Information theoretic measures on the two-photon transitions of hydrogen atom embedded in weakly coupled plasma environment

The quantum information theoretic measures in terms of Shannon entropy and Fisher entropy (both in position and momentum spaces) on the ground, excited as well as virtual states arising out of the two-photon transitions (1s -> nl; n = 2 - 4, l = 0, 2) of H atom embedded in classical weakly coupled plasma environment are done for the first time. Fourth order time dependent perturbation theory is adopted within a variational framework for calculating the two photon excitation energies and their respective wavefunctions from an analysis of the pole positions of the non linear response of the system. The representation of virtual state follows from an analysis of the linear response at such poles using a novel method developed by us. Ground and perturbed state wave functions of appropriate symmetries are represented by linear combination of Slater-type orbitals. The analytic form of the momentum space wave functions of ground, excited and virtual states are determined by taking Fourier transformation of the respective position space wave functions. The quantum information measures give interesting insights on the delocalization patterns of the all the real and virtual states under question w.r.t. the increase in plasma strength. The estimated data values are found to be in excellent agreement with the few existing in literature for the ground as well as excited states participating in the two-photon transitions. Such data for the virtual states are completely new and can be set as benchmark for future works in related disciplines.

Automated summary

For the first time, quantum information theoretic measures in terms of Shannon entropy and Fisher entropy were studied for the ground, excited, and virtual states resulting from two-photon transitions of an H atom embedded in a weakly coupled plasma environment. The two-photon excitation energies and wavefunctions were calculated using fourth order time dependent perturbation theory and a variational framework. A novel method was used to determine the representation of the virtual state based on the analysis of the linear response at poles. The quantum information measures provided insights on the delocalization patterns of the states with increasing plasma strength.