Photon-number statistics from resonance fluorescence of a two-level atom near a plasmonic nanoparticle

Abstract

The photon-number statistics from resonance fluorescence of a two-level atom near a metal nanosphere driven by a laser field with finite bandwidth is studied theoretically. Our analysis shows that all interesting physics here takes place in a small area around the nanosphere where the near field and the atom-nanosphere coupling essentially affect the radiative properties of the atom. Computer modeling estimates this area roughly as $r\ensuremath{\le}2a$ $(r$ is the distance from the center of the nanosphere to the atom), with $a$ being the radius of the nanosphere. At the larger distances, the influence of the nanoparticle vanishes and the atom tends to behave similarly to that in free space. It is shown that the distribution function $p(n,T)$ of the emission probability of $n$ photons in a given time interval $T$ in steady-state resonance fluorescence drastically depends on the atom location around the nanosphere for $r\ensuremath{\le}2a$, featuring a characteristic twist in the ridgelike dependence and a convergence time of up to $9\ensuremath{\mu}\text{s}$, two orders of magnitude slower than for the atom in free space. At large distances, the distribution converges to a Gaussian one, as for the atom in free space. The typical convergence time scale at large distances $r>2a$ tends to the convergence time of the atom in free space. There are also two areas symmetrical around the nanosphere in which $\ensuremath{\Omega}\ensuremath{\sim}\ensuremath{\gamma}$ and the convergence time goes to zero. This behavior is determined by the interplay of the radiative and nonradiative decay rates of the atom due to the coupling with the metal nanosphere and by the near-field intensity. Additional parameters are the normalized laser frequency detuning from the atomic resonance and the bandwidth of the incoming laser field.