Quantum Dynamics with Explicitly Time-Dependent Hamiltonians in Multiple Time Scales: A New Algorithm for (t, t′) and (t, t′, t″) Methods in Laser–Matter Interactions

Abstract

The (t, t′) method for quantum dynamics with general time-dependent Hamiltonians is exact yet expensive to implement, in the context of laser–atom, laser–molecule interactions. The evolution operator requires a huge storage space with a large operation count for the propagation. A new method is suggested in this work where an analytical block diagonalization of the Floquet Hamiltonian is proposed. The block diagonalization in this novel algorithm is based on Chebyshev polynomials of the second kind. This is combined with a split operator method of chosen order to approximate the full evolution operator. The number of operations are drastically reduced to that of a matrix-vector multiplication repeated only to the order of the number of Floquet channels. Hence, only matrices of the order of the number of position basis functions need to be stored. Thus, the presented algorithm is an effective tool for solving the (t, t′, t′′) problem for interactions with a bichromatic laser and a single-frequency laser pulse with explicit interactions of the pulse envelope. Hydrogen atom, helium, water, and ammonia, represented with Hamiltonians obtained from standard electronic structure packages, have been investigated in the presence of linearly polarized pulsed laser fields and bichromatic laser fields presenting various time-dependent properties from the program.

Time-dependent quantum mechanical wave packet dynamics

“…Pfeifer and Levine 88 and Peskin and Moiseyev 89 used the (t, t 0 ) method for this purpose. Very recently, Balanarayan and coworkers 90 have proposed a (t, t 0 , t 00 ) method to obtain exact results for molecules interacting with short pulse lasers. One of the bottlenecks in solving the TDSE has been in determining the operation of the kinetic energy operator on C for the reasons mentioned earlier.…”

Laser-Dressed Molecular Point Groups in the Kramers–Henneberger Oscillating Frame-of-Reference: Selection Rules for Higher Harmonic Generation

“…For testing, the HHG spectra for laser-molecule pairs were obtained by solving the length gauge TDSE using ( t , t ′, t ″) , method. The details of the method are given in the Supporting Information.…”

“…The details of the method are given in the Supporting Information. The HHG spectra are evaluated as a Fourier transform of the second derivative of the TD induced dipole moment, where σ­(ω) is the power spectrum given in log scale in all the plots. The predicted peak positions at Nk ± 1 are compared with the calculated peaks, in Figures –].…”