On the Casimir interaction between objects immersed in salted water

Abstract

The Quantum Electrodynamics has plenty of subjects of study, from high-energy physics of large particle accelerators to low-energy physics where the effects from quantum vacuum fields become more relevant. Although their microscopic nature, the effects from these interactions appear in our daily lives, being partially responsible for geckos sticking to walls, and the condensation of noble gases. The interest in Casimir forces, which for short distances are known as van der Waals forces, arose in the last century through studies of the effects of dispersive forces in colloids. We begin by briefly discussing the motivations for the study of dispersive forces, which has endured for so long and continues to be interesting. Then we present the context of our work: objects interacting in water in which we can control the amount of dissolved ions – with a careful addition of salt – thus also controlling the screening of the electrostatic force. The geometries in which we study the effect of salt injection are appealing for measurements in the laboratory. The very question ”How can we modify the Casimir interaction through adding salt?” becomes the focus of this research. The introduction of ions into water causes a current to propagate, which in turn allows the propagation of longitudinal waves of the electromagnetic field. Thus, we must take into account the scattering of these waves in the Casimir interaction. In this thesis, we discuss in detail how such a longitudinal contribution alters the Casimir interaction for the system of (i) two interacting planes, and we build the theoretical framework for (ii) two interacting spheres. For situation (i), we highlight that the addition of salt causes the Dzyaloshinskii- Lifshitz-Pitaevskii (DLP) repulsion paradigm to be violated at zero frequency, finding an attractive not screened contribution depending uniquely on the distance between the objects. In addition, we characterize a parameter space for performing experiments, and analytically derive the interaction energy for several situations. For situation (ii) we use a well-established method, the Scattering Method, and refine it to add a longitudinal scattering channel. The results are analyzed for the small-sphere limit, and the term corresponding to the zero Matsubara frequency is analyzed in particular.