Limit Of High Photon Densities Research Articles

Cooperative and dipole-dipole effects in the fluorescent spectra of two identical three-level atoms at high photon densities: II. Stimulated three-photon processes

We have studied stimulated three-photon processes arising from the interaction of a system of two-identical three-level atoms with a strong pump field and a weak signal field simultaneously. The atoms consist of an upper excited state and two lower states and they interact through their dipole-dipole and cooperative radiative interactions, respectively. The strong laser field, whose frequency mode ω b is initially populated, depletes the metastable state by bringing the electrons into the excited state from where the electrons emit photons and decay through the signal field into the lower ground states of the system. Using the Green function method in the limit of high photon densities of the laser field, the spectral functions for the signal field have been calculated describing stimulated three-photon processes of the symmetric and antisymmetric modes, respectively, which arise from the dipole-dipole and cooperative radiative interactions between the atoms. The stimulated three-photon excitations near the frequency ω≈ ω 21 − 2 ω b describe physical processes where one-photon of the signal field with frequency ω 21 is absorbed while simultaneously two photons of the laser field are emitted. At resonance and in the absence of the dipole-dipole interaction, the spectra consist of a doublet whose peaks are symmetrically located from frequency ω = ω 21 − 2 ω b, while the magnitude and sign of the intensity of the peaks depend on the value of the relative Rabi frequency η b. For η b = 3, the intensity of the doublet takes negative values and it becomes positive for η b⩾5. As the value of η b increases the magnitude of the intensity of the doublet decreases and it becomes nearly constant for values of η b between 50 and 100. The single atom spectra consist of a doublet having a constant negative intensity independent of η b. The difference between the single and two-atom spectra is attributed to the cooperative radiative interaction between the two atoms. In the presence of detunings, the symmetry in the positions and intensities of the two sidebands vanishes. In the presence of the dipole-dipole interaction and at resonance, the spectra consist of three sidebands whose position, line shape, and sign as well as magnitude of the intensities depend entirely on the strength of the dipole-dipole interactions between the atoms. In the presence of detunings, asymmetries arise, enhancing certain spectral peaks while diminishing the intensity of others. The computed spectra are graphically presented for different values of η b, dipole-dipole interactions, and detunings. Comparison between the single and two-atom spectra is made and discussed in detail.

Cooperative and dipole-dipole effects in the fluorescent spectra of two identical three-level atoms at high photon densities: I. Stimulated one-photon spectra

We have considered the stimulated one-photon spectra for a system consisting of two identical three-level atoms interacting simultaneously with a strong pump field and a weak signal field. The atoms consist of an upper excited state and two lower states and they interact through their dipole-dipole interaction and radiate to each other as well. The strong laser field depletes one of the lower ground states (metastable state) by bringing the electrons into the excited state from where the electrons decay through the signal field into the lower ground states of the system. Using the Green function formalism in the limit of high photon densities of the laser field, the spectral function for the signal field which describes the stimulated one-photon process of the symmetric and antisymmetric modes arising from the dipole-dipole and cooperative radiative interactions between the two atoms, has been calculated and compared with that of the single atom. In the absence of the dipole-dipole interaction between the atoms, the spectra consist of the main peak at the frequency of the signal field and two pairs of sidebands, which are symmetrically located from the position of the main peak. In this case, the difference between the single and two-atom spectra is caused by the cooperative radiative interaction between the atoms and amounts: i) to increase the lifetime of the main peak by a factor of two from that of the single atom; ii) to split the one pair of sidebands of the single atom spectrum into two pairs of sidebands; iii) to cause the intensity of the two pairs of sidebands to vary as a function of the Rabi frequency of the laser field; and iv) to induce strong asymmetries in the lineshapes of the sidebands. In the presence of the dipole-dipole interaction, the spectra consist of a main peak at the frequency of the signal field shifted by the magnitude of the dipole-dipole interaction and six sidebands whose positions and intensities are governed by the strength of the dipole-dipole interactions between the atoms. The lineshapes of all peaks are described by asymmetric Lorentzian lines and the extent of the asymmetry depends on the strength of the dipole-dipole interaction. The relative intensity of the main peak and those of the sidebands are either positive or negative depending on the strength of the dipole-dipole interaction. The amplification of the sidebands is found to be more pronounced in the two-atom spectra than in that of the single atom. The computed spectra are presented graphically for different values of the Rabi frequencies, dipole-dipole interactions and for different detunings.

Stimulated Raman amplification spectra in a four-level atomic system interacting with a strong bichromatic field

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.

Strong amplification of sidebands in a strongly driven three-level atomic system. II. Classical description of the laser field

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.

Strong amplification of sidebands in a strongly driven three-level atomic system

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.

Stimulated two-photon induced transitions at high photon densities

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).

Strong amplification of sidebands in a four-level atomic system interacting with a strong bichromatic field.

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.

Frequency mixing in a four-level atom interacting with a strong bichromatic field

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...

Resonance fluorescence spectra of a strong bichromatic field interacting with a three-level atom in the ‘‘V’’ configuration

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.

Sum third order frequency mixing of a strong bichromatic field interacting with a three-level atom

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 r...

