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Journal of Optics B Quantum and Semiclassical Optics

Interference spectra in four-level atomic systems

Constantine Mavroyannis

Published Nov 15, 2000• 4 citations
Publisher

Abstract

We have calculated the interference spectra of a single electron in the excited state of a four-level atom interacting with three laser fields, where two of them are on two-photon resonance with the three levels forming a `Λ' scheme while the third laser operates between the second ground and the second excited states of the atom. It is shown that in the low-intensity limit of all three laser fields, the third laser field destroys the destructive interference that occurs between the spontaneous radiative decay and the process arising from the combined field of all the three laser fields. The result is that the overall intensity of the peak at the centre of the line depends on the strength of the third laser field and it takes negative values indicating that light amplification without population inversion (LAWI) is likely to occur at the one-photon frequency. The antisymmetric two-photon state of the two lower levels as well as the two-photon process, where one laser photon is absorbed and another laser photon is emitted simultaneously by the second excited state of the atom, is found to exhibit LAWI at the one-photon frequency. The derived results are graphically presented and discussed.

DOI
10.1088/1464-4266/2/6/305

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We have calculated the interference spectra of a single electron in the excited state of a four-level atom interacting with three laser fields, where two of them are on two-photon resonance with the three levels forming a `Λ' scheme while the third laser operates between the second ground and the second excited states of the atom. It is shown that in the low-intensity limit of all three laser fields, the third laser field destroys the destructive interference that occurs between the spontaneous radiative decay and the process arising from the combined field of all the three laser fields. The result is that the overall intensity of the peak at the centre of the line depends on the strength of the third laser field and it takes negative values indicating that light amplification without population inversion (LAWI) is likely to occur at the one-photon frequency. The antisymmetric two-photon state of the two lower levels as well as the two-photon process, where one laser photon is absorbed and another laser photon is emitted simultaneously by the second excited state of the atom, is found to exhibit LAWI at the one-photon frequency. The derived results are graphically presented and discussed.
We have calculated the excitation spectra of a single electron in the excited state of a four-level atom interacting with three laser fields at low intensities, where two of them are on two-photon resonance with the three levels of the atom, while the third laser is a weak one operating between the fourth and excited level of the atom. It is shown that light is switched off at certain frequency due to the coherent population trapping while light is turned on at another frequency, where stimulated emission occurs leading to light amplification without population inversion.
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 consider the interference spectra arising from the competition between a spontaneous process and two processes induced by two laser fields, which are coupled with a three-level atom in the "Λ" configuration. In the low-intensity limit of both laser fields and on two-photon resonance, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, cancel each other out completely at the center of the line for zero detuning and at the finite values of the detuning as well. At high intensities of the laser fields and on two-photon resonance, the dynamic Stark effect dominates the spectra of the excited state of the atom. Expressions for the interference spectra and correlation functions are derived, which describe the physical process of the absorption of a laser photon at two different times by the ground state of the atom. Interference spectra and correlation functions are calculated for the two-photon off-resonance and for the proces of the absorption of a photon by the ground state of the atom. In this case, the intensities of the frequency dips take negative values indicating that stimulated emission prevails for certain values of the detunings. Using values for the parameters involved close to those for Ba+, the computed two-photon resonance and off-resonance spectra are graphically presented and discussed.
The interference spectra arising from the competition between a spontaneous process and an induced one by two laser fields, which interact on two-photon resonance with a three-level atom in the Lambda configuration have been considered. In the low intensity limit of both laser fields, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, respectively, cancel each other out completely at the centre of the line for zero detuning and at the finite values of the detuning as well. At those frequencies, the fluorescent light totally disappears. The interference spectra arising from the absorption of a laser photon by the ground state of the atom consists of two peaks describing the induced processes of absorption and stimulated emission, respectively.
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 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.