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AIP conference proceedings

Rabi-side bands generation in optically thick medium

F. P. Mattar, P. R. Berman

Published Jan 1, 1988• 0 citations
Publisher

Abstract

By adopting phase‐integral methods we compute how an off‐resonant probe coherently extracts more energy from an on‐resonance pump in an optically thick three‐level atom than a resonant probe from a larger pump. In both situations the time‐integrated area of the pump must exceed 5π. The population accumulated in the intermediate level exhibits a peak at a detuning equal to the pump Rabi frequency. This is a generalization of the Rabi side bands since propagation effects are accounted for. The pulse shape or pulse length affects the interaction.

DOI
10.1063/1.37406

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By adopting phase‐integral methods we compute how an off‐resonant probe coherently extracts more energy from an on‐resonance pump in an optically thick three‐level atom than a resonant probe from a larger pump. In both situations the time‐integrated area of the pump must exceed 5π. The population accumulated in the intermediate level exhibits a peak at a detuning equal to the pump Rabi frequency. This is a generalization of the Rabi side bands since propagation effects are accounted for. The pulse shape or pulse length affects the interaction.
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.
We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.
Analytic and numerical calculations for the propagational dependence of Rabi-Split resulting from a strong resonant pump and a coupled weak off-resonance probe are presented for a Lambda three-level atomic configuration. A semi-classical Maxwell-Bloch formulism was adopted for both the perturbational (using stationary phase and steepest descent asymptotic techniques) and the rigorous computational treatments. This calculation can be considered as a Double Self-Induced Transparency SIT' where the strong pump (multiple of 2n on-axis area) experiences coherent pulse break up, coherent self-focusing 2-4 and depletion as the weak probe (multiple of 0.02n area) cooperatively builds up. Different transition gain ratios (i.e., oscillator strength: p2w) are considered to insure that the weak probe does not get (a) delayed with respect to the pump or (b) get out of synchronization, and cease to overlap. The probe detuning can be as large as the input on-axis pump Rabi frequency. The interplay of nonlinear Raman gain action, dispersion and diffraction give rise concommitantly to a number of effects previously studied independently such as self-phase modulation, wave front encoding, transverse ring formation, self-focusing, quasi-trapping (when pump detuning is also allowed), and asymptotic three-level solitary waves.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.
The coherent frequency conversion between on-resonance pump and probe beams is examined in the physical situation where the medium nonlinearity balances the linear diffraction for each transition. Without diffraction neither soliton can occur. The paraxial-Maxwell Bloch formalism is adopted. To achieve optimally the energy transfer the pulse velocities must be equal to maintain maximum overlap throughout the propagation. The sequential evolution of probe soliton then pump soliton is reported in conjunction with pump depletion diffraction rigorously accounted for. Phase diagram of the pump and probe areas exhibit multi-value features.
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.