Laser-induced multiphoton dissociation of H2+as a function of the field frequency using parametric equations of motion

Abstract

We have applied parametric equations of motion (PEM) to study photodissociation dynamics of H 2 + . This is an application of PEM having frequency as the parameter to a non-Hermitian Hamiltonian. The resonances are extracted using the smooth exterior scaling method. Here we have studied how different resonance states behave with respect to the change in frequency of the laser field. The advantage of this method is that one can easily trace different resonance states that are changing as the parameter changes. It is observed that some higher lying vibrational states remain bound states in continuum with the decrease in frequency.

Application of parametric equations of motion to study the resonance coalescence in $\text{H}_{2}^{+}$H2+

“…Diagonalization procedure and the integration of the PEM are exactly the same as those given in our earlier publications. 13,14,21,22 At low intensity, one can recognize the resonance states by looking at the wavefunctions and matching that with field free state. But at higher intensity, wavefunctions might look very different from field free state and as a result it will be impossible to assign them a quantum number by inspection.…”

“…Hence PEM calculations with respect to the A 0 and can be implemented. 13,14 Though computationally matrix diagonalization is ten times faster than the PEM method, the efficiency of the PEM lies in the fact that the variation of a specific resonance state with respect to a range of field parameters (i.e., amplitude and frequency) can be easily traced. This tracing is impossible with the conventional diagonalization technique because the line number of a particular resonance state is rearranged every time in the output.…”

“…Superscript T stands for transpose.C R i andC L i follow the relationship CL i TC R i = 1. Evolution of eigenvalues (E) and eigenvectors (C) as a function of the linear perturbation parameter λ is given as 10,13,14 …”

“…The dimension of the Hamiltonian matrix will be (mN × mN) for a single photon excitation. The form of Floquet Hamiltonian (Ĥ f ) derived by Chu 7 including the SES absorbing term 13,14,19,21,22,25 is given by(…”

“…The advantage of PEM lies in the fact that one can trace the individual eigenstates in parameter space. 13,14 In this paper, a) gupta@iitg.ernet.in.…”