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Analytical investigation on the Autler–Townes splittings and the two-photon effects in a Doppler free signal lineshape of a double-$$\varvec{\lambda }$$ type four-level system

Monojit Kora, Swapan Mandal

Published Dec 13, 2022• 1 citation
Publisher
DOI
10.1007/s12043-022-02481-1

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Journal of Modern Optics•Jul 23, 2026•0 citations
Two electromagnetic fields (the stronger called the pump and the weaker called the signal) are allowed to interact with a four-level double λ-type system with two pairs of closely spaced levels. The present four-level system could also be viewed as an example of a double resonant system. Under the Doppler-free condition and using a semiclassical formulation of atom–field interaction, we derive the optical Bloch equations involving the said four-level system coupled to two external fields. These coupled optical Bloch equations are unsolvable in closed analytical form. In order to obtain the absorptive lineshapes, we use the usual perturbation method for getting the approximate analytical solution to the coupled optical Bloch equations for the density matrix elements. Through the off-diagonal complex density matrix elements, the introduction of phase angles between the levels participating in dipole-allowed transitions is automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. For on-resonance pump conditions, we obtain the usual Rabi splitting. The effects of two-photon resonances are clearly shown for off-resonance pump conditions.
The author investigates the Autler-Townes effect (also known as AC, optical or dynamical Stark splitting) on the Balmer- alpha transition of hydrogen in 0.5-5 Torr of helium. In the double optical resonance scheme. H(3p) is excited by absorption of two 243 nm photons and a 656 nm photon via the 2s resonant intermediate level. Calculated results show that in a Doppler-free or a 'Doppler-reduced' beam configuration, the required intensity of the 656 nm laser (0.2 cm -1 bandwidth) for observation of the Autler-Townes doublet has to be greater than 2*10 4 and 2*10 5 W cm -2 for 243 nm laser bandwidths of 0.1 and 0.5 cm -1 , respectively.
Using pump-probe spectroscopy, a four level system (FLS) with a double V-type configuration is investigated under Doppler-free conditions. The semiclassical description of the atom-field interaction is used to derive the optical Bloch equations (OBE). Under steady-state and rotating wave approximation, the coupled OBE reduces to a system of simultaneous equations. The analytical expressions for the signal absorption are parametrically computed using theoretical data. The signal lineshapes exhibit two perfectly symmetric Lorentzians corresponding to two signal resonance frequencies when the pump position is exactly in the middle of the two signal resonance frequencies. These two Lorentzians repel each other and, hence, the shifts of the signal peak frequencies. For on-resonant pump, the ac (dynamic) Stark splittings are obtained. The off-resonant pump produces the two-photon resonances. The nonlinear polarization and hence the hyperpolarizability involving the lower pair of levels exhibit interesting results. The hyperpolarizability is synonymous with those of the quadratic Stark effects.