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arXiv:quant-ph/0510111 · Journal of Optics B Quantum and Semiclassical Optics

Optical dipole trapping beyond the rotating wave approximation: the case of large detuning

Vassilios E Lembessis, Demosthenes Ellinas

Published Sep 30, 2005• 11 citations
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Abstract

We show that the inclusion of counter-rotating terms, usually dropped in evaluations of the interaction of an electric dipole of a two-level atom with the electromagnetic field, leads to significant modifications of the trapping potential in the case of large detuning. The results are shown to be in excellent numerical agreement with recent experimental findings for the case of modes of Laguerre–Gauss spatial profile.

DOI
10.1088/1464-4266/7/11/002

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We show that the inclusion of counter-rotating terms, usually dropped in evaluations of the interaction of an electric dipole of a two-level atom with the electromagnetic field, leads to significant modifications of the trapping potential in the case of large detuning. The results are shown to be in excellent numerical agreement with recent experimental findings for the case of modes of Laguerre–Gauss spatial profile.
The rotating-wave approximation (discarded of counter-rotating interactions) to light-matter interactions is widely used in the quantum electrodynamics Hamiltonian; however, its validity has long been a matter of debate. In this article, we explore the importance of counter-rotating interactions in the quantum dynamics of multiple molecules in complex dielectric environments within the framework of macroscopic quantum electrodynamics. Through our analytical analysis, we find that, in the weak coupling regime, the lack of counter-rotating interactions results in the absence of the Casimir-Polder potentials (medium-assisted energy shifts) in the ground-state molecules and a significant deviation of the intermolecule dipole-dipole interactions. Notably, the deviation of intermolecule dipole-dipole interaction can reach up to 50 percent in the near-field zone (short intermolecule distance). We also conduct a case study on the population dynamics of a pair of identical molecules above a plasmonic surface. Through analytical and numerical analysis, it is revealed that the lack of counter-rotating interactions can profoundly affect the dynamics, especially the oscillatory pattern due to intermolecule dipole-dipole interactions, of the molecules in both strong and weak coupling regimes, emphasizing the need for careful consideration when making the rotating-wave approximation in a multiple-molecule system coupled with quantum light.
We consider the case of interaction of a three-level atom with a high intensity pulse electromagnetic field. Rabi frequencies are assumed to be of the order of the transition frequency or greater. We demonstrate that coherent population trapping exists even in such a case when the usual rotating-wave approximation is no longer valid. However, a certain condition on the phases of electromagnetic wave components has to be satisfied in order to make coherent population trapping possible. This condition is specific for the strong field case in contrast to the case where the rotating-wave approximation is valid. Also we point out some elements for which a model of an atom with a finite number of levels may still be valid while the rotating-wave approximation breaks down.
At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.