Computational Studies of Microscopic Superfluidity in 4He Clusters

The onset of microscopic superfluidity has been reported in ultracold droplets of bosons (4He atoms or para-H2 molecules) containing a variety of molecular dopants. The physics of these droplets involve both Bose-Einstein condensation (BEC) and superfluidity. The two phenomena, while closely related, are not exactly the same. Superfluidity is fundamentally a microscopic effect and thermodynamic limit is necessary; it is still remarkable, though, that the signature of superfluidity has been reported in doped droplets consisting of as few as 4 4He atoms. The studies presented here adopt a molecular vantage point to investigate the quantum mechanics behind the rotational dynamics of dopant molecules in small droplets consisting of 4He atoms. The overarching goal is to develop a detailed quantum mechanical understanding of the onset of microscopic superfluidity. Physically small though these droplets are, they represent a significant challenge to many body quantum physics. The most direct method of investigation is to use Quantum Monte Carlo (QMC) algorithms to perform the calculations. Fixed node diffusion Monte Carlo (FNDMC), a type of QMC algorithm, is employed for these studies. Finding nodal surfaces for use in the calculation of the excited states is an essential part of this algorithm, which assumes the nodal topology of the target wave function is known in advance. To that end, we developed a novel approach utilizing a genetic algorithm version of the FNDMC method in which the nodal hypersurfaces are computed systematically and on-the-fly within the DMC procedure. This algorithm is then applied to elucidating the nodal topology of 4He-CO, 4He-HCN and 4He-NH3 and is then utilized to study the phenomenon of microscopic superfluidity and the renormalization of rotational constants in these clusters