Resolution of signals with varying frequency

Both a simple and a more refined analysis of signals with varying frequency have shown that optimum resolution of such signals can be achieved with records of length T = a^?0·5, where a is the rate of change of frequency. The resolution obtained is given by f = a^0·5. The results have been verified by analysis of a frequency modulated signal, and applied to two practical aircraft flyover noise cases.     

Quantum beats in two-photon resonance fluorescence

The two-photon resonance fluorescence spectrum of a three-level atom is shown to consist of the low frequency modes in addition to the high frequency ones in the limit of high photon densities. The spectral function for the low frequency modes consists of two lorentzian lines describing: the peak occuring at the renormalized beat frequency Δ₊ and that of the zero-photon excitation at the frequency Δ_-, where Δ_±=Δ-3Ω²/2ω_a±Ω²u/2ω_a, u²=1+(2Δω_a/Ω ²)². Here, 2Δ is the energy splitting between the two excited states, ω_a is the photon energy of the pump field and Ω is the Rabi frequency. The peak at the renormalized beat frequency Δ₊ occurs provided that the condition (2Δω_a/Ω²)² > 1 is satisfied. The two-photon laser spectroscopy is expected to be a useful tool for the observation of the low frequency modes in question.     

Infrared spectroscopy of the intermediate-valence semiconductor YbB12

The dynamic conductivity and permittivity spectra of the intermediate-valence compound YbB₁₂ are measured in the frequency range (6–10⁴) cm^?1 (quantum energy 0.75 meV-1.24 eV) at temperatures of 5–300 K. Analysis of the spectral singularities associated with the response of free charge carriers has made it possible for the first time to determine the temperature dependences of their microscopic parameters, viz., concentration, effective mass, relaxation frequency and time, mobility, and plasma frequency. It is shown that the relaxation frequency decreases upon cooling from 300 K to the coherence temperature T ^* = 70 K for YbB₁₂, which is mainly associated with the phonon mechanism of scattering of charge carriers. For cooling below the coherence temperature T ^* = 70 K, the temperature dependence of the relaxation frequency for charge carriers of the Fermi-liquid type is found to be γ ～ γ₀ + T ², while their effective mass and relaxation time increase, respectively, to m ^*(20 K) = 34m ₀ (m ₀ is the free electron mass) and τ(20 K) = 4 × 10^?13 s, indicating the establishment of coherent scattering of carriers from localized magnetic moments of the f centers. At a temperature of T = 5 K, the conductivity spectrum contains an absorption line at a frequency of 22 cm^?1 (2.7 meV); the origin of this line can be associated with the exciton-polaron bound state. Since such a state was observed earlier in other intermediate-valence semiconductors (such as SmB₆, TmSe_1?x Te, and (Sm, Y)S), it is probably typical of this class of compounds.     

Non-cyclic geometric phase of nuclear quadrupole resonance signals of powdered samples

The non-cyclic geometric phase of ¹⁴N and ³⁵Cl NQR signals induced by the character of trajectory of nuclear magnetization motion upon pulse r.f. excitation of powdered samples is studied. Analytical expressions for the geometric phases of NQR signals of the nuclei of spins I=1 and 3/2 upon nuclear magnetization rotation induced by means of r.f. pulses with frequency detuned from the resonance and for any impulse duration for a separate crystallite are obtained. It is shown that the geometric phase recorded for the signal from a powdered sample at Δω=0 can be different from zero and can oscillate upon changes in duration of the r.f. excitation pulse. An alternative variant of the nutation experiment aimed at obtaining the asymmetry parameter η from locations of frequency singularities in the nutation phase spectrum for nuclei of spin I=3/2 in powder substances is proposed.     

