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Coherent Optical Measurements in 1D
Published in Thomas C. Weinacht, Brett J. Pearson, Time-Resolved Spectroscopy, 2018
Thomas C. Weinacht, Brett J. Pearson
We now follow the same steps as with ESA, writing out the Hamiltonian operators to visualize the resonance condition in the rotating-wave approximation. We define an analogous expression for F to encompass the resonance condition factor for the case of GSB: F(R,t,τ)≡−12i∫0tdt2e−i(Vb(R)−Va(R)−ω2)t2μabE02(t2).
Picometer Detection by Adaptive Holographic Interferometry
Published in Klaus D. Sattler, Fundamentals of PICOSCIENCE, 2013
Δa is the detuning of the driving field from resonance Writing the time-dependent cosine function as a sum of exponentials and dropping the rapidly oscillating terms (the rotating wave approximation [13]), we arrive at the following time-independent Hamiltonian: Hˆg/s=12ℏΔa{|e⟩⟨e|-|g⟩⟨g|}+12ℏΩ{|e⟩⟨g|+|g⟩⟨e|}
Time-dependent state populations with and without the rotating wave approximation: a model-based study
Published in Journal of Modern Optics, 2019
Approximate methods play a very important role in quantum mechanics allowing a facile treatment of the processes under investigation. One of them, the rotating wave approximation (1, 2) (RWA) is widely applied in quantum optics, as well as in atomic and condensed matter physics in order to obtain simple analytic expressions for the solution of the Schrödinger equation (SE). The essence of the RWA relies on removing rapidly oscillating factors like from the light–matter interaction terms of the SE. Indeed, if the energy of the laser field () is in the order of the energy difference between the two considered states of the system (), then the integral can be neglected compared with (2). Because of this approximately zero time average of the high frequency components, one can expect a very good performance of the RWA in the resonance region. However, depending on the other laser parameters and the atomic structure, there are limitations to the validity of the RWA, the exploration of which is one of the principal aims addressed in this paper.