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.     

Collision-induced amplification of short-wave radiation on transitions to the ground state of atoms

A new version of obtaining short-wave lasing on transition between highly excited states and the ground state of active atoms in the buffer gas atmosphere is studied theoretically. The mechanism of obtaining population inversion on such a transition is associated with the establishment of the local Boltzmann distribution of populations in a group of highly excited levels due to frequent collisions. If the excitation of the upper-lying level is performed by two laser radiation sources with frequencies ω₁ and ω₂, short-wave lasing can be obtained at a frequency close to the total frequency ω₁ + ω₂. The conditions for the emergence of population inversion are analyzed and simple analytic formulas are derived. It is shown that collision-induced enhancement of short-wave radiation can occur for pumping intensities on the order of 100 W/cm². For pumping intensities on the order of 1000 W/cm², the amplification factor for short-wave radiation may attain values of 3 cm^?1 (for an active atom concentration of N ～ 10¹⁵ cm^?3), which is sufficient for the development of lasing per path through an active medium (superradiance condition) for a length of the active medium on the order of 10 cm.     

Photoinduced infrared activity in trans(CH)x: Inter[retation in terms of a lattice dynamical model

A lattice dynamical calculation for the photoinduced infrared vibrational modes is reported. By using the perturbed Green function method we have been able to compute the new frequencies and the integrated intensities of the photoinduced infrared modes at ω_1H⋍500 cm⁻¹, ω_2H⋍1260 cm⁻¹ and ω_3H⋍1370 cm⁻¹ in trans(CH)_x and at ω_1D⋍400 cm⁻¹ and ω_2D⋍1045 cm⁻¹ in trans(CD)_x. Most of the features of the photoinduced infrared spectra can be explained in terms of long conjugation length segment properties. Only the higher frequency tail of the band shape peaked at ω_1H and ω_1D can be related to the pertubbation determined by a photogenerated charge trapped in short segments. The calculated frequencies and integrated intensities are in good agreement with the experimental results.     

Picosecond measurements of the third order susceptibility tensor in liquids

Single frequency Jamin interferometry is used for observation of non-linear susceptibility tensor measurements in the picosecond range (25 ps). At low density, when avoiding the polarization state instabilities, the displacement of the fringes leads to the measurement of two components of the nonlinear susceptibility tensor. It is shown that X_xyyx (ω = ω + ω - ω) decreases when the pulse duration is reduced, whereas X_{xxxx (ω = ω + ω - ω)} remains constant. This is interpreted by the difference between the orientational and vibrational molecular contributions.     

Double resonance in the system of coupled Josephson junctions

The effect of LC shunting on the phase dynamics of coupled Josephson junctions has been examined. It has been shown that additional (rc) branches appear in the current-voltage characteristics of the junctions when the Josephson frequency ω_J is equal to the natural frequency of the formed resonance circuit ω_rc. The effect of the parameters of the system on its characteristics has been studied. Double resonance has been revealed in the system at ω_J = ω_rc = 2ω_LPW, where ω_LPW is the frequency of a longitudinal plasma wave appearing under the parametric-resonance conditions. In this case, electric charge appears in superconducting layers in the interval of the bias current corresponding to the rc branch. The charge magnitude is determined by the accuracy with which the double resonance condition is satisfied. The possibility of the experimental implementation of the effects under study has been estimated.     

On the low-temperature thermal conductivity of Ni-doped Al2O3

An attempt is made to explain the lower resonance anomaly in the thermal conductivity of Ni-doped Al₂O₃ by using τ_r ～ ω^-4s(ω² ? ω²_r)². An agreement between theory and experiment needs s = 0.71, and this is interpreted to mean that the frequency dependence of impurity-phonon coupling is approximately described by ω^0.71 for phonons having frequencies in close neighbourhood of ω_r.     

