The quest to manipulate light propagation in ways not possible with natural media has driven the development of artificially structured metamaterials. One of the most striking effects is negative refraction, where the light beam deflects away from the boundary normal. However, due to material characteristics, the applications of this phenomenon, such as lensing that surpasses the diffraction limit, have been constrained. Here, we demonstrate negative refraction of light in an atomic medium without the use of artificial metamaterials, employing essentially exact simulations of light propagation. High transmission negative refraction is achieved in atomic arrays for different level structures and lattice constants, within the scope of currently realised experimental systems. We introduce an intuitive description of negative refraction based on collective excitation bands, whose transverse group velocities are antiparallel to the excitation quasi-momenta. We also illustrate how this phenomenon is robust to lattice imperfections and can be significantly enhanced through subradiance.

Received 3 November 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.049004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective effects in quantum opticsFrustrated magnetismLight propagation, transmission & absorptionLong-range interactionsPhase transitionsSuperradiance & subradianceAtomic, Molecular & Optical

We show how to achieve single-photon control via a synthesized optical magnetic response without metamaterials, using quantum-mechanical electric dipole transitions of naturally occurring atoms. We demonstrate how arrays of atoms can be designed to absorb, store, and emit single photons and realize a quantum atomic Huygens' surface that allows for extreme wavefront engineering. The response can be further controlled by the quantum state of an optical cavity, generating entanglement between the cavity and the array, and hence the cavity and transmitted light.

We demonstrate the presence of an optical phase transition with frustration-induced spontaneous symmetry breaking in a triangular planar atomic array due to cooperative light-mediated interactions. We show how the array geometry of triangle unit cells at low light intensities leads to degenerate collective radiative excitations forming nearly flat bands. We drive degenerate pairs of collective excitations to be equally populated in both the case of the atomic polarization being in the lattice plane and the case of the atomic polarization being perpendicular to it. At higher intensities, above specific threshold values, this symmetry in the populations is spontaneously broken. We also develop an effective few-mode model that provides semianalytic descriptions of the symmetry-breaking threshold and infinite-lattice limit phase transition. Surprisingly, we find how excitations due to dipolar interactions correspond to optical analogs of those found in frustrated magnets and superfluids, with closely related symmetry-breaking mechanisms despite the significant physical differences between these systems, opening the potential for simulating even quantum magnetism. Transmitted light through the array conveys information about symmetry breaking in the hysteresis behavior of the spectrum. Moreover, in a Mott-insulator state, the atomic positions are subject to zero-point quantum fluctuations. Interpreting each stochastic realization as a light-induced quantum measurement of the atomic position configuration, we find how strong nonlinearities and even weak position uncertainties lead to considerable measurement-induced symmetry breaking, while ensemble averaging over many realizations restores the original symmetry and the unbroken state. Larger position uncertainty results in the formation of domains of different broken symmetries.

By analyzing the parameters of electronic transitions, we show how bosonic Sr atoms in planar optical lattices can be engineered to exhibit optical magnetism and other higher-order electromagnetic multipoles that can be harnessed for wavefront control of incident light. Resonant λ≃ 2.6μm light for the ^3D_1→^3P_0 transition mediates cooperative interactions between the atoms while the atoms are trapped in a deeply subwavelength optical lattice. The atoms then exhibit collective excitation eigenmodes, e.g., with a strong cooperative magnetic response at optical frequencies, despite individual atoms having negligible coupling to the magnetic component of light. We provide a detailed scheme to utilize excitations of such cooperative modes consisting of arrays of electromagnetic multipoles to form an atomic Huygens' surface, with complete 2π phase control of transmitted light and almost no reflection, allowing nearly arbitrary wavefront shaping. In the numerical examples, this is achieved by controlling the atomic level shifts of Sr with off-resonant ^3P_J→^3D_1 transitions, which results in a simultaneous excitation of arrays of electric dipoles and electric quadrupoles or magnetic dipoles. We demonstrate the wavefront engineering for a Sr array by realizing the steering of an incident beam and generation of a baby-Skyrmion texture in the transmitted light via a topologically nontrivial transition of a Gaussian beam to a Poincaré beam, which contains all possible polarizations in a single cross-section.

Two-dimensional regular arrays of atoms are a promising platform for quantum networks, with collective subradiant states providing long-lived storage and collimated emission allowing for natural coherent links between arrays in free space. However, a single-layer lattice can only efficiently absorb or emit light symmetrically in the forward and backward directions. Here we show how a bilayer lattice can absorb a single photon either incident from a single direction or an arbitrary superposition of forward and backward propagating components. The excitation can be stored in a subradiant state, transferred coherently between different subradiant states, and released, again in an arbitrary combination of highly collimated forward and backward propagating components. We explain the directionality of single and bilayer arrays by a symmetry analysis based on the scattering parities of different multipole radiation components of collective excitations. The collective modes may exhibit the conventional half-wave loss of fields near the array interface or completely eliminate it. The proposed directional control of absorption and emission paves the way for effective one-dimensional quantum communication between multiple arrays, with single-photons propagating backward and forward between quantum information-processing and storage stages.

