  The multiphoton Jaynes-Cummings model is investigated and applications in
quantum information science are explored. Considering the strong atom-field
coupling regime and an $N$-photon interaction, a nonlinear driving field can
perform an arbitrary rotation in the Fock space of the cavity mode involving
the vacuum and an $M$-Fock state, with $M<N$. Besides, driving the cavity mode
with a linear coherent field (superposition of many Fock states), only the
cavity states within the Fock subspace {$|0\rangle,|1\rangle,..., |N-1\rangle$}
can be populated, i.e., we show how to implement a Fock state filter, or
quantum scissor, that restricts the dynamics of a given bosonic mode to a
limited Hilbert space. Such a device can be employed as a generator of
finite-dimensional quantum-optical states and also as a quantum-optical
intensity limiter, allowing as a special case the deterministic generation of
single-photon pulses. On the other hand, our system also provides a very rich
physics in the weak atom-field coupling regime, multiphoton
electromagnetically-induced-transparency-like phenomena, inducing a narrow
(controllable) reflectivity window for nonlinear probe fields. These results
are useful for applications in quantum information processing and also motivate
further investigations, e.g., the use of an $N$-photon Jaynes-Cummings system
as a qudit with harmonic spectrum and the exploration of multiphoton quantum
interference.

Quantum Physics