Double wavelet transform of frequency-modulated nonstationary signal

A mathematical model is proposed for a frequency-modulated signal in the form of a system of Gaussian peaks randomly distributed in time. An analytic expression is obtained for continuous wavelet transform (CWT) of the model signal. For signals with time-varying sequence of peaks, the main ridge of the skeleton characterized by frequency ν _max ^MFB (t) is analyzed. The value of ν _max ^MFB (t) is determined for any instant t from the condition of the CWT maximum in the spectral range of the main frequency band (MFB). Double CWT of function ν _max ^MFB (t) is calculated for a frequency-modulated signal with a transition regions of smooth frequency variation (trend) as well as with varying frequency oscillations relative to the trend. The duration of transition periods of the signal is determined using spectral integrals E _ν(t). The instants of emergence and decay of low-frequency spectral components of the signal are determined. The double CWT method can be used for analyzing cardiac rhythms and neural activity, as well as nonstationary processes in quantum radio physics and astronomy.     

High frequency and static dielectric constants of zinc blende structured solids

A correlation is presented for the high frequency ε_∞ and static ε_o dielectric constants of A^IIB^{V I} and A^IIIB^V semiconductors with the zinc blende structure. The high frequency ε_∞ and static ε_o dielectric constants can be represented by an empirical linear relation that is a simple function of melting temperature T_m, atomic volume Ω and product of ionic charges (Z₁Z₂). Values of high frequency ε_∞ and static ε_o dielectric constants of A^IIB^{V I} and A^IIIB^V zinc blende semiconductors exhibit a linear relationship when plotted against the k_BT_m/Ω (k_B=Boltzmann’s constant), but fall on two straight lines according to the product of ionic charges of the compounds. The calculated results are compared with available experimental data and previous calculations based on phenomenological models.     

Dielectric dispersion in the microwave range of the incommensurate phase (NH4)2BeF4

The complex dielectric constant of (NH₄)₂BeF₄ single crystals was measured in the frequency range from 0.6 to 300 MHz in the vicinity of the transition temperature T_c. It was found that, the relaxation frequency is about 1 × 10⁸Hz atT_c. Dielectric relaxation can be described by a polydispersive process.     

Effect of an ac field on the conductance fluctuations for mescoscopic systems

With the use of perturbation theory to perform impurity averaging, the conductance fluctuations (CF) in mesoscopic systems are evaluated at finite frequency (ω) of the applied electric field. Calculations are carried out for frequencies much smaller than the inverse elastic mean free time, ω≪τ_el⁻¹. It is shown that the CF decrease monotonically as ω increases. Also, the frequency scale over which this decrease occurs is given by τ_diff⁻¹≪τ_el⁻¹, where τ_diff is the time for an electron to diffuse across the sample. This means that the universality of the CF at zero frequency is not preserved at finite frequency. These calculations are for a rectangular prism. Six leads covering the probe faces are attached to the cube. It is also shown that at finite frequency the sample-to-sample CF have the same size as the fluctuations of a given sample as a function of frequency.     

Pulsed NMR frequency shifts in superfluid 3He

We report the first measurements of the NMR frequency in ³He A and B under conditions where the net magnetization, M, is tipped far from its equilibrium direction along H_O. In ³He A the frequency shift ω - γH_O varies from the continuous wave value at tipping angle Φ = 0 to a negative shift at Φ = 180°. In ³He B no frequency shift is observed, however for Φ ? 100° a beat pattern is seen to develop in the free induction decay envelope.     

The self-consistent determination of HF electroconductivity of strongly coupled plasmas

Here is presented the calculation of the dynamic electrical conductivity of fully ionized, strongly coupled plasmas as a function of the external electric field frequency ω. The calculations are based on the formula for the energy-dependent collision frequency which is determined by means of the Green function theory methods, as a sum over the Matsubara frequencies. The domain of extremely high electron density: ¹⁰²¹?ne?¹⁰²⁴ cm−3, and for the temperature varying from 10 kK to 1000 kK was examined. The real and imaginary parts of the conductivity for every electron density are presented in the generalized Drude-like form as a two-parameter function of the frequency ω in the region 0<ω<0.5ωp, where ωp is the plasma frequency. A good agreement between the obtained results and the existing theoretical and computing simulation data is shown.     