Natural materials typically interact weakly with the magnetic component of light which greatly limits their applications. This has led to the development of artificial metamaterials and metasurfaces. However, natural atoms, where only electric dipole transitions are relevant at optical frequencies, can cooperatively respond to light to form collective excitations with strong magnetic, as well as electric, interactions, together with corresponding electric and magnetic mirror reflection properties. By combining the electric and magnetic collective degrees of freedom we show that ultrathin planar arrays of atoms can be utilized as atomic lenses to focus light to subwavelength spots at the diffraction limit, to steer light at different angles allowing for optical sorting, and as converters between different angular momentum states. The method is based on coherently superposing induced electric and magnetic dipoles to engineer a quantum nanophotonic Huygens' surface of atoms, giving full 2π phase control over the transmission, with close to zero reflection.

While artificially fabricated patterned metasurfaces are providing paradigm-shifting optical components for classical light manipulation, strongly interacting, controllable, and deterministic quantum interfaces between light and matter in free space remain an outstanding challenge. Here we theoretically demonstrate how to achieve quantum control of both the electric and magnetic components of an incident single-photon pulse by engineering the collective response of a two-dimensional atomic array. High-fidelity absorption and storage in a long-lived subradiant state, and its subsequent retrieval, are achieved by controlling classically or quantum mechanically the ac Stark shifts of the atomic levels and suppressing the scattering during the absorption. Quantum wavefront control of the transmitted photon with nearly zero reflection is prepared by coupling the collective state of the array to another photon in a cavity and by engineering a Huygens' surface of atoms using only a single coherent standing wave. The proposed schemes allow for the generation of entanglement between the cavity, the lattice, and hence the state of the stored, reflected or transmitted light, and for quantum-state transfer between the cavity and propagating photons. Bipartite entanglement generation is explicitly calculated between a stored single-photon excitation of the array and the cavity photon. We illustrate the control by manipulating the phase, phase superposition, polarization, and direction of a transmitted or reflected photon, providing quantum-optical switches and functional quantum interfaces between light and atoms that could form links in a larger quantum information platform.

Parity-Time (PT$\mathcal{P}\mathcal{T}$) symmetry has become an important concept in the design of synthetic optical materials, with exotic functionalities such as unidirectional transport and nonreciprocal reflection. At exceptional points, this symmetry is spontaneously broken, and solutions transition from those with conserved intensity to exponential growth or decay. Here, we analyze a quantum-photonic surface formed by a single layer of atoms in an array with light mediating strong cooperative many-body interactions. We show how delocalized collective excitation eigenmodes can exhibit an effective PT$\mathcal{P}\mathcal{T}$ symmetry and nonexponential decay. This effective symmetry is achieved in a passive system without gain by balancing the scattering of a bright mode with the loss from a subradiant dark mode. These modes coalesce at exceptional points, evidenced by the emergence of coherent perfect absorption where coherent incoming light is perfectly absorbed and scattered only incoherently. We also show how PT$\mathcal{P}\mathcal{T}$ symmetry can be generated in total reflection and by balancing scattering and loss between different polarizations of collective modes.

A toroidal dipole represents an often overlooked electromagnetic excitation distinct from the standard electric and magnetic multipole expansion. We show how a simple arrangement of strongly radiatively coupled atoms can be used to synthesize a toroidal dipole where the toroidal topology is generated by radiative transitions forming an effective poloidal electric current wound around a torus. We extend the protocol for methods to prepare a delocalized collective excitation mode consisting of a synthetic lattice of such toroidal dipoles and a nonradiating, yet oscillating charge-current configuration, dynamic anapole, for which the far-field radiation of a toroidal dipole is identically canceled by an electric dipole.

We show how an initial localized radiative excitation in a two-dimensional array of cold atoms can be converted into highly-directional coherent emission of light by protecting the spreading of the excitation across the array in a subradiant collective eigenmode with a lifetime orders of magnitude longer than that of an isolated atom. We demonstrate how to reach two such strongly subradiant modes, a uniform one where all the dipoles are oscillating in phase normal to the plane and an antiferromagnetic mode where each dipole is π out of phase with its nearest neighbor. The excitation, which can consist of a single photon, is then released from the protected subradiant eigenmode by controlling the Zeeman level shifts of the atoms. Hence, an original localized excitation which emits in all directions is transferred to a delocalized subradiance-protected excitation, with a probabilistic emission of a photon only along the axis perpendicular to the plane of the atoms. This protected spreading and directional emission could potentially be used to link stages in a quantum information or quantum computing architecture.

By utilizing strong optical resonant interactions in arrays of atoms with electric dipole transitions, we show how to synthesize collective optical responses that correspond to those formed by arrays of magnetic dipoles and other multipoles. Optically active magnetism with the strength comparable with that of electric dipole transitions is achieved in collective excitation eigenmodes of the array. By controlling the atomic level shifts, an array of spectrally overlapping, crossed electric and magnetic dipoles can be excited, providing a physical realization of a nearly reflectionless quantum Huygens' surface with the full 2π phase control of the transmitted light that allows for extreme wavefront engineering even at a single photon level. We illustrate this by creating a superposition of two different orbital angular momentum states of light from an ordinary input state that has no orbital angular momentum.

