Optimised polychromatic field-mediated suppression of H-atom tunnelling in a coupled symmetric double well: two-dimensional malonaldehyde model

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The cis–cis isomerisation motion of malonaldehyde can be modelled as a symmetric double well coupled with an asymmetric double well, which includes the effect of the cis–trans out-of-plane motion on the cis–cis motion. We have presented an effective method for having control over the tunnelling dynamics of the symmetric double well which is coupled with the asymmetric double well by monitoring tunnelling splitting. When a suitable external field is allowed to interact with the system, the tunnelling splitting gets modified. As the external time perturbation is periodic in nature, the Floquet theory can be applied to calculate the quasi-energies of the perturbed system and hence the tunnelling splitting. The Floquet analysis is coupled with a stochastic optimiser in order to minimise the tunnelling splitting, which is related to slowering of the tunnelling process. The minimisation has been done by one of the stochastic optimisers, simulated annealing. Optimisation has been performed on the parameters which define the external polychromatic field, such as intensities and frequencies of the components of the polychromatic field. With the optimised sets of parameters, we have followed the dynamics of the system and have found suppression of tunnelling which is manifested by a much higher tunnelling time.