[Paper Review] Near-field Electrodynamics of Atomically Doped Carbon Nanotubes

Igor V. Bondarev, Ph. Lambin|arXiv (Cornell University)|Jan 25, 2005

Carbon Nanotubes in Composites15 references4 citations

TL;DR

This paper develops a quantum electrodynamics framework to study near-field interactions between a single atom and a carbon nanotube, focusing on spontaneous emission and van der Waals forces. It reveals that strong atom-vacuum-field coupling leads to Rabi oscillations and that conventional weak-coupling models fail near the nanotube surface, necessitating a universal quantum approach for accurate description of the van der Waals energy in the strong-coupling regime.

ABSTRACT

We develop a quantum theory of near-field electrodynamical properties of carbon nanotubes and investigate spontaneous decay dynamics of excited states and van der Waals attraction of the ground state of an atomic system close to a single-wall nanotube surface. Atomic spontaneous decay exhibits vacuum-field Rabi oscillations -- a principal signature of strong atom-vacuum-field coupling. The strongly coupled atomic state is nothing but a 'quasi-1D cavity polariton'. Its stability is mainly determined by the atom-nanotube van der Waals interaction. Our calculations of the ground-state atom van der Waals energy performed within a universal quantum mechanical approach valid for both weak and strong atom-field coupling demonstrate the inapplicability of conventional weak-coupling-based van der Waals interaction models in a close vicinity of the nanotube surface.

Motivation & Objective

• To develop a universal quantum mechanical theory for near-field electrodynamics of atomically doped single-wall carbon nanotubes.
• To investigate spontaneous decay dynamics of excited atomic states near a carbon nanotube surface.
• To analyze the van der Waals interaction energy of a ground-state atom near a carbon nanotube, especially in the strong coupling regime.
• To demonstrate the inapplicability of conventional weak-coupling-based van der Waals models in close proximity to the nanotube surface.
• To establish a framework valid for both weak and strong atom-field coupling regimes in low-dimensional systems.

Proposed method

• The study employs a quantum electrodynamics formalism based on local photonic density of states (DOS) to describe atom-field interactions.
• The total Hamiltonian is expressed in terms of the local photonic DOS, enabling analysis of vacuum-field coupling effects.
• A two-level atomic model is used to describe the excited state, with spontaneous decay dynamics analyzed via the Markovian and single-resonance approximations.
• The van der Waals energy is calculated using a Green's tensor approach and a universal quantum mechanical formulation valid for both weak and strong coupling.
• The derivation involves analytical continuation into the complex plane and integration along the imaginary axis, leading to an exact expression for the vdW energy.
• The resulting expression is compared to the Casimir-Polder formula, confirming consistency in the limit of large nanotube radius and longitudinal dipole alignment.

Experimental results

Research questions

• RQ1 How does the spontaneous decay rate of an excited atom near a carbon nanotube deviate from the free-space value due to vacuum-field coupling?
• RQ2 What are the signatures of strong atom-vacuum-field coupling in the near-field electrodynamics of carbon nanotubes?
• RQ3 Why do conventional weak-coupling models fail to describe van der Waals interactions at sub-nanometer distances from a carbon nanotube surface?
• RQ4 How does the local photonic density of states near a carbon nanotube influence the atom-field coupling strength and decay dynamics?
• RQ5 To what extent does the geometry and dispersion of the carbon nanotube modify the vacuum electromagnetic modes accessible to a nearby atom?

Key findings

• Spontaneous decay of an excited atom near a carbon nanotube exhibits vacuum-field Rabi oscillations, indicating strong coupling and the formation of a quasi-1D cavity polariton.
• The stability of the strongly coupled atomic state is primarily governed by the atom-nanotube van der Waals interaction.
• Conventional weak-coupling-based van der Waals models are inapplicable in the immediate vicinity of the nanotube surface due to strong coupling effects.
• The derived van der Waals energy expression matches half the Casimir-Polder result for a perfectly conducting plane when the atom’s dipole is aligned along the nanotube axis.
• The exact analytical form of the vdW energy is obtained through integration over the imaginary frequency axis, incorporating the full frequency dependence of the atomic polarizability.
• The model confirms that the longitudinal dipole contribution accounts for half the total Casimir-Polder energy, with the transverse component neglected.