  Maxwell's demon principle of extracting valuable resources through measuring
fluctuations in the system already stimulated modern quantum physics. In
contrast to classical physics, a free coupling to a probe and its free
measurement fundamentally shape the system state. This becomes a new dimension
of the Maxwell demon effect, as in addition to the gained information, the back
action on the system can be exploited and essential for further applications.
We investigate quantum bosonic Maxwell's demon coupled to a two-level system to
address this issue straightforwardly. The deterministic multiple subtractions
of energy quanta by an energetically conservative Jaynes-Cummings interaction
leads to an out-of-equilibrium state. Although still super-Poissonian, it can
resonantly excite another two-level system better than any thermal state. To
further reduce the super-Poissonian statistics close to a Poissonian by a
Maxwell's demon operation and increase the excitation rate, we suggest
subsequent use of still energetically conservative multiphonon subtractions
performed by an available nonlinear Jaynes-Cummings interaction. The optimal
combination of both deterministic subtractions leads to statistics that
approaches a Poissonian distribution otherwise produced by shot-noise-limited
sources as an ideal laser requiring extreme bosonic nonlinear saturations.