Nonlinear mixing of oppositely travelling surface plasmons

A theoretical treatment of the nonlinear mixing of two contra-directional surface plasmons of frequency ω₁ and ω₂ propagating on a semi-infinite metal surface is presented. The nonlinear interaction is analysed in terms of (a) nonlinear surface currents due to the breaking of inversion symmetry and the rapid variation of the normal electric field component at the surface, and (b) the nonlinear response of the electron gas in the bulk of the metal. These currents are treated as source terms for Maxwell's equations and electromagnetic fields are found which satisfy the driven wave equation and boundary conditions at the frequencies ω₁ ± ω₂. At the difference frequency ω₁ ? ω₂ the solution fields decay exponentially into both the air and the metal. However, at the sum frequency ω₁ + ω₂, coupling to transverse electromagnetic waves in both the air and the metal is predicted under appropriate wavevector and frequency conditions. The free-space radiation field is treated in detail and the feasibility of its experimental detection is discussed. No coupling to longitudinal bulk plasmons is predicted in this model of the nonlinear interaction.     

Resonances of orientation and alignment of atoms in the case of inclined optical pumping

It is shown that, with pumping inclined relative to a constant magnetic field H₀, the radio-frequency (RF) magnetic field rotating at frequency Ω induces new resonances ω₀ = γ H ₀ and 2Ω for the Fourier components of orientation and ω₀ = ?Ω, Ω/2, 3Ω/2, 2Ω, and 3Ω for the components of alignment. New resonances excited by the oscillating RF field are also considered.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Nonlinear Raman scattering of photons by a channeled particle

Channeled particles are characterized by the discrete spectrum of bound transverse motion. The interaction of photons with channeled particles in single crystals can be accompanied by energy transitions between the levels of transverse motion of the channeled particle. The Raman scattering of photons at a quasibound channeled particle leads to the appearance of a combination of frequencies: the incident radiation frequency ω₀ and the frequency Δω_{m, n}, i.e., ω = ω₀ ± Δω_m,n where Δω_m,n = 2Δε_m,nγ²; Δε_{m, n} is the energy of the transition between quantum states (m and n) of the transverse motion of the channeled particle; and γ = E/mc² is the Lorentz factor of the channeled particle. The appearance of a violet satellite (the anti-Stokes component) in the Raman scattering spectrum is analyzed. The three-photon Raman-type transition, which is the process of the simultaneous absorption of two photons with the frequency ω₀ with the emission of a photon with the frequency ωs = 2ω₀ ± 2Δε_m,nγ², is considered. The conditions for resonance observation during the formation of the second harmonic (ω = 2ω₀) are discussed.     

Far-infrared reflection spectra,TO- and LO-phonon frequencies,coupled and decoupled plasmon-phonon modes,dielectric constants,and effective dynamical charges of manganese,iron, and platinum group pyrite type compounds

The far-infrared reflection spectra of hot-pressed samples of the pyrites MX₂ with M = Mn, Fe, Ru, and Os and X = S, Se, and Te and PtY₂ with Y = P, As, and Sb are presented in the range from 40 to 700 cm^?1. The spectra show five reststrahlen bands and more or less free carrier contributions due to deviation from stoichiometry. The oscillator parameters ω_j, ρ_j, γ_j, ω_p, and γ_o, the transverse optical phonon frequencies ω_TO, and the coupled plasmon-phonon frequencies Ω₊ and Ω_? were calculated. The uncoupled longitudinal optical phonon frequencies ω_LO were determined from ?Im $\text{(}\text{1}\text{}\text{?}\text{ge}\text{)}$ of the plasmon-free phonon spectra calculated from the oscillator parameters, neglecting the free carrier contributions. The obtained effective ionic charges (Szigeti charges) reveal an increasing covalency of the pyrites in the order pnictides > chalcides and Fe > Ru > Os > Mn compounds. The phonon frequencies reflect the increasing bond strengths on going from 3d to 4d and 5d metal compounds, discussed in a former work (Phys. Chem. Miner.9, 109 (1983)). The true intensities of the phonon modes for using them with respect to lattice dynamical calculations are discussed.     

