  Understanding strongly correlated quantum systems is a central problem in
many areas of physics. The collective behavior of interacting particles gives
rise to diverse fundamental phenomena such as confinement in quantum
chromodynamics, phase transitions, and electron fractionalization in the
quantum Hall regime. While such systems typically involve massive particles,
optical photons can also interact with each other in a nonlinear medium. In
practice, however, such interactions are often very weak. Here we describe a
novel technique that allows the creation of a strongly correlated quantum gas
of photons using one-dimensional optical systems with tight field confinement
and coherent photon trapping techniques. The confinement enables the generation
of large, tunable optical nonlinearities via the interaction of photons with a
nearby cold atomic gas. In its extreme, we show that a quantum light field can
undergo fermionization in such one-dimensional media, which can be probed via
standard photon correlation measurements.
