Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A quantum Monte Carlo study

Ali A. Shams, H. R. Glyde

Aranya B. Bhattacherjee

O. Morsch

Ali A. Shams, H. R. Glyde

We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.

M. Rossi, Davide Emilio Galli, L. Reatto

We give a variational Monte Carlo description at T = 0 K of 4He filling a porous glass within the shadow wave function technique. The confining media is modeled by a smooth cylindrical pore, and we have considered two different pore radii: R = 13 Å and R = 22.5 Å. The radial density profiles show a strong layering of the 4He atoms. In the R = 13 Å pore, as the density is increased, solidification takes place layer by layer, starting from the pore wall, and the radius is too small to allow a bulk‐like solid to nucleate in the small liquid region at the center of the pore. For the R = 22.5 Å pore we find an hcp lattice accommodated in the central region surrounded by four layers which turn out to be solid at the density of the computation. Computing the one‐body density matrix (in the R = 13 Å case) we are able to estimate the Bose‐Einstein condensate fraction, which is still non‐zero even when the whole system is in the solid phase.

M. Rossi, Davide Emilio Galli, L. Reatto

We give a variational Monte Carlo description at T = 0 K of 4He filling a porous glass within the shadow wave function technique. The confining media is modeled by a smooth cylindrical pore, and we have considered two different pore radii: R = 13 A and R = 22.5 A. The radial density profiles show a strong layering of the 4He atoms. In the R = 13 A pore, as the density is increased, solidification takes place layer by layer, starting from the pore wall, and the radius is too small to allow a bulk‐like solid to nucleate in the small liquid region at the center of the pore. For the R = 22.5 A pore we find an hcp lattice accommodated in the central region surrounded by four layers which turn out to be solid at the density of the computation. Computing the one‐body density matrix (in the R = 13 A case) we are able to estimate the Bose‐Einstein condensate fraction, which is still non‐zero even when the whole system is in the solid phase.