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A numerically exact solution to the many emitter -- cavity problem as an openmany body system is presented. The solution gives access to the full,nonperturbative density matrix and thus the full quantum statistics and quantumcorrelations. The numerical effort scales with the third power in the number ofemitters. Notably the solution requires none of the common approximations likegood/bad cavity limit. As a first application the recently discussed concept ofcoherent surface plasmon amplification -- spaser -- is addressed: A spaserconsists of a plasmonic nanostructure that is driven by a set of quantumemitters. In the context of laser theory it is a laser in the (very) bad cavitylimit with an extremely high light matter interaction strength. The methodallows us to answer the question of spasing with a fully quantized theory.

Numerically exact solution of the many emitter -- cavity laser problem: application to the fully quantized spaser emission