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Journal of Physics B Atomic Molecular and Optical Physics

Effects of field induced quantum coherence on the absorptive lineshape of a V-type three-level system

Swapan Mandal

Published Oct 6, 2000• 7 citations
Publisher

Abstract

A single electromagnetic field interacting with a V-type three-level system having two closely spaced upper levels is studied for the Doppler-free absorptive lineshape. The usual optical Bloch equations are constructed. Quantum interference between the probability amplitudes of the levels participating in a dipole allowed transition is taken into consideration. The quantum interference is manifested through the phase angle. It appears that these phases are significant only if the applied electromagnetic field is strong. The absorptive lineshape calculations are revisited in the light of such field induced coherence. The lineshape exhibits pushing between two spectral lines in addition to the usual pulling between them. It is found that the pushing of the spectral lines depends solely on the coherence induced by the strong field. The complete cancellation of field dependent shifts for the resonance peaks is possible by the suitable adjustment of the phase angles arising from the strong field induced coherence.

DOI
10.1088/0953-4075/33/21/304

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A single electromagnetic field interacting with a V-type three-level system having two closely spaced upper levels is studied for the Doppler-free absorptive lineshape. The usual optical Bloch equations are constructed. Quantum interference between the probability amplitudes of the levels participating in a dipole allowed transition is taken into consideration. The quantum interference is manifested through the phase angle. It appears that these phases are significant only if the applied electromagnetic field is strong. The absorptive lineshape calculations are revisited in the light of such field induced coherence. The lineshape exhibits pushing between two spectral lines in addition to the usual pulling between them. It is found that the pushing of the spectral lines depends solely on the coherence induced by the strong field. The complete cancellation of field dependent shifts for the resonance peaks is possible by the suitable adjustment of the phase angles arising from the strong field induced coherence.
The optical Bloch equations of a four-level atomic system with three closely spaced upper levels irradiated by a single mode of the electromagnetic radiation field are constructed. Under the rotating wave approximation and by using the slowly varying envelope approximation, we obtain the analytical solution to these optical Bloch equations. These solutions, which are obtained perturbatively, are used to calculate the polarization and hence the absorptive line shape. In particular, we examine the effects of the field-induced coherence arising from the interference between the probability amplitudes of the levels participating in dipole-allowed transitions. We obtain the shifts of the resonance peak positions due to two different reasons. The first is due to the nonlinear effects arising from the closely spaced nature of the peaks. The second is attributed to the field-induced coherence alone. It is found that the shifts of the positions of the resonance peaks due to field-induced coherence may be in the blue or in the red region.
A V-type three level system with two closely spaced upper levels interacting with a single mode of the electromagnetic field is studied for the absorptive and dispersive lineshapes. A semiclassical description for the atom-field interaction is being adopted to obtain the usual optical Bloch equations. The approximate analytical solutions for the density matrix elements are obtained by solving coupled optical Bloch equations. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed transitions are automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. These field dependent phases (coherence) are responsible for the reduction of the inversionless gain and the absorptionless dispersion. For large decay constants, it is found that the energy gap between the upper two levels has no role to play on the laser without inversion and on the absorptionless dispersion. However, for large population per unit decay, a significant increase of the absorptionless dispersion and the inversionless gain is obtained. The condition for large population decay and a possible experimental realization of the field dependent phases are discussed.
Under the Doppler free condition, a four-level system with three coherently prepared closely spaced upper levels coupled to a single electromagnetic field is being investigated for the absorptive and dispersive lineshapes. By using a perturbation method, the optical Bloch equations for the present four-level system are solved analytically to obtain the induced polarization and hence the spectral lineshapes. The field induced and field independent coherences appear automatically in the analytical expressions of the imaginary and real parts of the complex polarization. These field independent and field dependent coherences are the outcome of the quantum interference between the probability amplitudes of finding the atom in those energy levels. The phase sensitive field induced polarizations are extensively studied for two special conditions of the ground level populations. The influence of the closely spaced transitions on the quantum coherence and hence the subsequent effects on absorption despite inversion, electromagnetically induced transparency and on the ultrahigh index of refraction are discussed.
In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.
This paper investigates the effects of spontaneously induced coherence on absorption properties in a nearly equispaced three-level ladder-type system driven by two coherent fields. It find that the absorption properties of this system with the probe field applied on the lower transition can be significantly modified if this coherence is optimized. In the case of small spontaneous decay rate in the upper excited state, it finds that such coherence does not destroy the electromagnetically induced transparency (EIT). Nevertheless, the absorption peak on both sides of zero detuning and the linewidth of absorption line become larger and narrower than those in the case corresponding to the effects of spontaneously induced coherence; while in the case of large decay rate, it finds that, instead of EIT with low resonant absorption, a sharp absorption peak at resonance appears. That is, electromagnetically induced absorption in the nearly equispaced ladder-type system can occur due to such coherent effects.
We report here an effect in a four-level ladderlike system, which is in contrast to the usual quantum interference effects such as electromagnetically induced transperency (EIT) or coherent population trapping: we predict the occurrence of a narrow absorption peak within the EIT window when an EIT atomic system interacts with an additional driving rf field. The Doppler-free-central absorption appears when the three-photon resonance condition is satisfied. In the limit of the rf field strength ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{rf}}$\ensuremath{\rightarrow}0, the usual EIT profile is recovered.