There has been rapid development of systems that yield strong interactions between freely propagating photons in one dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing w
ith photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized input-output formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.
Intense efforts have been made in recent years to realize nonlinear optical interactions at the single-photon level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other quantum emitters
while the possibility of achieving strong second-order nonlinearities remains unexplored. Here, we describe a novel technique to realize such nonlinearities using graphene, exploiting the strong per-photon fields associated with tightly confined graphene plasmons in combination with spatially nonlocal nonlinear optical interactions. We show that in properly designed graphene nanostructures, these conditions enable extremely strong internal down-conversion between a single quantized plasmon and an entangled plasmon pair, or the reverse process of second harmonic generation. A separate issue is how such strong internal nonlinearities can be observed, given the nominally weak coupling between these plasmon resonances and free-space radiative fields. On one hand, by using the collective coupling to radiation of nanostructure arrays, we show that the internal nonlinearities can manifest themselves as efficient frequency conversion of radiative fields at extremely low input powers. On the other hand, the development of techniques to efficiently couple to single nanostructures would allow these nonlinear processes to occur at the level of single input photons.
We present a realistic scheme for how to construct a single-photon transistor where the presence or absence of a single microwave photon controls the propagation of a subsequent strong signal signal field. The proposal is designed to work with existi
ng superconducting artificial atoms coupled to cavities. We study analytically and numerically the efficiency and the gain of our proposal and show that current transmon qubits allow for error probabilities ~1% and gains of the order of hundreds.
