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 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 studied the fluorescent spectra arising from the 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 \ensuremath{\Vert}3〉 and \ensuremath{\Vert}4〉 and two lower states \ensuremath{\Vert}1〉 and \ensuremath{\Vert}2〉 and the two laser fields, whose frequency modes ${\ensuremath{\omega}}_{a}$ and ${\ensuremath{\omega}}_{b}$ are initially populated, operate between the states \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}4〉 and \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}3〉, respectively. Using the Green-function formalism and a model Hamiltonian, where all the free and interacting fields are quantized, we have studied the transitions \ensuremath{\Vert}4〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 and \ensuremath{\Vert}3〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 of the signal field in the limit of high photon densities of both laser fields. The expression of the spectral function for the \ensuremath{\Vert}1〉\ensuremath{\rightarrow}\ensuremath{\Vert}4〉 transition describes stimulated one-photon and three-photon processes, respectively. The one-photon spectra near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$ of the signal field consist of a central peak and two pairs of sidebands whose intensities take always positive and negative values indicating that attenuation and amplification (stimulated emission) of the signal field takes place at the frequencies in question, respectively. The spectral function for the three-photon process near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$-2${\ensuremath{\omega}}_{a}$ describes two pairs of sidebands whose intensities are always negative implying that strong amplification of the signal field occurs. The computed one-photon and three-photon spectra are presented graphically for different values of Rabi frequencies and detunings of both laser fields, respectively. Then using a classical description of both laser fields, the spectral functions describing one-photon and three-photon processes are calculated and the derived results are compared with the corresponding ones when the fields are quantized. It is found 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 photons which is lost in the classical treatment.
The fluorescent spectra arising from the interaction of a three-level atom with a strong pump field and a weak signal field have been studied simultaneously. The atom consists of an upper excited state ‖2〉 and two lower ground states ‖3〉 and ‖1〉, which arise by removing the degeneracy of the ground state by applying internal or external fields. The laser field depletes the metastable state ‖3〉 by bringing the electrons into the excited state ‖2〉 from where the electrons emit photons and decay into the lower states through the transitions ‖2〉 → ‖3〉 and ‖2〉 → ‖1〉, which are described by the signal field. Using a classical description of the laser field, where in the model Hamiltonian the laser–atom interaction is treated classically while the free and interacting electron and signal fields are quantized, the decay process ‖2〉 ↔ ‖1〉 of the signal field is considered by evaluating the appropriate Green’s function of the system. The spectral function for the ‖2〉 ↔ ‖1〉 transition of the signal field describes one-photon, three-photon, and two-photon Raman processes, respectively. The one-photon spectra consist of the main peak at the signal frequency and a pair of sidebands, which are symmetrically located from the position of the main peak. The intensity of the main peak is positive while that of the sidebands is negative indicating that the signal is attenuated and is amplified at the corresponding frequencies, respectively. The three-photon and two-photon Raman spectra are described by a doublet, respectively, whose intensities are always negative, implying amplification of the signal field. The computed spectra are presented graphically and compared with those derived in a recent study, where the laser field is quantized and photon–photon correlations are taken into consideration in the limit of high photon densities of the laser field. A detailed discussion of both treatments is given for the processes under investigation.
We have considered the excitation spectra for a three-level atom interacting simultaneously with a strong pump field and a weak signal field. The atom consists of an upper excited state ‖2〉 and two lower states ‖1〉 and ‖3〉 where the transition ‖1〉↔‖3〉 is electric-dipole forbidden from parity considerations. The pump field, whose frequency mode ωb is initially populated, operates near resonance between the states ‖2〉 and ‖3〉, ‖2〉↔‖3〉, while the signal field describes the radiative decays ‖2〉→‖3〉 and ‖2〉→‖1〉, respectively. Using the Green function method, the spectral functions for the signal field have been calculated in the limit of high photon densities of the pump field describing the following processes: (i) one-photon process; the spectra consist of a main peak at the signal frequency ω=ω21 and a pair of sidebands at ω=ω21±Ω−(ω23−ωb)/2, where Ω2=Ω2b/2+(ω23−ωb)2/4 with Ωb and (ω23−ωb) being the Rabi frequency and the detuning of the pump field, respectively. The intensity of the main peak at ω=ω21 is positive indicating signal-field absorption while those of the sidebands are always negative implying amplification (stimulated emission) of the signal field. The sum of the intensities (in absolute value) of the sidebands is twice that of the main peak at resonance while in the off-resonance case it depends on the value of the ratio (ω23−ωb)/2Ω. (ii) Stimulated three-photon process; the spectra consists of a pair of sidebands peaked at ω=ω21−2ωb±Ω−(ω23−ωb)/2 whose intensity is negative indicating amplification. At resonance the sidebands have equal intensities but at finite detuning asymmetry arises enhancing one peak while diminishing the intensity of the other. (iii) Stimulated two-photon process; the stimulated Raman spectra consist of a peak at ω=ω31, which has a delta function distribution, and a pair of strongly amplified sidebands at ω=ω31±Ω+(ω23−ωb)/2. The computed spectra for the three processes are presented graphically for different values of Rabi frequencies and detunings.
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 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 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.