Theory of Subradiant States of a One-Dimensional Two-Level Atom Chain

Strongly Interacting Photons in 2D Waveguide QED

One-dimensional confinement in waveguide quantum electrodynamics (QED) plays a crucial role to enhance light-matter interactions and to induce a strong quantum nonlinear optical response. In two or higher-dimensional settings, this response is reduced since photons can be emitted within a larger phase space, opening the question whether strong photon-photon interaction can be still achieved. In this study, we positively answer this question for the case of a 2D square array of atoms coupled to the light confined into a two-dimensional waveguide. More specifically, we demonstrate the occurrence of long-lived two-photon repulsive and bound states with genuine 2D features. Furthermore, we observe signatures of these effects also in free-space atomic arrays in the form of weakly subradiant in-band scattering resonances. Our findings provide a paradigmatic signature of the presence of strong photon-photon interactions in 2D waveguide QED.

Observation of millihertz-level cooperative Lamb shifts in an optical atomic clock

Collective couplings of atomic dipoles to a shared electromagnetic environment produce a wide range of many-body phenomena. We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions produce spatially dependent cooperative Lamb shifts when spectroscopically interrogating the millihertz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for optical atomic clocks. Additionally, we demonstrate that excitation of the atomic dipoles near a Bragg angle can enhance these effects by nearly an order of magnitude compared with nonresonant geometries. Our work demonstrates a platform for precise studies of the quantum many-body physics of spins with long-range interactions mediated by propagating photons.

Superradiant Detection of Microscopic Optical Dipolar Interactions

The interaction between light and cold atoms is a complex phenomenon potentially featuring many-body resonant dipole interactions. A major obstacle toward exploring these quantum resources of the system is macroscopic light propagation effects, which not only limit the available time for the microscopic correlations to locally build up, but also create a directional, superradiant emission background whose variations can overwhelm the microscopic effects. In this Letter, we demonstrate a method to perform "background-free" detection of the microscopic optical dynamics in a laser-cooled atomic ensemble. This is made possible by transiently suppressing the macroscopic optical propagation over a substantial time, before a recall of superradiance that imprints the effect of the accumulated microscopic dynamics onto an efficiently detectable outgoing field. We apply this technique to unveil and precisely characterize a density-dependent, microscopic dipolar dephasing effect that generally limits the lifetime of optical spin-wave order in ensemble-based atom-light interfaces.

Zeno Regime of Collective Emission: Non-Markovianity beyond Retardation

To build up a collective emission, the atoms in an ensemble must coordinate their behavior by exchanging virtual photons. We study this non-Markovian process in a subwavelength atom chain coupled to a one-dimensional (1D) waveguide and find that retardation is not the only cause of non-Markovianity. The other factor is the memory of the photonic environment, for which a single excited atom needs a finite time, the Zeno regime, to transition from quadratic decay to exponential decay. In the waveguide setup, this crossover has a time scale longer than the retardation, thus impacting the development of collective behavior. By comparing a full quantum treatment with an approach incorporating only the retardation effect, we find that the field memory effect, characterized by the population of atomic excitation, is much more pronounced in collective emissions than that in the decay of a single atom. Our results maybe useful for the dissipation engineering of quantum information processings based on compact atom arrays.

Non-Hermitian Waveguide Cavity QED with Tunable Atomic Mirrors

Optical mirrors determine cavity properties by means of light reflection. Imperfect reflection gives rise to open cavities with photon loss. We study an open cavity made of atom-dimer mirrors with a tunable reflection spectrum. We find that the atomic cavity shows anti-PT symmetry. The anti-PT phase transition controlled by atomic couplings in mirrors indicates the emergence of two degenerate cavity supermodes. Interestingly, a threshold of mirror reflection is identified for realizing strong coherent cavity-atom coupling. This reflection threshold reveals the criterion of atomic mirrors to produce a good cavity. Moreover, cavity quantum electrodynamics with a probe atom shows mirror-tuned properties, including reflection-dependent polaritons formed by the cavity and probe atom. Our Letter presents a non-Hermitian theory of an anti-PT atomic cavity, which may have applications in quantum optics and quantum computation.

