Casimir-Polder forces: A nonperturbative approach

Abstract

Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density-matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.

van der Waals interaction of excited media

“…But the methods based upon the linear response theory 9 10 or macroscopic quantum electrodynamics 11,12 are not suitable for us, since these methods involve classical polarizabilities of atoms. In a number of problems these methods yield correct results 9 10 11 12 , but, as we are going to show, in general case the van der Waals potential or the Casimir force can not be expressed in terms of classical polarizabilities.…”

Engineering p-wave interactions in ultracold atoms using nanoplasmonic traps

“…Here we provide a heuristic derivation of the CasimirPolder potential for an atom in its electronic ground state, while referring the reader to ref. 43 for details. Working within a two-level approximation with atomic ground and excited states |gS,|eS, the interaction between the electromagnetic field and an atom at position r is given by the dipole Hamiltonian H ¼ À d.E(r).…”

Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium

“…2). As we reminded before the DLN approach has an old history and was already used by Lifshitz and Rytov in order to justify the Casimir force formula [53][54][55] and later it was naturally used in the quantized version of the DLN [46][47][48][49][50]. The standard DLN approach apparently differs strongly in essence from the so-called scattering approach [77][78][79] that considers the radiation pressure exerted by scattered optical modes on the material system.…”

“…56 plays also a key role for the calculation of fluctuations and correlations [33] at different spatial positions and for evaluation of Casimir and thermal forces [46][47][48][49][50]. Here, within the new DLN formalism the calculations will become more transparent.…”

“…Instead, fluctuating currents are phenomenologically added to deal with the problem of dissipation and dispersion. This approach was intensively used in the literature [27][28][29][30][31][32][33][34][35][36], e. g., for describing optical Bloch equations in the weak or strong optical coupling in QNP [37][38][39][40][41][42][43][44][45], Casimir interactions, quantum frictions and thermal fluctuating forces [46][47][48][49][50], and more recently for modeling quantum optical non-linearities such as spontaneous down conversion of photon pairs [51,52]. It is central to observe that the DLN approach is a direct development of the historical works by Rytov and others [53][54][55][56] which, based on some considerations about the standard fluctuation dissipation theorem for electric currents [57], was used for justifying Casimir and thermal forces (for recent developments of such phenomenological 'fluctuational electrodynamics' techniques in the context of nanotechnology see [58][59][60][61][62][63]).…”