激光拍频波加速器的参数选择

本文研究了激光拍频波加速器中的三波相互作用过程。结果表明:适当地选择参数σ=ω_p/(ω₁-ω₂)以及β=ω₂/ω₁(ω_p,ω₁,ω₂分别为等离子体频率及两束激光频率),即可用较弱的激光造成很强的拍频等离子体波,并使注入等离子体的电子获得显著的能量增益。 关键词：     

Stimulated Raman spectra of a strong bichromatic field interacting with a three-level atom

We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω _a and ω _b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω _ab = ± (ω _a - ω _b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω _ab , four pairs of lorentzian lines peaked at the frequencies ω - ω _ab = ± Ω _a /√2, ± Ω _b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ₀/4. The parameter Ω is defined as Ω² = (Ω _a ² + Ω _b ²)/2, where Ω _a and Ω _b are the Rabi frequencies of the two laser fields and γ₀ is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.     

Effect of two-photon saturation on ordinary Raman scattering

The excitation profile of ordinary Raman scattering under steady-state excitation conditions and the time-resolved emission spectrum of ordinary Raman scattering under transient excitation conditions undergo considerable changes when the excitation frequency ω approaches $\text{1}\text{2}$ ω_mn, where ω_mn is the resonance frequency of a two-photon transition from the ground state |n to an excited state |m of a molecule. The appearance of ghost peaks, dips or dispersion-like features centred at ω ? $\text{1}\text{2}$ ω_mn in the excitation profile and of coherence effects such as Rabi nutations with unusual time-dependence in the time-resolved spectrum are predicted.     

The energy loss function of the polaron gas

The energy loss function Im 1/K(π, ω) of a gas of polarons is calculated in the RPA approximation. For typical densities of degenerate polar semiconductors, the energy loss function has pronounced structure. Up to three resonances appear. The coupled phonon-plasmon resonance, with frequency between ω_TO and ω_LO, leads to an extremely sharp peak in Im 1/K(π, ω), for appropriate values of wavevector and densities.     

Surface-plasmon-polariton dispersion of semiconductors with depletion layers

For a sample with plasma frequency varying exponentially from ω_ps at the surface to a larger value ω_pb in the bulk, and moderate damping, we find, contrary to other calculations, that the long wavelength surface plasmon dispersion has a single branch that is reentrant at ω = ω_ps.     

Point-contact spectroscopy of electron relaxation mechanisms in semiconductors

The I–V characteristic of a tiny semiconducting channel connecting bulk electrodes is shown to have singularities arising due to phonon emission by hot electrons at energies eV = n?ω₀, where ω₀ is the optical phonon frequency and n = 1, 2, 3,…. The nonlinear part of the I–V curve provides direct information concerning the energy dependence of the elastic-scattering time of charge carriers.     

A two—dimensional photonic crystal with six large bandgaps formed by a hexagonal lattice of anisotropic cylinders

The plane-wave expansion method is used to calculate the band structure of a two-dimensional photonic crystal formed by a hexagonal structure of anisotropic cylinders. Two cylindrical inclusions in the unit cell have two different radii, R₁ and R₂ (R₁2). By reducing the symmetry of the structure and choosing appropriately parameters R₂ and s=R₁/R₂ (s<1), we obtain six large complete bandgaps, among which three are over 0.05 ω_e (where ω_e=\frac{2πc}{a}) in the high region of the normalized frequency (however, one of these over 0.065 ω_e is not stable). There are two other stable complete bandgaps in the low-frequency region.     

Frequency Dependence of the Dielectric Loss Angle in Disordered Semiconductors in the Terahertz Frequency Range

Frequency dependence of the real part of the conductivity σ₁(ω) in the region of the transition from almost linear (s < 1) to quadratic (s ≈ 2) can indicate a change in the conduction mechanism (the transition from the variable-range to the fixed-range hopping with increasing frequency); in this case, the sharpness of the change in the slope of the frequency characteristic is related to the dependence of the preexponential factor of the resonance integral on the intercenter distance in the pair. The frequency dependence of the imaginary part of the conductivity σ₂(ω) has no kink in the vicinity of the transition frequency ωcr, remaining almost linear. A large dielectric loss angle |cotγ| = |σ₂|/σ₁ can indicate that the imaginary part of the conductivity at ω < ω_cr is defined by the larger zero-phonon contribution in σ₂^res the region of weak variation in the loss angle γ(ω), which significantly exceeds the relaxation contribution σ₂^res.