Optical Properties of Concentric Nanorings of Quantum Emitters

A ring of sub-wavelength spaced dipole-coupled quantum emitters features extraordinary optical properties when compared to a one-dimensional chain or a random collection of emitters. One finds the emergence of extremely subradiant collective eigenmodes similar to an optical resonator, which features strong 3D sub-wavelength field confinement near the ring. Motivated by structures commonly appearing in natural light-harvesting complexes (LHCs), we extend these studies to stacked multi-ring geometries. We predict that using double rings allows us to engineer significantly darker and better confined collective excitations over a broader energy band compared to the single-ring case. These enhance weak field absorption and low-loss excitation energy transport. For the specific geometry of the three rings appearing in the natural LH2 light-harvesting antenna, we show that the coupling between the lower double-ring structure and the higher energy blue-shifted single ring is very close to a critical value for the actual size of the molecule. This creates collective excitations with contributions from all three rings, which is a vital ingredient for efficient and fast coherent inter-ring transport. This geometry thus should also prove useful for the design of sub-wavelength weak field antennae.

Control of Localized Single- and Many-Body Dark States in Waveguide QED

Subradiant states in a finite chain of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and their controlled release. As one can maximally store one energy quantum per emitter, storing multiple excitations requires delocalized states, which typically exhibit fermionic correlations and antisymmetric wave functions, thus making them hard to access experimentally. Here we identify a new class of quasilocalized dark states with up to half of the qubits excited, which only appear for lattice constants of an integer multiple of the wavelength. These states allow for a high-fidelity preparation and minimally invasive readout in state-of-the-art setups. In particular, we suggest an experimental implementation using a coplanar waveguide coupled to superconducting transmon qubits on a chip. With minimal free space and intrinsic losses, virtually perfect dark states can be achieved for a low number of qubits featuring fast preparation and precise manipulation.

Coherent Control of Collective Spontaneous Emission through Self-Interference

As one of the central topics in quantum optics, collective spontaneous emission such as superradiance has been realized in a variety of systems. This Letter proposes an innovative scheme to coherently control collective emission rates via a self-interference mechanism in a nonlinear waveguide setting. The self-interference is made possible by photon backward scattering incurred by quantum scatterers in a waveguide working as quantum switches. Whether the interference is constructive or destructive is found to depend strongly on the distance between the scatterers and the emitters. The interference between two propagation pathways of the same photon leads to controllable superradiance and subradiance, with their collective decay rates much enhanced or suppressed (also leading to hyperradiance or population trapping). Furthermore, the self-interference mechanism is manifested by an abrupt change in the emission rates in real time. An experimental setup based on superconducting transmission line resonators and transmon qubits is further proposed to realize controllable collective emission rates.

Tailoring the superradiant and subradiant nature of two coherently coupled quantum emitters

The control and manipulation of quantum-entangled states is crucial for the development of quantum technologies. A promising route is to couple solid-state quantum emitters through their optical dipole-dipole interactions. Entanglement in itself is challenging, as it requires both nanometric distances between emitters and nearly degenerate electronic transitions. Here we implement hyperspectral imaging to identify pairs of coupled dibenzanthanthrene molecules, and find distinctive spectral signatures of maximally entangled superradiant and subradiant electronic states by tuning the molecular optical resonances with Stark effect. We demonstrate far-field selective excitation of the long-lived subradiant delocalized state with a laser field tailored in amplitude and phase. Optical nanoscopy of the coupled molecules unveils spatial signatures that result from quantum interferences in their excitation pathways and reveal the location of each emitter. Controlled electronic-states superposition will help deciphering more complex physical or biological mechanisms governed by the coherent coupling and developing quantum information schemes.

Efficient nano-photonic antennas based on dark states in quantum emitter rings

Nanoscopic arrays of quantum emitters can feature highly sub-radiant collective excitations with a lifetime exponentially growing with emitter number. Adding an absorptive impurity as an energy dump in the center of a ring shaped polygon allows to exploit this feature to create highly efficient single photon antennas. Here among regular polygons with an identical center absorbing emitter, a nonagon exhibits a distinct optimum of the absorption efficiency. This special enhancement originates from the unique emergence of a subradiant eigenstate with dominant center occupation. Only for nine emitters the sum of coupling strengths of each emitter to all others matches the center to the ring coupling. Analogous to a parabolic mirror the antenna ring then concentrates incoming radiation at its center without being significantly excited itself. Similar large efficiency enhancements, which even prevail for broadband excitation, can also be engineered for other antenna sizes by tailoring the frequency and magnitude of the central absorber. Interestingly, for very small structures a quantum treatment predicts an even stronger enhancement for the single photon absorption enhancement than a classical dipole model. As natural light harvesting structures are often based on ring shaped structures, the underlying principle might be exploited there as well.

