-body states in the metal matrix) at low temperatures.     

Population and current noise in semiconductor laser junctions

The population noise in a semiconductor laser is calculated by means of the quantum mechanical Langevin method. The resulting population noise is given by 〈δ N _c ² 〉=(T _c/2) (rate in+rate out)+K(¯n), whereN _c is the total number of electrons in the conduction band in the active region,T _c is a relaxation time. The first expression is the usual shot noise term. The transition rates are the sum of the rates due to the light field, the pumping and the spontaneous emission. The last termK(¯ n) is caused by the light field fluctuations;¯n is the mean number of photons in the laser mode.K(¯ n) consists of two parts: a) The main part is proportional to the intensity noise of the light field, which increases below but near threshold and gets constant above threshold. b) There is a second term due to the fact that parts of the fluctuations of the population and of the light field are correlated. — The noise spectrumS _I(ω) of the junction currentI is calculated for low frequencies. Beyond the usual shot noise termS _I(0)=2eI, additional noise is found in and above the threshold region, a) mainly because of the fluctuations of the light field in the laser mode and b) to a small amount, because the absorption processes due to the laser photons weaken the forward current, which is carried by emission processes, while the absorption noise adds to the emission noise.     

Thermophysical study of structural phase transitions in Na<Subscript>0.95</Subscript>Li<Subscript>0.05</Subscript>NbO<Subscript>3</Subscript> solid solution

Temperature dependences of specific heat C_p(T) and coefficient of thermal expansion ;(T) for Na_0.95Li_0.05NbO₃ sodium-lithium niobate ceramic samples are investigated in the temperature range of 100–800 K. The C_p(T) and α(T) anomalies at T₃ = 310 ± 3 K, T₂ = 630 ± 8 K, and T₁ = 710 ± 10 K are observed, which correspond to the sequence of phase transitions N ? Q ? S(R) ? T2(S). The effect of heat treatment of the samples on the sequence of structural distortions was established. It is demonstrated that annealing of the samples at 603 K leads to splitting of the anomaly corresponding to the phase transition Q → R/S in two anomalies. After sample heating to 800 K, the only anomaly is observed in both the C_p(T) and ;(T) dependence. Possible mechanisms of the observed phenomena are discussed.     

Spectral representation for singlet and triplet green's functions

Spectral representations of special Green functions are given explicitly. We consider the density correlation functionG ₂(x ₁ η ₁ x ₂ η ₂,x ₁ ⁺ η ₁ x ₂ ⁺ η′₂) and the functionG ₂(x ₁ η ₁ x ₁ ^? η₂,x ₂ η ₁ ^′ x ₂ ^? η ₂ ^′ Coupling the field operators Ψ^? (x, η), Ψ(x, η) to singlet and triplet operatorsA _{SMs TT3} (x), we obtain spectral representations for theseG-functions. The formulae derived may be of use when studying the system of equations for the Green functions, which describe many particle systems from a microscopic point of view.     

Lichtausbeute von α-Teilchen in kristallinem und dampfförmigem Anthrazen

The light output,S _v by α-particles stopped in anthracene vapour has been measured as a function of vapour pressure (10–700 mm Hg) and temperature (250°C–385°C). The comparison of the results for an idealised vapour neglecting collisions with the light output,S _c, from anthracene crystals by α-particles impinging parallel to thec′-axis yields the unexpected results: S_v(8.78 MeV)/S_c(8.78 MeV)=0.46±0.05 andS _v(6.05 MeV)/S _c(6.05 MeV)=0.57±0.08. A simple model assuming quenching by collisions of the vapour molecules could explain the observed dependence of the light output on the vapour pressure at fixed temperature. The path lengthsR _v of α-particles in anthracene vapour were determined to be R_v(8.78 MeV)=(9.0±0.6) mg/cm²,R _v(6.05 MeV)=(4.9±0.6) mg/cm² and the ratio of the light output by the two different α-energiesS _v(8.78 MeV)/S _v(6.05 MeV)=1.42±0.2.     

A new emission band spectrum of sulphur

A new emission band system of S₂ has been obtained in the region λ 3050–λ 2670 when sulphur is excited in a 30 mc/S. high frequency discharge from a 1/2 kW oscillator. The bands appear single sharp headed and are degraded towards red. Analysis of these new bands as belonging to a single system has led to the following vibrational formula.ν=36624·7+428·5(v′+1/2)?3·45(v′+1/2)² ?699·2(v″+1/2)+3·2(v″+1/2)². This system disignated as (b?x) is tentatively assigned to the electronic transition¹∑ _u ⁺ ?¹∑ _g ⁺ . The¹∑ _g ⁺ (x) state is found as the common lower state of three of the far ultraviolet systems of S₂ recently reported byTanaka andOgawa.     

Proximity effect of a superconductor on an antiferromagnetic metal

There should be two contributions to the pair breaking energy in an antiferromagnetic metal. The first, already discussed byde Gennes andSarma, is due to disorder on the magnetic sites. The second is a temperature dependent contribution from electron magnon scattering. This term is calculated for the temperature rangeT _N(J/μ)²?T?T _N and found to be of orderT ²/T _N. (T _N = Néel temperature,μ = Fermi energy,J = exchange coupling between conduction electrons and magnetic ions.)     

Anomalous temperature dependence of magnetic relaxation in YBa<Subscript>2</Subscript>Cu<Subscript>2</Subscript>O<Subscript>7 − δ</Subscript> oxygen-deficient single crystals

The dependence of the magnetization relaxation rate S = ?d lnM/dlnt on temperature T is measured in YBa₂Cu₃O_{7 ? δ} samples with various oxygen concentrations. It is found that the S(T) curve changes qualitatively when oxygen deficit δ exceeds the threshold value δ_th = 0.37. For δ < δ_th (T _c > 60 K, where T _c is the superconducting transition temperature), function S(T) has the well-known peak at T/T _c = 0.4. For δ > δ_th (at T _c < 51 K), this peak transforms into a plateau and a new sharp peak appears at T/T _c = 0.1. The threshold value δ_th of the oxygen deficit corresponds to the transition of the sample from the disordered state into the ordered state of oxygen vacancies. We consider the change in the shape of the S(T) curve as a macroscopic manifestation of this transition.     

Absorptive corrections to associated production of strange baryon and meson resonances in πp scattering

Absorptive corrections are calculated for the reactionsπ ⁺ p→K ^*+∑⁺(K ^*+ Y ₁ ^*+ ) mediated byK-exchange andπ ⁺p→K⁺ Y ₁ ^*+ withK ^*-exchange. The effect of the finite width of the resonances is included. Numerical results are given for 5 and 8 GeV/c.