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.
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.
We have considered the excitation spectra arising from stimulated two-photon transitions between two atomic levels of the same parity. The system consists of a three-level atom in the cascade configuration interacting with two strong electromagnetic fields whose initially populated modes ωa and ωb are in resonance with the two atomic transition frequencies, respectively. The Green function formalism is used to calculate the spectral function of the system near the frequencies ω=ωa+ωb, in the limit of high photon densities. The excitation spectra consist of Lorentzian lines peaked at the frequencies ω−ωa−ωb=0, ±Ωa/√2, ±Ωb/√2, ±Ω, and ±2Ω, where Ω2=(Ω2a+Ω2b)/2 and Ωa,Ωb are the Rabi frequencies of the two laser fields, respectively. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. The computed two-photon spectra are compared with those arising from the third-order nonlinear mixing of frequencies near ω=ωa+2ωb and ωb+2ωa, respectively, as well as with those of the stimulated Raman spectra near ω=±(ωa−ωb).
We have studied the excitation spectrum arising from the interaction of a two-level atom with two strong electromagnetic fields whose initially populated modes ω a and ω b are near resonance with the atomic transition frequency In the limit of high photon densities the Green's function of the system describing the electronic transition in question has been derived in a closed form and includes processes arising from the interaction of seven photon modes of both laser fields. The spectral function of the system is calculated when the frequency ω a of the one laser field is in resonance with the atomic transition frequency while the frequency ω b of the other field is varied. The excitation spectrum is found to consist, apart from the central peak at the excitation frequency ω a , of several lorentzian lines which are peaked in the neighbourhood of the frequencies ω a ± Δ, ω a ± 2Δ, ω a ± 3Δ and ω a ± 4Δ, where Δ = ω a - ω b and describe the type of optical mixing of light modes which is of the third, fifth, seventh and ninth order, respectively. Additional peaks appear in the spectra, which result from the interaction between the frequency modes in question. The probability amplitudes describing the relative intensities of the peaks in question are expressed as functions of the parameters η a = Ω a /Δ and η b = Ω b /Δ, where Ω a and Ω b are the Rabi Frequencies of the two laser fields, respectively. It is found that when η a ⩾ 1 and η b ⩾ 1 the expression for the relative intensities of the bands in question are remarkably enhanced and take extremely large positive or negative values. Results of numerical calculations for a wide range of values of η a and η b when η a = η b ⩾ 1 are presented graphically and the complete excitation spectrum is discussed in detail. The method may be useful to investigate the behaviour of excited states as well as those close to the limit of ionization.
We have considered the fluorescent spectra arising from the interaction of a four-level atom with two strong electromagnetic fields whose initially populated modes ω a and ω b are in resonance with three of the atomic transition frequencies. Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ±(2ω a - ω b ). Expressions for the total relative intensity of the system have been derived as a function of the parameter ζ = Ω2 b /Ω2 a , where Ω a and Ω b are the Rabi frequencies of the two laser fields, respectively. For ζ = 0, the spectra consist of a central peak at ω = 2ω a - ω b and a pair of sidebands at ω = 2ω a - ω b ± Ω a √2, both having spectral widths of the order of γ0, where γ0 is the spontaneous emission probability. The relative intensity of the central peak for Ω a ≠ 0 is reduced by 25 per cent of its original value obtained for Ω a = 0. For ζ ≠ 0, the relative intensity of the central peak increases slowly as ζ increases while that of the pair of sidebands at ω = 2ω b - ω b ± Ω a √2 is reduced by a factor of two of its given value for ζ = 0. This destructive interference is due entirely to the presence of the second laser field with Ω b ≠ 0. A new pair of sidebands, which arise from the cooperative effect of both laser fields, is peaked at ω = 2ω a - ω b ± Ω a √(2 + 0·5ζ) and has a spectral width equal to γ0. A set of four pairs of sidebands also appear at ω = 2ω a - ω b ± Cj (ζ)Ω a with j = 1, 2, 3, 4, respectively, which have spectral widths of the order of 3γ0/2. The existence of these pairs of sidebands depends strongly on the value of the parameter ζ. Numerical estimates for the coefficients Cj (ζ) and the relative intensities of these sidebands are tabulated for a wide range of values of ζ and discussed in detail.
