- eigenfunctions of the energy operator χ (n. - n-th order susceptibility of the medium, (erg/cm 3 ) (1 − n)/2 =(Hs) 1 − n ψ, Ψ, wave function. - 2.3.7 ◦ Degeneracy of the levels. - 3.1.4 ◦ More general definition of the density matrix. - 3.1.5 Properties of the density matrix. - 3.3 Evolution of the density matrix. - 4.1.4 ◦ Susceptibility of the vacuum. - 4.3.1 Applicability of the model. - 6.1.5 The role of the material symmetry. - 7.2 Basic concepts of the statistical optics. - 7.3.3 ◦ Hamiltonian of the field and the matter. - 7.4 Quantization of the field. - 7.4.3 Quantization of the field in a cavity. - 7.5 ◦ States of the field and their properties. - The released energy, E 2 − E 1 , is transferred to the electromagnetic field in the form of the second photon. - lasers appeared at the beginning of the 1960s.. - The parameters of the lasers (power, monochromaticity, directivity, stability, tunability) were con- tinuously improving. - beginning of the 1950s in the fields of radio and optical spectroscopy. - 7.2) in 1956, had ‘explosive’ development in the end of the last century. - In the absence of the alternating field, the wave function can be represented as Ψ (0) (r, t. - (b) corresponding con- figurations of the electron cloud.. - (This possibility follows from the completeness of the eigenfunctions set ϕ n (r. - Thus, due to the effect of the incident light, the relative populations | c n (t. - 2 of the levels are redistributed (with the normalization condition (2.7) maintained). - which can be considered as the wavefunction of the system in the energy representation (while Ψ(r) is the wave function in the coordinate repre- sentation). - Thus, we look for the solution to (2.14) in the form of the sum c n = c (0) n + c (1) n. - a ) The squared mod- ulus of the transition amplitude. - therefore, c mn is the amplitude of the transition n → m.. - 0) under the condition that the frequency of the field (ω >. - Let us first find the energy E of the wave. - Maximal (resonance) value of the absorption coefficient in the case of a Lorentzian line shape (2.39) is. - of the observed resonance at α <. - according to one of the delta-function representations,. - 3.1, we discuss the definition and the general properties of the density matrix. - 3.1 Definition and properties of the density matrix 3.1.1 Observables. - Let us define the entropy operator in terms of the density operator in the following way: ˆ S. - (3.30) i.e., the effective temperature is simply a logarithmic measure of the population ratio. - One can easily show that this requires degeneracy of the carriers in the bands,. - 3.3 Evolution of the density matrix 3.3.1 Non-equilibrium systems. - Here, we used the Hermiticity of the energy operator, H. - (3.58) with T being the temperature of the thermostat. - (4.27) In the last equation, we have used the symmetry of the χ tensor. - Therefore, the internal energy of the matter in the presence of the field is. - The next step is calculating χ(ω) in the framework of the microscopic theory.. - Thermal motion of charges can be taken into account in the framework of the kinetic theory. - 0 outside of the resonance).. - (ω) by the absence of the damping parameter γ.. - In the. - c.c., (4.86) where E 0 (t) is the slowly varying amplitude of the field. - This effect, leading to the Bennett hole burn- ing in the velocity distribution of the molecules (Fig. - (ω 0 −ω)/k on the direction k of the wave propagation. - In the latter case, the observable is the magnetic moment h µ i of the particle or magnetization M = N h µ i . - Therefore, the Hamiltonian of the system scales as the ˆ σ z operator,. - Let us find the length of the R vector. - [1 + (ω 0 − ω) 2 T and the length of the R vector, according to (4.92), is. - 4.9 Relaxation of the Bloch vector R. - c mn | 2 for a multi-level system in the first order of the perturbation theory. - ϕ 0 is the initial phase of the field at the center of the atom. - 0 or π, then, due to the effect of the field, R moves along a meridian with the longitude ϕ 0 ± π/2.. - 5.1 Nutation of the Bloch vector R. - Then (5.3) is satisfied by the following functions of the. - The last equation can be understood in terms of the transition probability. - Note that the amplitude of the field required for stationary saturation, E 0. - Absorption of the field. - (4.15), by the imag- inary part of the susceptibility. - 5.3) due to the free precession of the R vector. - However, the second half of the pulse. - Assuming that it is equal to the initial energy of the atom. - therefore h d 2 i = d 0 2 regardless of the state of the atom. - At t 1/A, the energy of the field is ~ ω 0 /2 only on the average. - Let us consider the time dependence of the dipole emission power.. - Due to the optical anharmonicity of the matter (Sec. - 0, then the frequency of the anti-Stokes satellite (the right-hand one, on the frequency scale) is. - The mean dipole moment of the system is h d i = h ψ | X. - nonlinear absorption scaling as the square of the light intensity. - Let us first reduce the consideration to the case of the nonlinearity quadratic in the external field. - case where the field frequencies and their combinations are in the transparency windows of the matter. - Thus, every component of the ¯ χ(ω, ω 0 ) tensor, considered. - Comparison of the latter with (6.3) yields (6.14).. - Note that the signs and the values of the powers P n depend on the field phases.. - The role of the material symmetry. - where m + 1 is the rank of the tensor. - where r e ≡ e 2 /mc cm is the classical radius of the electron. - where I = c | E 1 | 2 /8π is the intensity of the plane wave. - 5.2), then the width of the resonance is minimal (the natural width), 2γ rad = A. - Now, let all frequencies of the field be in the transparency range of the matter.. - where ρ is the density of the matter. - ∆N/N = ∆ρ/ρ = β T ∆p, (6.65) where β T is the isothermic compressability of the medium. - and the corresponding sidebands ω 2 = ω 1 ± Ω appear in the spectrum of the scattered light. - 1 , i.e., the relaxation time of the temperature grating.. - The mechanism of the stimulated temperature scattering (StTR) and the corre- sponding anharmonicity is evident in the presence of some absorption (StTR-2).. - therefore, the wave of the susceptibility has the amplitude χ Ω = ωχ 00 /c p ρ. - τ T , (6.104) where τ E = n/αc is the relaxation time of the field. - Let us estimate the contribution of the electrocaloric effect in the temperature anharmonicity. - Let us estimate the contribution of the orientation anharmonicity in the cubic susceptibility. - We are interested in the stationary response of the system to a periodic pertur- bation. - (6.134) Susceptibility of the next order is calculated similarly. - frequencies coincides with the frequency of the transition a → b. - as well as the imaginary part of the cubic susceptibility χ (3) (ω 2. - After summing over all modes in the vicinity of the frequency ω ba − ω 1 , we find