We have calculated the excitation spectra of a single electron in the excited state of a three-level atom interacting with two off-resonant laser fields at high intensities. We have also considered the process where one laser photon is absorbed by the ground state, as well as a Raman-type process where one photon of one of the laser fields is emitted while another photon of the other laser field is absorbed simultaneously by the second excited state of the atom. The net excitation spectra of the three processes in question consist of two peaks having always positive intensities indicating induced absorption (attenuation) and a third peak which has positive, zero and negative intensities for values of the Rabi frequencies , and , respectively. When , the Raman-type process prevails over the other two, and the resulting peak has a negative intensity indicating that significant amplification is likely to occur at the corresponding frequency.
We have calculated the excitation spectra of a single electron in the excited state of a three-level atom interacting with two off-resonant laser fields at high intensities. We have also considered the process where one laser photon is absorbed by the ground state, as well as a Raman-type process where one photon of one of the laser fields is emitted while another photon of the other laser field is absorbed simultaneously by the second excited state of the atom. The net excitation spectra of the three processes in question consist of two peaks having always positive intensities indicating induced absorption (attenuation) and a third peak which has positive, zero and negative intensities for values of the Rabi frequencies , and , respectively. When , the Raman-type process prevails over the other two, and the resulting peak has a negative intensity indicating that significant amplification is likely to occur at the corresponding frequency.
We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.
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.
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.
The author has considered the interference spectra arising from the competition between absorption and stimulated emission processes, which have been induced by two laser fields operating at a two-photon resonance with a three-level atom in the ' Lambda ' configuration. In the low intensity limit of both laser fields, the induced spectrum in the ground state consists mainly of a peak, whose height and asymmetry depend strongly on the value of the detuning of the laser fields. In the absence of detuning, the height of the induced peak takes positive values implying that the physical process of absorption (attenuation) takes place, while at finite detunings the height of the peak becomes negative indicating the frequencies at which stimulated emission (amplification) is likely to occur. The spectra arising from the emission of a laser photon by the excited state consist of two peaks describing stimulated emission and induced absorption, respectively, where the former dominates the latter for small values of the Rabi frequencies but for higher ones, cancel each other out.
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.
Studies the competition between absorption and stimulated emission induced by two laser fields at low intensities interacting on a two-photon resonance with a three-level atom. The induced spectrum into the ground state consists of a peak whose height and asymmetry depend strongly on the detuning. The spectra arising from the emission of a laser photon by the excited state consists of two peaks describing stimulated emission and induced absorption, respectively, where the former dominates the latter for small values of the Rabi frequencies but for higher ones, they cancel each other out.