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Laser Physics Letters

Bunch-type dipole spectrum of a weakly excited two-level system

R. Parzyński, T. Kopyciuk

Published Jun 5, 2018• 1 citation
Publisher

Abstract

Abstract We derive a compact formula for the electric dipole induced in a weakly laser-driven two-level system. The dipole is shown to oscillate at frequencies being different combinations of even multiplicities of the transition frequency and odd multiplicities of the laser frequency. Applying this formula to laser frequencies much lower than the transition frequency in the system, we explain the numerical dipole spectra reported in literature, particularly the bunches of spectral lines grouped around even multiplicities of the transition frequency. These bunches form a part of spectrum additional to the ordinary odd laser-light harmonics.

DOI
10.1088/1612-202x/aac199

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Abstract We derive a compact formula for the electric dipole induced in a weakly laser-driven two-level system. The dipole is shown to oscillate at frequencies being different combinations of even multiplicities of the transition frequency and odd multiplicities of the laser frequency. Applying this formula to laser frequencies much lower than the transition frequency in the system, we explain the numerical dipole spectra reported in literature, particularly the bunches of spectral lines grouped around even multiplicities of the transition frequency. These bunches form a part of spectrum additional to the ordinary odd laser-light harmonics.
In the limits of weak and strong excitation, we solve analytically the Riccati-type differential equation for a two-level system in the field of two different lasers and then use these solutions to find easy to handle formulae for the induced electric-dipole moment of the system.We apply these formulae to describe the effects of strong excitation in both the higher harmonics generation and multiphoton frequency mixing, namely the diminishing of the generation of harmonics of a given laser when an additional laser is turned on and the diminishing of the radiation at mixed frequencies with increasing strength of lasers under the condition of multiphoton excitation.
Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laserdriven two-level system is used to calculate analytically the induced electric dipole moment.The formula found for the dipole moment is valid for weak excitations by smooth-shape pulses of arbitrary off-resonant frequencies, i.e., those producing neither exact one-photon nor odd multiphoton resonances.For a given pulse shape, the formula allows to express the Fourier components of the induced dipole moment as functions of both laser frequency and intensity and to find the field-dependent refractive index of the system versus laser frequency.
Numerical calculations are presented for the interference spectra of a laser-excited three-level atom, where the strong and the weak atomic transitions are driven by resonant and nonresonant laser fields, respectively. The spectral functions describing the interference spectra for the electric dipole allowed excited state have been considered in the low- and high-intensity limit of the laser field operating in the strong transition. The interference spectra arise from the competition between short-lifetime spontaneous processes and short- and long-lifetime excitations induced by the strong and the weak laser fields, respectively. Both laser fields have been treated as quantized and as classical entities. The computed spectra have been presented graphically for different values of the Rabi frequencies and detunings of the weak laser field. It is shown that the decrease in the intensity of the short-lifetime excitation may provide a measure of the spectral width of the long-lifetime excitation.
We considered the excitation spectra for the excited states of a three-level atom, where the strong and the weak atomic transitions are driven by resonant and nonresonant laser fields, respectively. The spectral functions describing the excitation spectra for the electric dipole allowed excited state and for the metastable state of the atom have been derived when both laser fields are quantized as well as when they are treated as classical entities. In the low-intensity limit of the laser field operating in the strong transition, there are two short-lifetime excitations, the spontaneous one and the induced one, which appear at the same frequency, and a long-lifetime excitation induced by the weak laser field. These excitations compete with each other at resonance as well as at finite detunings of the weak laser field. In the high-intensity limit of the laser field operating in the strong transition, the competition is between the short- and the long-lifetime side bands, which are induced by the strong and the weak laser fields, respectively. The ratio of the maximum intensities of the peaks describing the long- and the short-lifetime excitations exhibits a resonance variation with the detuning of the weak laser field. Comparison between the results obtained when the laser fields are treated as quantized and as classical entities is made.
The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.