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Rate equations for a three-level system interacting with radiation

H G Venkatesh, Shyamal Guha, Satyanarayana Prasad

Published Feb 1, 1975• 0 citations
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The interaction of a single equidistant three-level radiator (same transition frequencies, dipole moments, and decay rates for both one-photon transitions) with a leaky optical cavity mode that at the same time is driven by an external coherent field is investigated via a generalized Fokker–Planck equation. It is shown that the steady-state behaviors of such an equidistant three-level sample differ from the corresponding ones of a general three-level system. We suppose that this difference appears due the fact that a single equidistant three-level radiator is equivalent to a pair of indistinguishable two-level atoms, provided that the separation between the pair is smaller than the wavelength of the cavity field.
It is shown that the density matrix equations for a three-level quantum system interacting with external radiation fields can lead to negative populations if arbitrary dephasing rates and shifts are included in these equations. To guarantee non-negative populations, the equations themselves impose certain restrictions on the dephasing widths and shifts. The constraints on the widths are shown to be identical to those that can be derived from a model of Markovian dephasing events, independent of any atom-field interaction.
A study is made of the resonant interaction of monochromatic radiation with many-level weakly nonequidistant systems and also of the interaction of ultrashort radiation pulses with systems of the same kind when the carrier frequency of the pulses is near a resonance frequency. In both cases, equations are obtained that describe the interaction of the radiation with the many-level systems. Analytic solutions of the problem are obtained for a three-level equidistant system under certain additional assumptions. A way of reducing the problem to a set of homogeneous algebraic equations is indicated for the case of monochromatic radiation.