We have considered the stimulated Raman spectra arising from interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states ‖3〉 and ‖4〉 and two lower states ‖1〉 and ‖2〉, where the metastable state ‖2〉 is depleted through the action of two strong laser fields operating between the states ‖2〉↔‖4〉 and ‖2〉↔‖3〉, respectively. Using a model Hamiltonian, where all the free and interacting fields are quantized, and the Green function method in the limit of high photon densities of both laser fields, we have studied stimulated two-photon processes near the frequencies ±ω≊ω21≊ω41 −ωa≊ω31 −ωb for the ‖1〉→‖2〉 electric dipole forbidden transition describing physical processes, where one photon of the signal field with frequency ω41(ω31) is absorbed while a photon of the laser field with frequency ωa(ωb) is emitted and vice versa; ωij refers to an atomic transition frequency between the states ‖i〉 and ‖j〉. The spectral function for the stimulated two-photon processes consists of a central peak at the frequency ω=ω21, which has a delta function distribution indicating the stability of the mode in question, and three pairs of sidebands, where one pair of sidebands is induced by each laser field, respectively, while the third pair of sidebands is induced by both laser fields simultaneously. The intensities of the sidebands are always negative indicating that strong amplification (stimulated emission) takes place at the corresponding frequencies. The computed resonance and off-resonance spectra are graphically presented and discussed. When a classical description for both laser fields is used, the spectral function is found to describe one pair of sidebands, which is induced by both laser fields simultaneously; this classical result is graphically presented and compared with those obtained when the fields are quantized. It is shown that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photon fields which is lost in the classical picture. The effect of the quantum nature or, equivalently, the boson character of the photon is to split the ‘‘classical’’ spectrum described by one pair of sidebands into three pairs, whose sum of relative intensities is equal to that of the original pair derived classically.
We have considered the excitation spectra of three-photon processes arising from the interaction of a three-level atom, in the cascade configuration, with two strong electromagnetic fields whose initially populated modes ω a and ω b are near resonance with the atomic transition frequencies ω21 and ω32, respectively. In the limit of high photon densities, expressions for the Green's functions are derived in a closed form describing third order nonlinear processes in the region of frequencies ω = ω a + 2ω b and ω = ω b + 2ω a , respectively. Numerical calculations are then performed and the computed spectra are presented graphically for different values of the Rabi frequencies Ω a and Ω b , and detunings ζ a and ζ b , respectively. The excitation spectrum near ω = ω a + 2ω b is calculated as a function of the parameters η a = Ω a /γ0, η b = Ω b /γ0, ζ a = (ω21 - ω a )/γ0 and ζ b = (ω32 - ω b )/γ0 where γ0 is the spontaneous transition probability. With no detuning the spectral intensities vary slowly with respect to variations of the Rabi frequencies and are shifted by amounts governed by the field strengths η a and η b . In the presence of detunings, asymmetries, characteristics of such off-resonance situations, arise enhancing certain spectral peaks while diminishing the intensity of others.
We have studied the excitation spectrum arising from the optical mixing of the frequencies of a strong bichromatic field interacting with a three-level atom, where the two initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. In the limit of high photon densities, the excitation spectrum near the frequency ω = ωa – 2ωb has been calculated as a function of the parameter η = Ωa2/Ωb2, where Ωa and Ωb are the Rabi frequencies of the two laser fields, respectively. For [Formula: see text] and for weak fields for which [Formula: see text], the spectral function describes a Lorentzian line peaked at the frequency ω = ωa – 2ωb and has a width of the order of γ0, where γ0/2 is the natural width for a two-level atom. When Ωb2 > γ02 and [Formula: see text], the band at ω = ωa – 2ωb splits into two bands described by two Lorentzian lines peaked at ω = ωa – 2ωb ± Ωb/√2 and have spectral widths of the order of 3γ0/4. The ratio of the height of the band ω = ωa – 2ωb to the height ω = ωa – 2ωb ± Ωb/2 is 3:2. The probability amplitudes for both bands take large negative values indicating that optical amplification of the signal field may be expected to occur at these frequencies. When Ωa = Ωb = Ω, η = 1, and for Ω2 < γ02, the spectral function describes a single band at ω = ωa – 2ωb while for Ω2 > γ02, the single band splits into five pairs of bands which are separated from the frequency ω = ωa – 2ωb by frequency shifts which are equal to: ± Ω/√2, [Formula: see text], ± Ω, ± Ω√2, and ± Ω√3, respectively, and have spectral widths of the order of 3γ0/4. For [Formula: see text] and for laser fields for which Ωa2 > γ02 and Ωb2 > γ02, the spectral function consists of three pairs of bands. The probability amplitudes for these bands vary linearly with η and may take large values for [Formula: see text]. A complete discussion of the excitation spectrum as well as a graphical representation of the derived results has been given.