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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Fully quantized spaser physics: towards exact modeling of mesoscopic CQED systems

Michael Gegg, T. Sverre Theuerholz, Andreas Knorr, Marten Richter

Published Mar 13, 2015• 2 citations
Publisher

Abstract

We present a theoretical discussion on the feasibility of spasing for a specific spaser setup. For this purpose we develop a numerically exact and feasible solution to the open system Tavis-Cummings model in the Born- Markov Lindblad formalism. The complexity of the solution scales with the third power in the number of two level systems- a considerable advance compared to the exponential scaling of the brute force solution. The question of spasing is answered negatively in agreement with the literature.

DOI
10.1117/12.2073293

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We present a theoretical discussion on the feasibility of spasing for a specific spaser setup. For this purpose we develop a numerically exact and feasible solution to the open system Tavis-Cummings model in the Born- Markov Lindblad formalism. The complexity of the solution scales with the third power in the number of two level systems- a considerable advance compared to the exponential scaling of the brute force solution. The question of spasing is answered negatively in agreement with the literature.
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and qqq-deformed binomial statistics.
A numerically exact solution to the many emitter--cavity problem as an open many body system is presented. The solution gives access to the full, nonperturbative density matrix and thus the full quantum statistics and quantum correlations. The numerical effort scales with the third power in the number of emitters. Notably the solution requires none of the common approximations such as good/bad cavity limit. As a first application the recently discussed concept of coherent surface plasmon amplification---spaser---is addressed: A spaser consists of a plasmonic nanostructure that is driven by a set of quantum emitters. In the context of laser theory it is a laser in the (very) bad cavity limit with an extremely high light matter interaction strength. The method allows us to answer the question of spasing with a fully quantized theory.
We demonstrate that it is possible to derive an approximate analytical expression to characterize the spasing (L-L) curve of a coherently enhanced spaser with 3-level gain-medium chromophores. The utility of this solution stems from the fact that it enables optimization of the large parameter space associated with spaser designing, a functionality not offered by the methods currently available in the literature. This is vital for the advancement of spaser technology towards the level of device realization. Owing to the compact nature of the analytical expressions, our solution also facilitates the grouping and identification of key processes responsible for the spasing action, whilst providing significant physical insights. Furthermore, we show that our expression generates results within 0.1% error compared to numerically obtained results for pumping rates higher than the spasing threshold, thereby drastically reducing the computational cost associated with spaser designing.