We introduce a simple method to realize and detect photonic topological Chern insulators with one-dimensional circiut quantum electrodynamics arrays. By periodically modulating the couplings of the array, we show that this one-dimensional model can be mapped into a two-dimensional Chern insulator model. In addition to allowing the study of photonic Chern insulators, this approach also provides a natural platform to realise experimentally Laughlin's pumping argument. Based on scattering theory of topological insulators and input-output formalism, we show that the photonic edge state can be probed directly and the topological invariant can be detected from the winding number of the reflection coefficient phase.
We demonstrate the effects of cavity quantum electrodynamics for a quantum dot coupled to a photonic molecule, consisting of a pair of coupled photonic crystal cavities. We show anti-crossing between the quantum dot and the two super-modes of the photonic molecule, signifying achievement of the strong coupling regime. From the anti-crossing data, we estimate the contributions of both mode-coupling and intrinsic detuning to the total detuning between the super-modes. Finally, we also show signatures of off-resonant cavity-cavity interaction in the photonic molecule.
This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a "full and complete" 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light within a tiny nanoscale volume (aka "a nanobox for light"), 3) the introduction of a gain medium leading to thresholdless lasers, 4) breaking of the weak-coupling approximation of cavity QED, both in the frequency and in the time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations by a 3D photonic bandgap. In addition, we list and evaluate …
Photonic crystals provide an extremely powerful toolset for manipulation of optical dispersion and density of states, and have thus been employed for applications from photon generation to quantum sensing with NVs and atoms. The unique control afforded by these media make them a beautiful, if unexplored, playground for strong coupling quantum electrodynamics, where a single, highly nonlinear emitter hybridizes with the band structure of the crystal. In this work we demonstrate that such hybridization can create localized cavity modes that live within the photonic band-gap, whose localization a…
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.
We show that a scalable photonic crystal nanocavity array, in which single embedded quantum dots are coherently interacting, can perform as an universal single-operation quantum gate. In a passive system, the optical analogue of electromagnetically-induced-transparency is observed. The presence of a single two-level system in the array dramatically controls the spectral lineshapes. When each cavity couples with a two-level system, our scheme achieves two-qubit gate operations with high fidelity and low photon loss, even in the bad cavity limit and with non-ideal detuning and decoherence.
Cavity quantum electrodynamics studies light-matter interactions at single quanta level. Chiral photon-emitter coupling in photonic structures is characterized as unidirectional propagation locked by the local polarization of light. However, to realize the strong interaction of photon-emitter with direction-locked propagation, which will bring novel applications in nonreciprocal quantum devices, has not been reported yet. Here, we propose the coupled photonic crystal and metallic nanoparticle structure, where through strong local field with high helicity, the rate of circularly polarized photo…
Topological photonics provides a new paradigm in studying cavity quantum electrodynamics with robustness to disorder. In this work, we demonstrate the coupling between single quantum dots and the second-order topological corner state. Based on the second-order topological corner state, a topological photonic crystal cavity is designed and fabricated into GaAs slabs with quantum dots embedded. The coexistence of corner state and edge state with high quality factor close to 2000 is observed. The enhancement of photoluminescence intensity and emission rate are both observed when the quantum dot i…
We address two issues in the quantum electrodynamical description of photonic media with some disorder, neglecting material dispersion. When choosing a gauge in which the static potential vanishes, the normal modes of the medium with disorder satisfy another transversality condition than the modes of the ideal medium. Our first result is an integral equation for optical modes such that all perturbation-theory solutions automatically satisfy the desired transversality condition. Secondly, when expanding the vector potential for the medium with disorder in terms of the normal modes of the ideal …
One of the most striking predictions of quantum electrodynamics is that vacuum fluctuations of the electromagnetic field can lead to spontaneous emission of atoms as well as photon-mediated interactions among them. Since these processes strongly depend on the nature of the photonic bath, a current burgeoning field is the study of their modification in the presence of photons with non-trivial energy dispersions, e.g., the ones confined in photonic crystals. A remarkable example is the case of isotropic Dirac-photons, which has been recently shown to lead to non-exponential spontaneous emission …
Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly nontrivial in photonic systems as there is no direct analog of quantized Hall conductance for bosonic photons. Here we propose a scheme of investigating topological photonics in superconducting quantum circuits by a simple parametric coupling method, the flexibility of which can lead to the effective \textit{in situ} tunable artificial gauge field for photon…
The periodic changes in the physical and chemical properties of the chemical elements are caused by the periodic change of the ionization energies, which are constant for each element that manifested in the Periodic Table. However, as has been recently shown the modification of the electromagnetic field in the photonic crystals gives rise to the modification of the electron electromagnetic mass. We show that the effect can significantly change the ionization energy of atoms placed in voids of photonic crystals consisting of metamaterials with a highly tunable refractive index and voids. The co…