Improved deuterium bromide 1-0 band molecular constants from heterodyne frequency measurements

Heterodyne frequency measurements have been made on selected deuterium bromide 1-0 band transitions ranging from P(20) to R(17). Difference frequency beat notes between a tunablediode laser whose frequency was locked to the DBr absorption lines and a CO laser whose frequency was either locked or adjusted to a reference synthesized from CO₂ laser frequency standards were measured. The beat note frequency was then combined with the measured CO laser frequency to give the DBr frequency. For two of the measurements, frequency-doubled CO₂ laser radiation was substituted for the CO laser radiation. The measurements included electric quadrupole split triplets comprising the R(0) and P(1) transitions in the D⁷⁹Br isotope. New DBr constants have been determined, and a table of frequencies is presented for the calibration of spectrometers and tunable lasers in the wavenumber range 1600 to 1990 cm^?1. A table of far-infrared frequencies is also given for DBr covering the range from 50 to 206 cm^?1.     

Isotope shift and HFS ofD 1 lines in Na-22 and 23 measured by saturation spectroscopy

High resolution saturation spectroscopy was applied to measure the relative isotope shift of theD ₁ lines in radioactive²²Na against²³Na in vapour cells. The result,δν=758.5(7) MHz, combined with other known values, indicates that the field shift is negligible in sodium isotopes. The hyperfine coupling constant of the² P _1/2 level in²²Na was found to be 37.0(1) MHz. A frequency offset locking technique is described which renders an accurate frequency calibration and achieves a long-term frequency stabilization.     

Observation of dynamical effects in paramagnetic resonance of Eu in Yb - metal

Electron-spin-resonance measurements of Eu²⁺ in Yb-metal have shown that, in the g- is almost totally suppressed by dynamical effects. By adding nonmagnetic Ca-impurities the g-shift is increased, revealing a temperature and frequency dependent g-value and linewidth, which can be described by the formulas of Hasegawa. The exchange-integral between 4f electrons of the Eu²⁺-ion and the conduction electrons was determined to be J = +0.09 eV.     

Radiation damping of magnetostatic modes in yig

The radiation induced linewidth of magnetostatic modes in spheres of Yttrium Iron Garnet has been measured in microwave experiments. The linewidths of the lowest order modes (n m 0) have a ω²ⁿ⁺¹ frequency dependence which can be explained by multipole radiation.     

Electrical conduction and dielectric properties of vanadium phosphate glasses doped with lithium

AC conductivity and dielectric studies on vanadium phosphate glasses doped with lithium have been carried out in the frequency range 0.2-100 kHz and temperature range 290-493 K. The frequency dependence of the conductivity at higher frequencies in glasses obeys a power relationship, σ_ac=Aω^s. The obtained values of the power s lie in the range 0.5≤s≤1 for both undoped and doped with low lithium content which confirms the electron hopping between V⁴⁺ and V⁵⁺ ions. For doped glasses with high lithium content, the values of s≤0.5 which confirm the domination of ionic conductivity. The study of frequency dependence of both dielectric constant and dielectric loss showed a decrease with increasing frequency while they increase with increasing temperature. The results have been explained on the basis of frequency assistance of electron hopping besides the ionic polarization of the glasses. The bulk conductivity increases with increasing temperature whereas decreases with increasing lithium content which means a reduction of the V⁵⁺.     

