Giant atoms are attracting interest as an emerging paradigm in the quantum optics of engineered waveguides. At variance with the well-known artificial giant atoms for microwave photonics, here we propose the archetype of a giant atom working in the optical regime by considering a pair of interacting Rydberg atoms coupled to a photonic crystal waveguide (PCW) and also driven by a coherent field. Giant-atom effects are observed as a phase-dependent decay of the double Rydberg excitation during the initial evolution stage while a nontrivial internal entanglement is exhibited at later times. Such an entanglement onset occurs in the presence of intrinsic atomic decay toward nonguided vacuum modes and is accompanied by antibunching in the emitted photons. Our predictions should be observable in current Rydberg-PCW experiments and may open the way toward giant-atom optical photonics for quantum information processing.

Two interacting Rydberg atoms coupled to a waveguide may realize a giant-atom platform that exhibits controllable (phase-dependent) chirality through which the direction of nonreciprocally scattered photons can be switched on demand, e.g., by the geometrical tuning of an external driving field. In our platform, at variance with traditional setups, the chirality arises from a simple optical implementation of the local phase difference between two coupling points of the Rydberg giant atom. When employing two (or more) driving fields, this platform can also be used as a frequency converter with its strongly asymmetric efficiency being significantly enhanced via the chiral couplings. Our Rydberg giant-atom platform is well suited for chiral quantum optics applications and further offers direct scalability for reaching tunable frequency conversion in the optical domain.

Wave propagation through rapidly but continuously varying media is surprisingly subtle, and in a pair of recent papers [Horsley et al., J. Opt. 18, 044016 (2016); Longhi, Eur. Phys. Lett. 112, 64001 (2015)] it was found that planar media with a spatially varying permittivity $\epsilon \left(x\right)$ obeying the spatial Kramers-Kronig relations do not reflect waves incident from one side, however rapid the changes in $\epsilon \left(x\right)$. Within this large class of media there are some examples where the dissipation or gain is not asymptotically negligible and it has been pointed out [Longhi, Eur. Phys. Lett. 112, 64001 (2015)] that it is impossible to define meaningful reflection and transmission coefficients in such cases. Here we show—using an exactly soluble example—that despite the lack of any meaningful reflection and transmission coefficients, these profiles are still reflectionless from one side in the sense that the profile generates no counterpropagating wave for incidence from one side. This finding is demonstrated through examining the propagation of pulses through the profile, where from one side we find that no second reflected pulse is generated, while from the other there is. We conclude with a discussion of the effect of truncating these infinitely extended profiles, illustrating how the reflectionless behavior may be retained over a wide range of incident angles.

Tunable Rydberg interactions in cold atoms can be used to generate strongly correlated photon pairs through a spontaneous four-wave-mixing process in which all driving fields are allowed to work on resonance. The scheme relies on electromagnetically induced transparency and an imbalanced dark state with most atoms trapped in a ground state and a weakly populated Rydberg state. We show in particular that the combination of these two effects results in negligible linear absorption and Raman gain at the Stokes and anti-Stokes frequencies of generated photon pairs, while the nonlocal (Rydberg) nonlinearities contribute significantly to the enhancement of photon-pair generation rates and cross correlations at very low pump strengths and optical depths.

Phase gratings, each period of which consists of even numbers of equal-width and equal-thickness elements, can be devised to attain asymmetric diffraction patterns. We show that engineering of offset refractive indices in different elements exhibiting a spatially odd symmetry leads to the elimination of a single diffraction order (directional elimination), while further manipulations on offset refractive indices may lead to the elimination of all odd or even orders (grouped elimination) or all orders but one or two selected (directional selection). These intriguing effects arise from destructive interference between diffracted amplitudes contributed by paired or successive elements, and violation of Friedel's law in such transparent gratings is an effect of higher order multiple scattering.

We propose a scheme for realizing nonreciprocal optical scattering with non-Hermitian four-wave mixing (FWM) in a double-$\mathsf{\Lambda }$ system of cold atoms driven by coupling and dressing phase-mismatched standing-wave (SW) fields. Four scattering channels—direct transmission, cross transmission, direct reflection, and cross reflection—can be established for a probe and a signal field, some of which are nonreciprocal due to non-Hermitian spatial modulations when the two SW driving fields exhibit a $\pi /4$ phase shift. We find in particular that it is viable to attain single-color unidirectional transport, dual-color unidirectional transport, and single-color directional blockade with respect to a probe and a signal field incident upon this atomic sample from the same side, due to perfect destructive interference between direct and cross scattering channels. This work provides a new paradigm for studying non-Hermitian nonlinear optics and offers a theoretical foundation for designing all-optical atomic devices based on multi-channel nonreciprocal scattering.