We have performed a numerical calculation for the excitation spectra arising from the interaction of a three-level atom in the lambda configuration with a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered for equal detunings, which refer to the cooperative two-photon resonance process, as well as for different detunings. The computed cooperative two-photon resonance spectra are compared with those derived by analytical methods. In the presence of different detunings, conditions are established under which the laser field induces sidebands at the frequency equal to that for the forbidden transition. Numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically. Detailed discussion of the computed spectral intensities is given and a comparison is made between the spectra of three-level atoms in the lambda and cascade configurations.
We have performed a numerical calculation for the excitation spectra arising from the interaction of a three-level atom in the lambda configuration with a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered for equal detunings, which refer to the cooperative two-photon resonance process, as well as for different detunings. The computed cooperative two-photon resonance spectra are compared with those derived by analytical methods. In the presence of different detunings, conditions are established under which the laser field induces sidebands at the frequency equal to that for the forbidden transition. Numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically. Detailed discussion of the computed spectral intensities is given and a comparison is made between the spectra of three-level atoms in the lambda and cascade configurations.
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 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 consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.
We have considered the fluorescence spectra arising from the interaction of a three-level atom in the ‘‘V’’ configuration with two strong electromagnetic fields whose initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. The excitation spectra are calculated by making use of the Green function formalism where the hierarchy of the Green functions is truncated by a decoupling scheme which takes into account photon–photon correlations from each laser field in the limit of high photon densities. The excitation spectra consist of the central peak of the excitation frequency ωa and four pairs of sidebands, which are peaked at the frequencies ωa±η1(2)1/2, ωa±η2/(2)1/2, ωa±(η21+η22)1/2/(2)1/2, and ωa±2(η21+η22)1/2/(2)1/2, where η1 and η2 are the Rabi frequencies of the two laser fields, respectively. Similar spectra are exhibited near the excitation frequency ωb. Numerical calculations for selected values of the Rabi frequencies are graphically presented and compared with those known in the literature. In the Appendix expressions for the excitation spectra are derived first when the two laser fields are treated classically, and second, when the fields are quantized but photon–photon correlations are neglected. It is shown that when the two laser fields are treated classically, the derived results are identical to those obtained when the fields are quantized only when photon–photon correlations arising from each laser field are discarded. The derived results when the fields are quantized but without photon–photon correlations taken into account are also identical to those obtained by the use of the dressed-atom approach. The appearance of the new sidebands reveals the boson character of the photon fields in question. The merit of the method is that it yields results describing both the classical as well as the quantum nature of the photon fields involved.
We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.
We have calculated numerically the excitation spectra arising from the interaction of a two-level atom with two strong electromagnetic fields. In the limit of high photon densities, the excitation spectra are considered when one of two laser fields is at resonance while the frequency of the other laser field is varied as well as when both laser fields are off resonance. At resonance, the spectra consist of a central peak and several sidebands peaked at the frequencies ω = ω a ± m(ω a - ω b ), corresponding to the multi-frequency mixing of both laser fields where m is a positive integer. Sidebands also appear at fractional multiples of frequencies and are due to contributions arising from energy shifts induced by the laser fields. The computed spectra at resonance are discussed and compared with the observed ones. The off-resonance spectra are computed for a wide range of values of Rabi frequencies and detunings, and are presented graphically. It is found that in the off-resonance case, mixing of a larger number of light frequencies occurs from that in the resonance case. The intensity of the peaks in the off-resonance case are immensely enhanced in comparison with those at resonance. The enhancement of the intensities is in agreement with the observed ones and its occurrence is theoretically explained. It is shown that if the detunings are properly chosen then the desired peak describing the required mixing of frequencies of the laser fields can be immensely enhanced. The method may be useful to investigate multi-frequency resonances of the rotation or rotation-vibration spectra of excited states or excited states near their ionization continua.