We consider light scattering off a two-dimensional (2D) dipolar array and show how it can be tailored by properly choosing the lattice constant of the order of the incident wavelength. In particular, we demonstrate that such arrays can operate as nearly perfect mirrors for a wide range of incident angles and frequencies close to the individual atomic resonance. These results can be understood in terms of the cooperative resonances of the surface modes supported by the 2D array. Experimental realizations are discussed, using ultracold arrays of trapped atoms and excitons in 2D semiconductor materials, as well as potential applications ranging from atomically thin metasurfaces to single photon nonlinear optics and nanomechanics.

Whenever several quantum light emitters are brought in proximity with one another, their interaction with common electromagnetic fields couples them, giving rise to cooperative shifts in their resonance frequency. Such collective line shifts are central to modern atomic physics, being closely related to superradiance[1] on one hand and the Lamb shift[2] on the other. Although collective shifts have been theoretically predicted more than fifty years ago [3], the effect has not been observed yet in a controllable system of a few isolated emitters. Here, we report a direct spectroscopic observation of the cooperative shift of an optical electric dipole transition in a system of up to eight Sr + ions suspended in a Paul trap. We study collective resonance shift in the previously unexplored regime of far-field coupling, and provide the first observation of cooperative effects in an array of quantum emitters. These results pave the way towards experimental exploration of cooperative emission phenomena in mesoscopic systems.Soon after the discovery of superradiance by Dicke[1], it was realized [3][4][5] that superradiance phenomena are accompanied by a dispersive counterpart that shifts the resonance energies of the collective excitations relative to those of isolated emitters. The superradiance effects and the resonance shift originate, respectively, from the real and imaginary parts of resonant dipole-dipole interaction between emitters. The collective shifts arise via emission and reabsorption of virtual photons, and are therefore referred to as cooperative Lamb shift [6][7][8][9][10].Although cooperative phenomena have received a great deal of scientific attention, the experimental observations of collective Lamb shift have been relatively few. Cooperative shifts have been detected in a three-photon excitation resonance in Xenon [11] and, recently, in the absorption line of Rubidium vapor confined to an ultrathin cell [7]. In both cases, the cooperative shifts, arising from statistically averaged interaction of a large ensemble of atoms, were proportional to the atomic density.In a different approach, the energy level shifts due to resonant dipole-dipole interaction in the near field were studied in a system of two fluorescent molecules embedded in a dielectric film [12]. Such near-field interactions * These authors contributed equally to this work have also played an essential role in a number of experiments with Rydberg atoms [13][14][15]. In particular, the near-field cooperative shift in a system of two atoms has been utilized to prevent the transition of more than one atom to the Rydberg state, bringing about a phenomenon known as Rydberg blockade [16][17][18].Cooperative phenomena can be amplified by placing the emitters inside a resonator. Cavity-enhanced cooperative frequency shift in a nuclear excitation has been observed in a layer of Fe atoms embedded in a planar waveguide [8]. The coupling between emitters can also be enhanced by interaction with a single mirror. Such arrangement enabled the observation...

We show that nonradiative interactions between atomic dipoles placed in a waveguide can give rise to deterministic entanglement at ranges much larger than their resonant wavelength. The range increases as the dipole-resonance approaches the waveguide's cutoff frequency, caused by the giant density of photon modes near cutoff, a regime where the standard (perturbative) Markov approximation fails. We provide analytical theories for both the Markovian and non-Markovian regimes, supported by numerical simulations, and discuss possible experimental realizations.Comment: 9 pages, 2 figure

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We consider the dispersion energy of a pair of dipoles embedded in a metallic waveguide with transverse dimension $a$ smaller than the characteristic dipolar wavelength. We find that $a$ sets the scale that separates retarded, Casimir-Polder-like, from quasistatic, van der Waals-like, interactions. Whereas in the retarded regime, the energy decays exponentially with inter-dipolar distance, typical of evanescent waves, in the van der Waals regime, the known free-space result is obtained. This short-range scaling implies that the additivity of the dispersion interactions inside a waveguide extends to denser media, along with modifications to related Casimir effects in such structures.Comment: 8 pages, 4 figure

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 spatially-homogeneous conditional phase shift of pi for two single-photon pulses, realizing a deterministic photonic phase gate, or to implement a quantum nondemolition measurement of the photon number in the signal pulse by a coherent probe, thereby achieving a heralded source of single or few photon pulses

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

Quantum electromagnetic fluctuations induce forces between neutral particles, known as the van der Waals and Casimir interactions. These fundamental forces, mediated by virtual photons from the vacuum, play an important role in basic physics and chemistry and in emerging technologies involving, e.g., microelectromechanical systems or quantum information processing. Here we show that these interactions can be enhanced by many orders of magnitude upon changing the character of the mediating vacuum modes. By considering two polarizable particles in the vicinity of any standard electric transmission line, along which photons can propagate in one dimension, we find a much stronger and longer-range interaction than in free space. This enhancement may have profound implications on many-particle and bulk systems and impact the quantum technologies mentioned above. The predicted giant vacuum force is estimated to be measurable in a coplanar waveguide line.Casimir physics | quantum vacuum | circuit quantum electrodynamics | dispersion forces T he seminal works of London (1), Casimir and Polder (2), and Casimir (3) identified quantum electromagnetic fluctuations to be the source of both short-range [van der Waals (vdW)] and retarded, long-range (Casimir) interactions between polarizable objects, which may be viewed as an exchange of virtual photons from the vacuum. Subsequent studies of these interactions (4-14) revealed their modifications, such as retardation and nonadditivity (15), brought about by the geometry of the polarizable objects. The ability to design these interactions is important for their possible use and exploration in emerging quantum technologies such as microelectromechanical systems (16), quantum information processing (17, 18), and circuit quantum electrodynamics, where the dynamical Casimir effect has been recently demonstrated (19,20). Here we show that effectively one-dimensional (1D) transmission-line environments can induce strongly enhanced and longer-range van der Waals and Casimir interactions compared with free space. Such enhanced interactions may have profound implications on the quantum technologies mentioned above and give rise to a variety of new many-body phenomena involving polarizable particles in effectively 1D environments.A key point in determining how these interactions depend on distance is the spatial propagation and scattering of the virtual photon modes that mediate them. Like any other waves, photons are scattered differently off objects with different geometries. For example, light is much more effectively scattered off a mirror than off a point-like atom. This explains the stronger and longerrange vacuum interaction between mirrors (3), compared with that between atoms (2). This idea also underlies the dependence of Casimir forces on the geometrical shape of the interacting objects. Here, we take a somewhat different approach toward the geometry dependence of vdW-and Casimir-related phenomena. Instead of considering the interaction energy of extended objects with different ...