On the Casimir-Like Effect in System of Two Segregated Bose–Einstein Condensates Restricted by Two Hard Walls

Abstract

The Casimir-like effect in the system of two segregated Bose–Einstein condensates restricted by two hard walls (optical walls) is studied by means of the Gross–Pitaevskii theory in the double-parabola approximation. After determining the boundary conditions (BCs) at hard walls, we obtain the analytical expressions for both condensates and the interface tensions corresponding, respectively, to the Neumann, Robin and Dirichlet BCs. We discover two finite-size effects which closely connect with interface tensions: (a) Beside the conventional Casimir force caused by the zero-point energy there still emerges in the system a new type of long-range forces associated with different interface tensions. They are called the Casimir-like forces. (b) The second finite-size effect is directly associated with the BCs, it claims that the Neumann BC leads to stable state while the two other BCs provide unstable states of the underlying system. Therefore, the Casimir-like force derived from the Neumann BC is the dominant one in the system since it is present in the stable state. As a by-product, we conjecture that the above-mentioned effects could be present in all two-components systems confined by two walls.