Theoretical study of plasmonic lasing in junctions with many molecules

Abstract

We calculate the quantum state of the plasmon field excited by an ensemble of molecular emitters, which are driven by exchange of electrons with metallic nano-particle electrodes. Assuming identical emitters that are coupled collectively to the plasmon mode but are otherwise subject to independent relaxation channels, we show that symmetry constraints on the total system density matrix imply a drastic reduction in the numerical complexity. For N m three-level molecules we may thus represent the density matrix by a number of terms scaling as (N m + 8)!/(8!N m !) instead of 9 N m , and this allows exact simulations of up to N m = 10 molecules. Our simulations demonstrate that many emitters compensate strong plasmon damping and lead to the population of high plasmon number states and a narrowed linewidth of the plasmon field. For large N m , our exact results are reproduced by an approximate approach based on the plasmon reduced density matrix. With this approach, we have extended the simulations to more than 50 molecules and shown that the plasmon number state population follows a Poisson-like distribution. An alternative approach based on nonlinear rate equations for the molecular state populations and the mean plasmon number also reproduce the main lasing characteristics of the system.

Amplified emission and lasing in a plasmonic nanolaser with many three-level molecules

“…For two-level systems, this is utilized in collective representations of the density matrix with Dicke states [41,42], SU(4) group theory [43] and collective numbers [34,44]. Here, we choose the latter representation since it can be easily extended to systems with multi-level molecules [45,46]. We consider the density matrix element ρ β ν,α µ (t) between plasmon number states |µ and |ν and molecular product states N m +8 (N pl + 1) 2 of ρ µν n is order of magnitudes smaller than the number (3 N m • (N pl + 1)) 2 of ρ β ν,α µ .…”

Analysis of a Multimode Plasmonic Nanolaser with an Inhomogeneous Distribution of Molecular Emitters

“…2 (b). If all the molecules have the same distance to the sphere-surface, they are equivalent and the resulting ideal system has been already analyzed in [52]. There, we focused on the pumping mechanism and found the optimal parameters of the system leading to the strongest plasmon excitation, cf.…”

“…To account for multimolecules and multimodes, we have extended significantly the density matrix laser theory of Lamb for two-level emitters and single lasing mode in our model. By following the procedure developed in refs and , we first establish a reduced density operator equation for the entire system and then derive a quantum master equation for the reduced density matrix (RDM) of the plasmon modes. Our extended theory allows us to analyze how the molecular distribution affects the plasmon statistics and the molecule-induced mode correlations.…”