Few-Photon Nonlinear Optics In Photonic Bandgap Fibers

Abstract

The ability to control light with light at ultralow powers has been a major avenue of research in photonics with applications to optical communications, computation, and signal processing. Such light-by-light scattering is achieved in a medium with a strong light-matter interaction, and for the development of quantum information networks it is important to demonstrate such effects near the single-photon level. Alkali-metal vapors such as rubidium (Rb) enable strong light-matter interactions due to the large cross section per atom and well-defined energy level structure, while the use of optical fibers offers the advantage of possible integration with modern optical communication systems. Hollow-core photonic band-gap fibers (PBGFs) can combine both these technologies such that both the atoms and the optical fields are transversely confined to a region that is a few wavelengths in size, which offers the prospect of exploring few-photon nonlinear interactions. We generate large optical depths in such a Rb-PBGF system, and the tight light confinement, high vapor density and long interaction length allow us to perform nonlinear optics at ultralow power. We demonstrate large signal amplification (>100) and frequency conversion using a four-wave mixing process with only microwatts of pump power. This is, to our knowledge, the largest gain observed at such low power. We perturb the coherence of this four-wave mixing to demonstrate all-optical modulation at unprecedented bandwidths (~300 MHz) for an atomic-vapor system, with an energy density of only tens of pho- tons per atomic cross-section, comparable to that achieved in more elaborate setups based on cold-atomic clouds. We then demonstrate an enhancement of several orders of magnitude in degenerate two-photon absorption in our RbPBGF system over that achieved in bulk vapor cells in a focused beam geometry. This allows us to directly measure two-photon absorption from a beam by detecting its intensity on a photodiode. Further, employing a near-resonant, non-degenerate two-photon transition in Rb, we demonstrate all-optical intensity modulation with just a few photons (<20), or only a few attojoules of energy, at relatively large bandwidths (~50 MHz) for such a sensitive scheme. This result takes us to within an order of magnitude of single-photon switching, and improves upon previous experiments for freely propagating optical fields, including those in cold-atoms. Finally, we produce relatively large cross-phase shifts of a few milliradians on a meter beam with <20 signal photons by tuning slightly away from resonance on the same non-degenerate two-photon transition. This corresponds to a phase shift of 0.3 milliradian per photon, with a fast response time of <5 ns. This represents, to our knowledge, the largest such nonlinear phase shift induced in a single-pass through a room temperature medium. Our Rb-PBGF system can thus potentially be employed to realize weak-nonlinearity based quantum computation and quantum non-demolition measurement of photon number. Through these experiments, we show the potential of a Rb-PBGF system for exploring quantum nonlinear optics at ultralow powers. Moreover, our system is simpler and easier to control and manipulate than setups based on cold atomic clouds and/or high-finesse cavities, and holds promise for integration with fiber-optic communication networks.