We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only \textit{one step} of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encod…
We investigate some aspects of the Maxwell-Chern-Simons electrodynamics focusing on physical effects produced by the presence of stationary sources and a perfectly conducting plate (mirror). Specifically, in addition to point charges, we propose two new types of point-like sources called topological source and Dirac point, and we also consider physical effects in various configurations that involve them. We show that the Dirac point is the source of the vortex field configurations. The propagator of the gauge field due to the presence of a conducting plate and the interaction forces between th…
We study the polaritonic bandstructure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having resonant atomic transitions to excited states with different angular momentum. We employ a computational method based on the recently proposed Dirichlet-to-Neumann (DtN) map technique which accurately models non-Markovian dynamics as well as interactions involving higher-order electric and magnetic multipole transitions. We design topologically robust edge states…
A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. Highly engineered optical cavities are generally implemented requiring nanoscale fabrication precision. We demonstrate a fundamentally different approach in which disorder is used as a resource rather than a nuisance. We generate strongly confined Anderson-localized cavity modes by deliberately adding disorder to photonic crystal waveguides. The emission rate of a semiconductor quantum dot embedded in the waveguide is enhanced by a factor of 1…
We have investigated the one-way surface plasmon-polariton (SPP) at the interface of a continuous magneto-plasma material and metal. We demonstrated that TM modes inside a continuous material can be assigned non-trivial Chern numbers analogous to those of topological photonic crystals; moreover these Chern numbers can be calculated analytically. This leads to the appearance of topologically protected surface modes propagating at frequencies inside the bandgap of the magneto-plasma. Previous works considered 2D structures; here we consider the effects of 3D defects, and show that, although back…
In a cavity quantum electrodynamics (QED) system, where atoms coherently interact with photons in a cavity, the eigenstates of the system are the superposition states of atoms and cavity photons, the so-called dressed states of atoms. When two cavities are connected by an optical fiber with negligible loss, the coherent coupling between the cavities gives rise to photonic normal modes. One of these normal modes is the fiber-dark mode, in which photons are delocalized in the two distant cavities. Here we demonstrate the setting of coupled-cavities QED, where two nanofiber cavity-QED systems are…
We propose a deterministic scheme for teleporting an unknown qubit through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states brings a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. This scheme further enables applications for quantum information processing in the same architecture of circuit-QED suc…
We study Landau-Zener-Stückelberg (LZS) interferometry in a cQED architecture under effects of dissipation. To be specific, we consider a superconducting qubit driven by a dc+ac signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for arbitrary amplitude of the drive and different time scales. We unveil important differences in the…
The embedding of tunable quantum emitters in a photonic bandgap structure enables the control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite range emitter-emitter interactions via bound photonic states. Here we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant ($λ/60$). The metamaterial is formed by periodi…
We investigate the appearance of Chern-Simons terms in electrodynamics at the surface/interface of materials. The requirement of locality, gauge invariance and renormalizability in this model is imposed. Scattering and reflection of electromagnetic waves in three different homogeneous layers of media is determined. Snell's law is preserved. However, the transmission and reflection coefficient depend on the strength of the Chern-Simons interaction, and parallel and perpendicular components are mixed.
Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-André-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In c…
We present a general framework for cavity quantum electrodynamics with strongly frequency-dependent mirrors. The method is applicable to a variety of reflectors exhibiting sharp internal resonances as can be realized, for example, with photonic-crystal mirrors or with two-dimensional atomic arrays around subradiant points. Our approach is based on a modification of the standard input--output formalism to explicitly include the dynamics of the mirror's internal resonance. We show how to directly extract the interaction tuning parameters from the comparison with classical transfer matrix theory …
Architectures based on waveguide quantum electrodynamics have emerged as promising candidates for quantum networks. In this paper, we analyze the propagation of single-photons in disordered many-atom waveguides. We pay special attention to the influence of chirality (directionality of photon transport) on the formation of localized photonic states, considering separately the cases of the disorder in the atomic positions and in the atomic transition frequencies.
We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of existence of edge states in system with nonzero reflection phase winding number is given. The method is illustrated for one- and two-dimensional photonic crystals of nontrivial topology.
This chapter will primarily focus on the studies of quantum optics with semiconductor, epitaxially grown quantum dots embedded in photonic crystal cavities. We will start by giving brief introductions into photonic crystals and quantum dots, then proceed with the introduction to cavity quantum electrodynamics (QED) effects, with a particular emphasis on the demonstration of these effects on the quantum dot-photonic crystal platform. Finally, we will focus on the applications of such cavity QED effects.