Tunable Directional Emission and Collective Dissipation with Quantum Metasurfaces

Subwavelength atomic arrays, recently labeled as quantum metamaterials, have emerged as an exciting platform for obtaining novel quantum optical phenomena. The strong interference effects in these systems generate subradiant excitations that propagate through the atomic array with very long lifetimes. Here, we demonstrate that one can harness these excitations to obtain tunable directional emission patterns and collective dissipative couplings when placing judiciously additional atoms nearby the atomic array. For doing that, we first characterize the optimal square array geometry to obtain directional emission patterns. Then, we characterize the best atomic positions to couple efficiently to the subradiant metasurface excitations and provide several improvement strategies based on entangled atomic clusters or bilayers. Afterward, we also show how the directionality of the emission pattern can be controlled through the relative dipole orientation between the auxiliary atoms and the one of the array. Finally, we benchmark how these directional emission patterns translate into to collective, anisotropic dissipative couplings between the auxiliary atoms by studying the lifetime modification of atomic entangled states.

Free-Fermion Multiply Excited Eigenstates and Their Experimental Signatures in 1D Arrays of Two-Level Atoms

One-dimensional (1D) subwavelength atom arrays display multiply excited subradiant eigenstates which are reminiscent of free fermions. So far, these states have been associated with subradiant states with decay rates ∝N^{-3}, with N the number of atoms, which fundamentally prevents detection of their fermionic features by optical means. In this Letter, we show that free-fermion states generally appear whenever the band of singly excited states has a quadratic dispersion relation at the band edge and, hence, may also be obtained with radiant and even superradiant states. 1D arrays have free-fermion multiply excited eigenstates that are typically either subradiant or (super)radiant, and we show that a simple transformation acts between the two families. Based on this correspondence, we propose different means for their preparation and analyze their experimental signature in optical detection.

Bound Photonic Pairs in 2D Waveguide Quantum Electrodynamics

We theoretically predict the formation of two-photon bound states in a two-dimensional waveguide network hosting a lattice of two-level atoms. The properties of these bound pairs and the exclusive domains of the parameter space where they emerge due to the interplay between the on-site photon blockade and peculiar shape of polariton dispersion resulting from the long-range radiative couplings between the qubits are investigated in detail. In addition, we analyze the effect of the finite-size system on localization characteristics of these excitations.

Quantum Nonlinear Optics Based on Two-Dimensional Rydberg Atom Arrays

We propose the combination of subwavelength, two-dimensional atomic arrays and Rydberg interactions as a powerful platform to realize strong, coherent interactions between individual photons with high fidelity. The atomic spatial ordering guarantees efficient atom-light interactions without the possibility of scattering light into unwanted directions, allowing the array to act as a perfect mirror for individual photons. In turn, Rydberg interactions enable single photons to alter the optical response of the array within a potentially large blockade radius R_{b}, which can effectively punch a large "hole" for subsequent photons. We show that such a system enables a coherent photon-photon gate or switch, with a significantly better error scaling (∼R_{b}^{-4}) than in a disordered ensemble. We also investigate the optical properties of the system in the limit of strong input intensities and show that this many-body quantum driven dissipative system can be modeled well by a semiclassical model based on holes punched in a classical mirror.

Optical cooperative effects of multiemitters in a one-dimensional (1D) dense array

We theoretically explore cooperative effects of equally spaced multiemitters in a 1D dense array driven by a low-intensity probe field propagating through a 1D waveguide by modeling the emitters as point-like coupled electric dipoles. We calculate the collective optical spectra of a number of 1D emitter arrays with any radiation-retention coefficient η using both exact classical-electrodynamics and mean-field-theory formalisms. We illustrate cooperative effects of lossless 1D emitter arrays with η = 1 at the emitter spacings, which are displayed by steep edges accompanied by a deep minimum and Fano resonances in the plots of transmissivities as a function of the detuning of the incident light from the emitter resonance. Numerical simulation of the full width of such optical bandgaps reveals that cooperativity between emitters is greater in a small array of size N ≤ 8 than in a larger one of size N > 8. For a lossy 1D emitter array in which the radiation retention coefficient is equal to or less than 0.1 the transmissivity obtained by exact-electrodynamics scheme exhibits no bandgap structures, being in good agreement with the mean-field-theory result. We propose that a 1D multiemitter array may work as a nanoscale filter blocking transmission of light with a frequency in the range of optical bandgaps.

