Highly nonlocal optical nonlinearities in atoms trapped near a waveguide

Abstract

Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically-induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly-nonlocal interactions of optical fields in one dimension.Comment: 16 pages, including appendices and 5 figure

Colloquium : Quantum matter built from nanoscopic lattices of atoms and photons

“…In the PCW case, instead of a Rydberg level, one uses a metastable state jsi as the third level [see the inset of Fig. 15(a)] and engineers a dispersive interaction similar to Rydberg states using a band gap Σ j≠l fðz j ; z l Þσ j ss σ l ss (Douglas, Caneva, and Chang, 2016;Shahmoon et al, 2016). Given the extra tunability of atom-atom interactions mediated by nanophotonic interfaces, These interaction-induced shifts create new transparencies for different components of the input probe.…”

“…A first step has been made in this direction, by a perturbative treatment that reveals weak crystal-like correlations in the many-body excitations of the photons (Shahmoon et al, 2016). Developing a more general understanding of the dynamics of strongly interacting photons, in PCWs and in other platforms, is challenging and constitutes one of the exciting frontiers of quantum optics (Noh and Angelakis, 2017).…”

Optical properties of an atomic ensemble coupled to a band edge of a photonic crystal waveguide

“…Our model is then a minimal description that produces longrange interactions, and allows their effect to be probed. In particular, the level structure is considerably simplified compared to previous schemes to realize optical nonlinearities in PCWs [12,14]. The single-atom coupling strength to the TM band is denoted G 1D , and the associated wavevector k a is shown in figure 1(a).…”

“…An exciting example of the latter [9][10][11][12][13][14][15] is the ability to engineer long-range coherent interactions between atoms. The emission properties of an atom coupled to a PCW differ markedly from those in free space when the resonant transition frequency of the atom, w a , is inside a band gap, i.e.…”

“…The photonic component of this state constitutes an effective cavity mode that can mediate coupling to other atoms, resulting in effective dipole-dipole interactions which acquire the spatial features of the cavity mode. These interactions can in turn be exploited to realize novel regimes of quantum many-body physics and nonlinear optics [12,14,19].…”