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.
A method for performing nonlocal interferometry using phase-entangled macroscopic coherent states is described. The required entanglement can be generated using weak nonlinearities while Bell's inequality can be violated using single photons as a probe. The entanglement is relatively robust against photon loss and Bell's inequality can be violated over a relatively large distance in optical fibers despite the fact that a large number of photons are absorbed in the process.
We present a novel method for detecting nonlinearities, due to quantum electrodynamics through photon-photon scattering, in Maxwell's equation. The photon-photon scattering gives rise to self-interaction terms, which are similar to the nonlinearities due to the polarisation in nonlinear optics. These self-interaction terms vanish in the limit of parallel propagating waves, but if instead of parallel propagating waves the modes generated in wavesguides are used, there will be a non-zero total effect. Based on this idea, we calculate the nonlinear excitation of new modes and estimate the strengt…
We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogous to the Marchenko integral equation in integrable systems. We show explicitly how this can be achieved through several examples including reaction-diffusion systems with nonlocal quadratic nonlinearities and the nonlinear Schrodinger equation with a…
Strong amplification in integrated photonics is one of the most desired optical functionalities for computing, communications, sensing, and quantum information processing. Semiconductor gain and cubic nonlinearities, such as four-wave mixing and stimulated Raman and Brillouin scattering, have been among the most studied amplification mechanisms on chip. Alternatively, material platforms with strong quadratic nonlinearities promise numerous advantages with respect to gain and bandwidth, among which nanophotonic lithium niobate is one of the most promising candidates. Here, we combine quasi-phas…
Exciton-polaritons are hybrid light-matter excitations arising from the non-perturbative coupling of a photonic mode and an excitonic resonance. Behaving as interacting photons, they show optical third-order nonlinearities providing effects such as optical parametric oscillation or amplification. It has been suggested that polariton-polariton interactions can be greatly enhanced by inducing aligned electric dipoles in their excitonic part. However direct evidence of a true particle-particle interaction, such as superfluidity or parametric scattering is still missing. In this work, we demonstra…
We demonstrate scattering of laser light from two InAs quantum dots coupled to a photonic crystal waveguide, which is achieved by strain-tuning the optical transitions of the dots into mutual resonance. By performing measurements of the intensity and photon statistics of transmitted laser light before and after tuning the dots into resonance, we show that the nonlinearity is enhanced by collective scattering. In addition to providing a means of manipulating few-photon optical nonlinearities, our approach establishes new opportunities for multi-emitter quantum optics in a solid-state platform.
A general method for extending a non-dissipative nonlinear Schrödinger and Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is completely separable, which is the strongest condition one can impose on dynamics of composite systems. It requires that for all initial states (entangled or not) a subsystem not only cannot be influenced by any action undertaken by an observer in a separated system (strong separability), but additionally that the self-consistency condition $Tr_2\circ ϕ^t_{1+2}=ϕ^t_{…
Prospective integrated quantum optical technologies will combine nonlinear optics and components requiring cryogenic operating temperatures. Despite the prevalence of integrated platforms exploiting $χ^{(2)}$-nonlinearities for quantum optics, for example used for quantum state generation and frequency conversion, their material properties at low temperatures are largely unstudied. Here, we demonstrate the first second harmonic generation in a fiber-coupled lithium niobate waveguide at temperatures down to 4.4K. We observe a reproducible shift in the phase-matched pump wavelength within the te…
While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock state or coherent state inputs. We identify rules to compare light transport properties, the Kerr, and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized descriptio…
The very small size of optical nonlinearities places wide ranging restrictions on the types of novel physics one can explore. For an ensemble of multi-level systems one can synthesize a large effective optical nonlinearity using quantum coherence effects but such non-linearities are technically extremely challenging to demonstrate at the single atom level. In this work we describe how a single artificial multi-level Cooper Pair Box molecule, interacting with a superconducting microwave coplanar waveguide resonator, when suitably driven, can generate extremely large optical nonlinearities at mi…
Nonlinear frequency conversion is ubiquitous in laser engineering and quantum information technology. A long-standing goal in photonics is to integrate on-chip semiconductor laser sources with nonlinear optical components. Engineering waveguide lasers with spectra that phase-match to nonlinear processes on the same device is a formidable challenge. Here, we demonstrate difference-frequency generation in an AlGaAs Bragg reflection waveguide which incorporates the gain medium for the pump laser in its core. We include quantum dot layers in the AlGaAs waveguide that generate electrically driven l…
We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodina…
A quantum emitter efficiently coupled to a nanophotonic waveguide constitutes a promising system for the realization of single-photon transistors, quantum-logic gates based on giant single-photon nonlinearities, and high bit-rate deterministic single-photon sources. The key figure of merit for such devices is the $β$-factor, which is the probability for an emitted single photon to be channeled into a desired waveguide mode. We report on the experimental achievement of $β= 98.43 \pm 0.04\%$ for a quantum dot coupled to a photonic-crystal waveguide, corresponding to a single-emitter cooperativit…
Aluminum gallium arsenide has highly desirable properties for integrated parametric optical interactions: large material nonlinearities, maturely established nanoscopic structuring through epitaxial growth and lithography, and a large band gap for broadband low-loss operation. However, its full potential for record-strength nonlinear interactions is only released when the semiconductor is embedded within a dielectric cladding to produce highly confining waveguides. From simulations of such, we present second and third order pair generation that could improve upon state-of-the-art quantum optic…
Hollow-core photonic-crystal waveguides filled with cold atoms can support giant optical nonlinearities through nondispersive propagation of light tightly confined in the transverse direction. Here we explore electromagnetically induced transparency is such structures, considering a pair of counter-propagating weak quantum fields in the medium of coherently driven atoms in the ladder configuration. Strong dipole--dipole interactions between optically excited, polarized Rydberg states of the atoms translate into a large dispersive interaction between the two fields. This can be used to attain a…
We numerically demonstrate that "mode-entangled states" based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.
We show that the spin-charge separation predicted for correlated fermions in one dimension, could be observed using polarized photons propagating in a nonlinear optical waveguide. Using coherent control techniques and employing a cold atom ensemble interacting with the photons, large nonlinearities in the single photon level can be achieved. We show that the latter can allow for the simulation of a strongly interacting gas, which is made of stationary dark-state polaritons of two species and then shown to form a Luttinger liquid of effective fermions for the right regime of interactions. The s…