Dimerization of Many-Body Subradiant States in Waveguide Quantum Electrodynamics

We theoretically study subradiant states in an array of atoms coupled to photons propagating in a one-dimensional waveguide focusing on the strongly interacting many-body regime with large excitation fill factor f. We introduce a generalized many-body entropy of entanglement based on exact numerical diagonalization followed by a high-order singular value decomposition. This approach has allowed us to visualize and understand the structure of a many-body quantum state. We reveal the breakdown of fermionized subradiant states with increase of f with the emergence of short-ranged dimerized antiferromagnetic correlations at the critical point f=1/2 and the complete disappearance of subradiant states at f>1/2.

Controlling Interactions between Quantum Emitters Using Atom Arrays

We investigate the potential for two-dimensional atom arrays to modify the radiation and interaction of individual quantum emitters. Specifically, we demonstrate that control over the emission linewidths, resonant frequency shifts, and local driving field enhancement in impurity atoms is possible due to strong dipole-dipole interactions within ordered, subwavelength atom array configurations. We demonstrate that these effects can be used to dramatically enhance coherent dipole-dipole interactions between distant impurity atoms within an atom array. Possible experimental realizations and potential applications are discussed.

Quantum Chaos Driven by Long-Range Waveguide-Mediated Interactions

We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide. Our calculation reveals two-polariton eigenstates that have a highly irregular wave function in real space. This indicates the Bethe ansatz breakdown and the onset of quantum chaos, in stark contrast to the conventional integrable problem of two interacting bosons in a box. We identify the long-range waveguide-mediated coupling between the atoms as the key ingredient of chaos and nonintegrability. Our results provide new insights in the interplay between order, chaos, and localization in many-body quantum systems and can be tested in state-of-the-art setups of waveguide quantum electrodynamics.

Quantum Energy and Charge Transfer at Two-Dimensional Interfaces

Energy and charge transfer processes in interacting donor-acceptor systems are the bedrock of many fundamental studies and technological applications ranging from biosensing to energy storage and quantum optoelectronics. Central to the understanding and utilization of these transfer processes is having full control over the donor-acceptor distance. With their atomic thickness and ease of integrability, two-dimensional materials are naturally emerging as an ideal platform for the task. Here, we review how van der Waals semiconductors are shaping the field. We present a selection of some of the most significant demonstrations involving transfer processes in layered materials that deepen our understanding of transfer dynamics and are leading to intriguing practical realizations. Alongside current achievements, we discuss outstanding challenges and future opportunities.

Subradiant Emission from Regular Atomic Arrays: Universal Scaling of Decay Rates from the Generalized Bloch Theorem

The Hermitian part of the field-mediated dipole-dipole interaction in infinite periodic arrays of two-level atoms yields an energy band of the singly excited states. In this Letter, we show that a dispersion relation, ω_{k}-ω_{k_{ex}}∝(k-k_{ex})^{s}, near the band edge of the infinite system leads to the existence of subradiant states of finite one-dimensional arrays of N atoms with decay rates scaling as N^{-(s+1)}. This explains the recently discovered N^{-3} scaling and it leads to the prediction of power law scaling with higher power for special values of the lattice period. For the quantum optical implementation of the Su-Schrieffer-Heeger topological model in a dimerized emitter array, the band gap closing inherent to topological transitions changes the value of s in the dispersion relation and alters the decay rates of the subradiant states by many orders of magnitude.

Geometric Control of Collective Spontaneous Emission

Dipole spin-wave states of atomic ensembles with wave vector k(ω) mismatched from the dispersion relation of light are difficult to access by far-field excitation but may support rich phenomena beyond the traditional phase-matched scenario in quantum optics. We propose and demonstrate an optical technique to efficiently access these states. In particular, subnanosecond laser pulses shaped by a home-developed wideband modulation method are applied to shift the spin wave in k space with state-dependent geometric phase patterning, in an error-resilient fashion and on timescales much faster than spontaneous emission. We verify this control through the redirection, switch off, and recall of collectively enhanced emission from a ^{87}Rb gas with ∼75% single-step efficiency. Our work represents a first step toward efficient control of electric dipole spin waves for studying many-body dissipative dynamics of excited gases, as well as for numerous quantum optical applications.

Waveguide Quantum Optomechanics: Parity-Time Phase Transitions in Ultrastrong Coupling Regime

We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest setup of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The PT phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.

Optical Magnetism and Huygens' Surfaces in Arrays of Atoms Induced by Cooperative Responses

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.

