Ultrahigh-resolution spectroscopy with atomic or molecular dark resonances: Exact steady-state line shapes and asymptotic profiles in the adiabatic pulsed regime

Abstract

Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation

\ndescribing a set of closed three-level atomic or molecular states including decoherences, relaxation rates,

\nand light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-

\nTownes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and

\nthe Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency

\nshifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations

\nin the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent

\nsuperposition of long-lived states is established. For a highly asymmetrical configuration with different decay

\nchannels, a strong two-photon resonance based on a lower states population inversion is established when the

\ndriving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses

\nare applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long

\nenough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into

\na new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey

\noscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect.

\nFrequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman

\ndecoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement.

\nWe point out that different observables experience different shifts on the lower-state clock transition.