Multiphoton Jaynes-Cummings Model: Arbitrary Rotations in Fock Space and Quantum Filters

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.