Casimir force for geometrically confined ideal Bose gas in a harmonic-optical potential

TL;DR

This paper derives an explicit formula for the Casimir force in an ideal Bose gas confined between slabs within a harmonic-optical potential, highlighting how the force's behavior changes across the Bose-Einstein condensation temperature.

Contribution

It provides a closed-form expression for the Casimir force in a harmonic-optical lattice, revealing temperature-dependent decay behaviors and emphasizing the potential's role in quantum systems.

Findings

Casimir force decays as 1/d^5 below T_c

Exponential decay of Casimir force above T_c

Harmonic-optical potential influences quantum phase transitions

Abstract

In this study, we have derived close form of the Casimir force for the non-interacting ideal Bose gas between two slabs in harmonic-optical lattice potential by using Ketterle and van Druten approximation. We find that Bose-Einstein condensation temperature $T_{c}$ is a critical point for different physical behavior of the Casimir force. We have shown that Casimir force of confined Bose gas in the presence of the harmonic-optical potential decays with inversely proportional to $d^{5}$ when $T\leq T_{c}$. However, in the case of $T>T_{c}$, it decays exponentially depends on separation $d$ of the slabs. Additionally we have discussed temperature dependence of Casimir force and importance of the harmonic-optical lattice potential on quantum critical systems, quantum phase transition and nano-devices.