In linear optics, modes correspond to a set of fields that are mutually orthogonal, however, in the nonlinear regime the principle of linear superposition is no longer valid and consequently, the method of mode decomposition breaks down. This is the case when considering sum-frequency generation in a nonlinear crystal. Here, we use the non-depleting pump approximation to describe the nonlinear interaction with low-intensity multiphoton fields. We show that the description of multiphoton fields using the propagation eigenmodes simplifies the Fock state quantum behaviour of the system while remaining equivalent to the standard approach.

When light scatters from an object, it can impart some physical quantity such as momentum or angular momentum. This can act as a measurement on the photon, which collapses on to an eigenstate of the measurement operator. However the corresponding operator is not the same as that describing the total linear or angular momentum in free space. Optical eigenmodes provide a powerful method to describe this interaction by expanding the field as a linear combination of some basis modes and examining the eigenvalues and eigenvectors of the quadratic measure in question. We extend this to the quantum case by writing the quantum operator corresponding to a given measurement such as energy, momentum or angular momentum as a superposition of creation and annihilation operators for each eigenmode. Upon measurement we find that the possible states of a single photon are simply the classical eigenmodes of the measurement. As an application, we examine the force and torque on a general, possibly anisotropic, material. By looking at eigenvalues of the measurement operator we show that the amount of a given quantity transferred in an interaction with matter is not in general the expected amount which a photon carries in free space, even at the single photon level. In particular the difference in linear or angular momentum from before and after is in general not equal to hk or h which are the eigenvalues of these quantities in free space.

Optical cavity QED provides a platform with which to explore quantum many-body physics in drivendissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic position. Specifically, we experimentally show that the interference of near-degenerate cavity modes leads to both a strong and tunable-range interaction between Bose-Einstein condensates (BECs) trapped within the cavity. We exploit the symmetry of a confocal cavity to measure the interaction between real BECs and their virtual images without unwanted contributions arising from the merger of real BECs. Atom-atom coupling may be tuned from short range to long range. This capability paves the way toward future explorations of exotic, strongly correlated systems such as quantum liquid crystals and driven-dissipative spin glasses.

As recently realized experimentally [Nature (London) 543, 87 (2017)], one can engineer models with continuous symmetries by coupling two cavity modes to trapped atoms via a Raman pumping geometry. Considering specifically cases where internal states of the atoms couple to the cavity, we show an extended range of parameters for which continuous symmetry breaking can occur, and we classify the distinct steady states and time-dependent states that arise for different points in this extended parameter regime.

Previous realizations of synthetic gauge fields for ultracold atoms do not allow the spatial profile of the field to evolve freely. We propose a scheme which overcomes this restriction by using the light in a multimode cavity with many nearly degenerate transverse modes, in conjunction with Raman coupling, to realize an artificial magnetic field which acts on a Bose-Einstein condensate of neutral atoms. We describe the evolution of such a system and present the results of numerical simulations which show dynamical coupling between the effective field and the matter on which it acts. Crucially, the freedom of the spatial profile of the field is sufficient to realize a close analogue of the Meissner effect, where the magnetic field is expelled from the superfluid. This backaction of the atoms on the synthetic field distinguishes the Meissner-like effect described here from the Hess-Fairbank suppression of rotation in a neutral superfluid observed elsewhere.

Rapid functionalisation of carbon surfaces using pulsed UV lasers offers a novel method for capturing fluorinated ligands or pollutants.

Propagating surface plasmon polaritons (SPPs) at metal–dielectric interfaces allow extreme light confinement enabling important technologies such as label-free real-time sensing and nanoscale optical wave guiding. In this work, we experimentally and theoretically map the surface plasmon dispersion of thin films of sequentially deposited silver and gold based on the Kretschmann–Raether configuration using spectroscopic ellipsometry. The results show efficient excitation of SPP modes related to the symmetric and antisymmetric modes of an insulator–metal–insulator waveguide. Since the symmetric modes have a larger electric field inside the bimetallic layer than the antisymmetric modes, we show that the dispersion for both modes can be tuned independently by controlling the thickness ratio and deposition order of metals in the film. This behavior is fundamentally different than modes in a single film or a thin film alloy. Results are in agreement with the analytical eigenmode dispersion of these modes and with a full transfer matrix model. Our results provide a complete understanding of surface plasmon modes in thin bilayer or multilayer metallic films and their ability to influence the propagation of surface plasmon waves.

The angular momentum of light plays an important role in many areas, from optical trapping to quantum information. In the usual three-dimensional setting, the angular momentum quantum numbers of the photon are integers, in units of the Planck constant ħ. We show that, in reduced dimensions, photons can have a half-integer total angular momentum. We identify a new form of total angular momentum, carried by beams of light, comprising an unequal mixture of spin and orbital contributions. We demonstrate the half-integer quantization of this total angular momentum using noise measurements. We conclude that for light, as is known for electrons, reduced dimensionality allows new forms of quantization.