Superatom Picture of Collective Nonclassical Light Emission and Dipole Blockade in Atom Arrays

We show that two-time, second-order correlations of scattered photons from planar arrays and chains of atoms display nonclassical features that can be described by a superatom picture of the canonical single-atom g_{2}(τ) resonance fluorescence result. For the superatom, the single-atom linewidth is replaced by the linewidth of the underlying collective low light-intensity eigenmode. Strong light-induced dipole-dipole interactions lead to a correlated response, suppressed joint photon detection events, and dipole blockade that inhibits multiple excitations of the collective atomic state. For targeted subradiant modes, the nonclassical nature of emitted light can be dramatically enhanced even compared with that of a single atom.

Fast electrical modulation of strong near-field interactions between erbium emitters and graphene

Combining the quantum optical properties of single-photon emitters with the strong near-field interactions available in nanophotonic and plasmonic systems is a powerful way of creating quantum manipulation and metrological functionalities. The ability to actively and dynamically modulate emitter-environment interactions is of particular interest in this regard. While thermal, mechanical and optical modulation have been demonstrated, electrical modulation has remained an outstanding challenge. Here we realize fast, all-electrical modulation of the near-field interactions between a nanolayer of erbium emitters and graphene, by in-situ tuning the Fermi energy of graphene. We demonstrate strong interactions with a  >1000-fold increased decay rate for  ~25% of the emitters, and electrically modulate these interactions with frequencies up to 300 kHz - orders of magnitude faster than the emitter's radiative decay (~100 Hz). This constitutes an enabling platform for integrated quantum technologies, opening routes to quantum entanglement generation by collective plasmon emission or photon emission with controlled waveform.

Supercorrelated Radiance in Nonlinear Photonic Waveguides

We study the collective decay of two-level emitters coupled to a nonlinear waveguide, for example, a nanophotonic lattice or a superconducting resonator array with strong photon-photon interactions. Under these conditions, a new decay channel into bound photon pairs emerges, through which spatial correlations between emitters are established by regular interference as well as interactions between the photons. We derive an effective Markovian theory to model the resulting decay dynamics of an arbitrary distribution of emitters and identify collective effects beyond the usual phenomena of super- and subradiance. Specifically, in the limit of many close-by emitters, we find that the system undergoes a supercorrelated decay process where all the emitters are either in the excited state or in the ground state but not in any of the intermediate states. The predicted effects can be probed in state-of-the-art waveguide QED experiments and provide a striking example of how the dynamics of open quantum systems can be modified by many-body effects in a nonharmonic environment.

Light reflection and transmission in planar lattices of cold atoms

Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Here we present a theoretical scheme that enables efficient computation of collective optical responses of mono- and bi-layer planar square lattices of dense, cold two-level atoms using classical electrodynamics of coupled dipoles in the limit of low laser intensity. The steady-state transmissivity and reflectivity are obtained at a field point far away from the atomic lattices in the regime with no Bragg reflection. While our earlier method was based on exact solution of the electrodynamics for a small-scale lattice, here we calculate the dipole moments assuming that they are the same at all lattice sites, as for an infinite lattice. Atomic lattices with effectively over one hundred times more sites than in our earlier exact computations can then be simulated numerically with fewer computational resources. We have implemented an automatic selection of the number of sites under the given convergence criteria. We compare the numerical results from both computational schemes. We also find similarities and differences of a stack of two atomic lattices from a two-atom sample. Such aspects may be exploited to engineer a stack for potential applications.

Magnon Accumulation in Chirally Coupled Magnets

We report strong chiral coupling between magnons and photons in microwave waveguides that contain chains of small magnets on special lines. Large magnon accumulations at one edge of the chain emerge when exciting the magnets by a phased antenna array. This mechanism holds the promise of new functionalities in nonlinear and quantum magnonics.

Photon-Mediated Localization in Two-Level Qubit Arrays

We predict the existence of a novel interaction-induced spatial localization in a periodic array of qubits coupled to a waveguide. This localization can be described as a quantum analogue of a self-induced optical lattice between two indistinguishable photons, where one photon creates a standing wave that traps the other photon. The localization is caused by the interplay between on-site repulsion due to the photon blockade and the waveguide-mediated long-range coupling between the qubits.

Inelastic Scattering of Photon Pairs in Qubit Arrays with Subradiant States

We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded into a waveguide. Our analysis reveals a strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering, such as superradiant, subradiant, and twilight states, as a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to storage and processing of quantum information.