Cavities embedded in photonic crystal waveguides offer a promising route towards large scale integration of coupled resonators for quantum electrodynamics applications. In this letter, we demonstrate a strongly coupled system formed by a single quantum dot and such a photonic crystal cavity. The resonance originating from the cavity is clearly identified from the photoluminescence mapping of the out-of-plane scattered signal along the photonic crystal waveguide. The quantum dot exciton is tuned towards the cavity mode by temperature control. A vacuum Rabi splitting of ~ 140 \mueV is observed a…
In this dissertation, we study the implications generated by the Lorentz breaking symmetry in quantum electrodynamics. We analyze fermions interacting with an electromagnetic field in the contexts of quantum mechanics and make radiative corrections. In quantum mechanics, the terms of the Lorentz breaking symmetry were treated as perturbations to the Dirac equation, and their expected values were obtained in a vacuum. In the radiative corrections, the Lorentz breaking symmetry was introduced in this interaction for the Chern-Simons like term could be induced in (3 +1) dimensions. We also discus…
Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the …
While designing the energy-momentum relation of photons is key to many linear, non-linear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically-induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects.…
The bichromatic driving of a solid state cavity quantum electrodynamics system is used to probe cavity dressed state transitions and observe coherent interaction between the system and the light field. We theoretically demonstrate the higher order cavity-dressed states, supersplitting, and AC stark shift in a solid state system comprised of a quantum dot strongly coupled to a photonic crystal cavity for on- and far off-resonant cases. For the off-resonant case, phonons mediate off-resonant coupling between the quantum dot and the photonic resonator, a phenomenon unique to solid state cavity qu…
Bounds on the Topological Charge of Photonic Systems
University of Lisbon – Instituto Superior Técnico and Instituto de Telecomunicações（里斯本大学 - 高等理工学院与电信研究所）；Instituto Universitário de Lisboa (ISCTE-IUL)（里斯本大学学院）；Centro de Física de Materiales, Universidad del País Vasco（巴斯克大学材料物理中心）
Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. Therefore, it is important to have control over the generation of these resonances. In this work, we show through ab initio simulations of coupled light-matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to …
We introduce a new scalable cavity quantum electrodynamics platform which can be used for quantum computing. This system is composed of coupled photonic crystal (PC) cavities which their modes lie on a Dirac cone in the whole super crystal band structure. Quantum information is stored in quantum dots that are positioned inside the cavities. We show if there is just one quantum dot in the system, energy as photon is exchanged between the quantum dot and the Dirac modes sinusoidally. Meanwhile the quantum dot becomes entangled with Dirac modes. If we insert more quantum dots into the system, the…
We discuss the impact of gain and loss on the evolution of photonic quantum states and find that PT-symmetric quantum optics in gain/loss systems is not possible. Within the framework of macroscopic quantum electrodynamics we show that gain and loss are associated with non-compact and compact operator transformations, respectively. This implies a fundamentally different way in which quantum correlations between a quantum system and a reservoir are built up and destroyed.
We realize a photonic analog simulator of the quantum Rabi model, based on light transport in femtosecond-laser-written waveguide superlattices, which provides an experimentally accessible testbed to explore the physics of light-matter interaction in the deep strong coupling regime. Our optical setting enables to visualize dynamical regimes not yet accessible in cavity or circuit quantum electrodynamics, such as bouncing of photon number wave packets in parity chains of Hilbert space.
The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical Schrödinger equation, writing both in Hamiltonian form. However, the aforementioned quantities are not necessarily quantum in nature, and for photonic systems they can be explained using only classical concepts. Here we provide a derivation and description of PTI quantities using classical Maxwell's equations, we demonstrate how an electromagnetic mode can acquire Berry p…
The ability to achieve ultra-strong coupling between light and matter promises to bring about new means to control material properties, new concepts for manipulating light at the atomic scale, and fundamentally new insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. In this Letter, we develop a variational theory of general non-relativistic QED systems of coupled light and matter. Essential to our ansatz is the notion of an effective photonic vacuum whose modes are different than the mo…
We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator for the spinor field is then constructed. We discuss the role of time-dependent renormalization in the propagator and focus on the possibility of obtaining dynamically induced superselection rules. Finally, we derive the master equation for the case of the field being in an one-particle state in a non-relativistic regime and discuss whether EM vacuumm fluctuations are sufficient to produce decoherence in the position basis.
Optical nonlinearities sensitive to individual photons may be extremely useful as elements in quantum logic circuits for photonic qubits. A much cited example is the work of Turchette et al. [Phys. Rev. Lett. 75, 4710 (1995)], in which a phase shift of about 10 degrees was reported. To improve this result, we propose a single sided cavity geometry with minimal cavity losses. It should then be possible to achieve a nonlinear phase shift of 180 degrees.
