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

TL;DR

This paper explores the multiphoton Jaynes-Cummings model's ability to perform arbitrary Fock space rotations and implement quantum filters, with applications in quantum information processing and state generation.

Contribution

It introduces methods for arbitrary Fock space rotations and Fock state filtering using multiphoton interactions in the Jaynes-Cummings model, expanding quantum control capabilities.

Findings

Arbitrary rotations in Fock space achieved via nonlinear driving fields.

Implementation of Fock state filters restricting dynamics to limited Hilbert spaces.

Observation of electromagnetically-induced-transparency-like phenomena in the weak coupling regime.

Abstract

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.