Quantum beats in the two-photon resonance flourescence of a three-level atom

The low-frequency modes pertaining to quantum beats in the two-photon resonance fluorescence of a three-level atom in the limit of high photon densities of the pump field is investigated without making the “rotating-wave approximation” in the coupling between the atom and the pump field. A somewhat different spectral function for the low-frequency modes from that predicted before is obtained.

Third-order optical mixing of frequencies of a strong bichromatic field interacting with a three-level atom in the “Lambda” configuration

We have considered the excitation spectra of three-photon processes arising from the interaction of a three-level atom, in the “lambda” configuration, with two strong electromagnetic fields whose initially populated modes ω a and ω b are at resonance with the two atomic transition frequencies, respectively. In the limit of high photon densities, expressions for the spectral functions are derived describing third-order nonlinear processes near the frequencies ω = ± (ω a − 2ω b) and ω = ± (ω b − 2ω a), respectively. Analytical calculations are then performed and the computed spectra are presented graphically for different values of the Rabi frequencies Ω a and Ω b, respectively. Expressions for the spectral function near the frequence ω = ω a − 2ω b are derived for specific values ω ⪡ η b, η b ≈ 2η a, η a ≈ η b, η a ≈ 2η a and η a ⪢ η b, where η a = Ω a/γ 0 and η b = Ω b/γ 0 are the reduced Rabi frquencies of the laser fields, respectively, and γ 0 is the s pontaneous emission probability. The computed spectra are compared with the corresponding ones for an atom in the “V” configuration.

Non-linear optical mixing of frequencies of a strong bichromatic field interacting with a two-level atom at high photon densities

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.

Non-linear optical mixing of frequencies of a strong bichromatic field interacting with a two-level atom at high proton densities

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.

Stimulated hyper-Raman scattering at high photon densities

We have studied the stimulated hyper-Raman scattering process in the presence of two strong electromagnetic fields whose frequency modes are initially populated and are near resonance with the two atomic transition frequencies. Using the Green's-function formalism, the excitation spectra are calculated in the limit of high photon densities of both laser fields. Expressions are derived for the relative intensities describing the following processes when (i) both pump fields are at resonance, (ii) the detunings take opposite values corresponding to the cooperative two-photon resonance, and (iii) both laser fields are off resonance. In processes (i) and (ii), the spectra consist of a single peak describing the stimulated hyper-Raman scattering and two pairs of sidebands induced by the laser fields. A new peak appears in process (iii) in addition to those appearing in processes (i) and (ii). The induced spectra are symmetric at resonance but asymmetric in the off-resonance processes, and the extent of the asymmetry depends strongly on the numerical values of the detunings. 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. Numerical calculations for selected values of Rabi frequencies and detunings are graphically presented and discussed.

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 ...

Nonlinear effects. Three-photon process at high photon densities

We have considered the excitation spectra of three-photon process arising from the iteraction 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 ω 21. In the limit of high photon densities, an expression for the Green function is derived in a closed form describing three-photon processes. The Green function is then calculated numerically and the computed spectra are presented graphically for a wide range of values of the Rabi frequencies η a and η b and detunings. The excitation spectra are considered when: (a) both laser fields are at resonance, (b) one of the laser fields is at resonance while the frequency of the other is varied, (c) both laser fields are off-resonance and (d) the detunings take opposite values, which refers to the cooperative resonance, when ω 21 = ( ω a + ω b )/2. The excitation spectra consists of several peak which are positioned at the frequencies ω = 3 ω a ± m( ω b − ω a ) corresponding to the multi-frequency mixing of both laser fields; m is a positive number. Peaks appearing at fractional multiples of frequencies are due to contributions arising from energy shifts induced by the laser fields. It is found then when the two laser fields have different intensities, and in the limit when (η b /η a ) >1, the intensities of the peaks vary as (η b /η a ) 2 and thus the intensities of the peaks in question are immensely enhanced.

Optical mixing of frequencies of a strong bichromatic field interacting with a three-level atom. II. Numerical results

We have numerically calculated the excitation spectra arising from the 3rd order mixing of the frequencies ωa and ωb of two laser fields interacting with a three-level atom, where each laser field resonantly couples the ground state with each excited state of the atom, respectively. In the limit of high photon densities, the excitation spectra near the reduced frequency X = (ω−ωa + 2ωb)/γ0 ≈ 0 are considered as a function of the reduced Rabi frequencies ηa and ηb of the two laser fields, respectively and γ0 is the spontaneous emission probability. For ηa < ηb the spectra consist of a doublet peaked at [Formula: see text] and its intensity is constant. When ηa = ηb, the spectra are composed of five pairs of bands peaked at [Formula: see text], and [Formula: see text]. When ηa < ηb the computed spectra consist of five pairs of bands, where the intensities of the peaks at [Formula: see text] and [Formula: see text] are positive indicating absorption, those at [Formula: see text] are negative implying amplification, and the two pairs of peaks at [Formula: see text] have positive and negative components describing the mixed process of absorption–amplification. The intensities of these bands are found to vary as (ηa/ηb)2 for (ηa/ηb) > 1 and, therefore, the intensities of the bands are immensely enhanced as the value of the ratio (ηa/ηb) increases. The computed spectra for a wide selection of Rabi frequencies are graphically presented and compared with those derived by analytical methods.

Optical mixing of frequencies of a strong bichromatic field interacting with a three-level atom

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.

One- and two-photon resonance fluorescence of a three-level atom at high photon densities

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 det...