Rydberg states in the D layer of the atmosphere and the GPS positioning errors

The noncoherent radiation in the frequency range 0.8–8.0 (GHz) formed in the D layer of the ionosphere at high solar activity due to transitions between Rydberg states is considered. The emitting layer thickness located 80–110 km above ground surface is estimated. A complicated irregular behavior of the frequency dependence of the radiation intensity for different values of å electron concentration n _e and temperature T _e due to different characteristics of electron scattering on the nitrogen and oxygen molecules is revealed. The dependences of the flux power of UHF radiation from the D layer in the indicated frequency range on the concentration and temperature of free electrons are calculated. It is shown that, at a frequency of ν = 1.44 GHz, the UHF radiation spectrum features a characteristic waist point, the position of which is almost independent of the electron temperature T _e ; i.e., a one-parameter dependence of the power flux on the electron n _e density takes place. In the frequency range of 4.0–8.0 GHz, the radiation spectrum exhibits a family of curves that, for each value of n _e and a wide range of T _e , give rise to a relationship known as the “bottleneck.” It was found that, with increasing frequency, the bottleneck moves upwards along a curve described by a quadratic dependence on the radiation frequency. For a frequency of ～5 GHz, and a certain range of temperature T _e and electron concentration within 5 · 10³ cm^?3 < n _e < 2 · 10⁴ cm^?3, an almost linear dependence of the UHF radiation power on n _e is observed. A comparative analysis of GPS signal delays at frequencies ν _f ⁽¹⁾ = 1.57 and ν _f ⁽²⁾ ≈ 5 GHz for various states of the ionosphere is performed. It is shown that, under the same condition, the use of the second frequency is more advantageous and informative. The ways of further development of the theory and experiment in studying the role of quantum resonant properties in the distortion of global satellite positioning system signals and in solving the fundamental problem of their elimination are discussed.     

Influence of mobile space charges on electrical properties of ferroelectric Bi3.5La0.5Ti3O12 thin films

Lanthanum-substituted bismuth titanate, Bi_3.5La_0.5Ti₃O₁₂ (i.e., x=0.5 in Bi_4−xLa_xTi₃O₁₂), thin films have been grown on Pt/Ti/SiO₂/Si substrates using pulsed laser deposition. The frequency dependence of the real part ε′(ω) and the imaginary part ε″(ω) of the dielectric constant has been studied. The ε′(ω) does not show any sudden change within the frequency range of 10²-10⁶ Hz. In contrast, the ε″(ω) shows a large dispersion as frequency decreases. The observed relaxation behavior in ε″(ω) can be explained in terms of a migration of oxygen vacancies in (Bi₂O₂)²⁺ layers, not in Bi₂Ti₃O₁₀ perovskite layers.     

The optical conductivity of free carriers in GaAs

The optical conductivity of free electrons in polar semiconducting compounds has recently been calculated by use of a generalized Boltzmann equation derived from the equation of motion of the quantum density matrix. This reduces to the quasi-classical Boltzmann transport equation in the low frequency limit: the optical conductivity thus obtained spans a spectral range from around 30cm^?1 to 1.2 × 10⁴cm^?1 in GaAs. In this paper, the optical conductivity is calculated for GaAs as a function of carrier concentration in terms of a frequency dependent relaxation time which reduces to the usual relaxation time in the limit of low frequencies and an elastic scattering mechanism. The low frequency limit of the relaxation time is used to estimate the mobility as a function of carrier concentration. The frequency dependent relaxation time is given for GaAs at 298 K over the spectral region from 45 cm^?1 to 2.3 × 10³cm^?1 for carrier concentrations from 3.4 × 10¹⁵cm^?3 to 8.7 × 10¹⁸cm^?3.     

Dipolar and quadrupolar detection using an FT-ICR MS setup at the MPIK Heidelberg

Dipolar and single-phase two-electrode quadrupolar detection schemes have been investigated at a Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) setup built for the KATRIN experiment at the Max-Planck-Institute for Nuclear Physics (MPIK) in Heidelberg. We present first experimental results of ⁷Li^?+? signals from a cylindrical Penning trap configuration for both detection schemes. While the prominent signal of the conventional dipolar detection scheme marks the reduced cyclotron frequency, the main signal for the quadrupolar detection appears at the sum of the reduced cyclotron frequency and the magnetron frequency. For ideal trapping fields, this sum frequency equals the ion cyclotron frequency ?? _c ?=?qB/(2??m). Sidebands due to the combined motions of the cyclotron mode and magnetron mode are observed by quadrupolar detection which allows the determination of the respective combinations of eigenfrequencies.