In this article, we show that in the level of quantum mechanics, a photon position operator with commuting components can be obtained in a more natural way; in the level of quantum field theory, the photon position operator corresponds to the center of the photon number. It is most interesting for us to show that, a photon inside a waveguide can be localized in the same sense that a massive particle can be localized in free space, and just as that it is impossible to localize a massive particle with a greater precision than its Compton wavelength, one can also arrival at a similar conclusion: it is impossible to localize a photon inside a waveguide with a greater precision than its equivalent Compton wavelength, which owing to evanescent-wave or photon-tunneling phenomena.
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 report on a direct experimental observation of dynamic localization (DL) of light in sinusoidally-curved Lithium-Niobate waveguide arrays which provides the optical analog of DL for electrons in periodic potentials subjected to ac electric fields as originally proposed by Dunlap and Kenkre [D.H. Dunlap and V.M. Kenkre, Phys. Rev. B 34, 3625 (1986)]. The theoretical condition for DL in a sinusoidal field is experimentally demonstrated.
In the paper, we show that there exists a close analogy between the behavior of de Broglie matter waves and that of electromagnetic waves inside a hollow waveguide, such that the guided photons can be treated as free massive particles subject to a relativistic quantum-mechanical equation. Inspired by the effective rest mass of guided photons and the zitterbewegung phenomenon of the Dirac electron, at variance with the well-known Higgs mechanism we present some different heuristic ideas on the origin of mass.
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 exten…
Light transport in a disordered ensemble of resonant atoms placed in a waveguide is found to be very sensitive to the sizes of cross section of a waveguide. Based on self-consistent quantum microscopic model treating atoms as coherent radiating dipoles, we have shown that the nature of radiation transfer changes from Anderson localization regime in a single-mode waveguide to a traditional diffuse transfer in a multi-mode one. Moreover, the transmittance magnitude undergoes complex step-like dependence on the transverse sizes of a waveguide.
We consider the propagation of light beams through disordered lattices of coupled waveguides searching for Anderson localization and investigating the evolution of nonclassical properties of injected quantum states. We assume that the beam is initially in a variety of states, such as the complementary coherent state, the reciprocal binomial state, and the polynomial state. The statistical properties of the evolved states were analyzed numerically as functions of the localization/delocalization parameters averaged over many realizations of disorder. We also numerically reconstruct the Wigner fu…
We analyze coherent transport of photons, which propagate in a one-dimensional coupled-resonator waveguide (CRW) and are scattered by a controllable two-level system located inside the CRW. Our approach, which uses discrete coordinates, unifies "low" and "high" energy effective theories for single photon scattering. We show that the controllable two-level system can behave as a quantum switch for the coherent transport of photons. This study may inspire new electro-optical single-photon quantum devices. We also suggest an experimental setup based on superconducting transmission line resonators…
Correlation Localization in Waveguide QED with Delayed Interactions
Universidad de Concepción（康塞普西翁大学）；Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México（墨西哥国立自治大学应用数学与系统研究所）
Artificial gauge fields enable the intriguing possibility to manipulate the propagation of light as if it were under the influence of a magnetic field even though photons possess no intrinsic electric charge. Typically, such fields are engineered via periodic modulations of photonic lattices such that the effective coupling coefficients after one period become complex-valued. In this work, we investigate the possibility to introduce randomness into artificial gauge fields by applying local random phase shifts in the modulation of lattices of optical waveguides. We first study the elemental uni…
We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in closed form for different level structures. Several possible applications are discussed: The state of the emitter can be switched deterministically by Raman scattering, thus enabling applications in quantum computing such as a single photon transistor. An array of emitters gives rise to a photonic band gap structure, which can be tuned by a classical drivin…
We put forward an experimental configuration to observe transverse Anderson localization of partially coherent light beams with a tunable degree of first-order coherence. The scheme makes use of entangled photons propagating in disordered waveguide arrays, and is based on the unique relationship between the degree of entanglement of a pair of photons and the coherence properties of the individual photons constituting the pair. The scheme can be readily implemented with current waveguide-on-a-chip technology, and surprisingly, the tunability of the coherence properties of the individual photons…
We present a quantum inspired image augmentation protocol which is applicable to classical images and, in principle, due to its known quantum formulation applicable to quantum systems and quantum machine learning in the future. The augmentation technique relies on the phenomenon Anderson localization. As we will illustrate by numerical examples the technique changes classical wave properties by interference effects resulting from scatterings at impurities in the material. We explain that the augmentation can be understood as multiplicative noise, which counter-intuitively averages out, by samp…
Quantum memory is the core device for the construction of large-scale quantum networks. For scalable and convenient practical applications, integrated optical memories, especially on-chip optical memories, are crucial requirements because they can be easily integrated with other on-chip devices. Here, we report the coherent optical memory based on a type-IV waveguide fabricated on the surface of a rare-earth ion-doped crystal (i.e. $\mathrm{Eu^{3+}}$:$\mathrm{Y_2SiO_5}$). The properties of the optical transition ($\mathrm{{^7}F{_0}\rightarrow{^5}D{_0}}$) of the $\mathrm{Eu^{3+}}$ ions inside t…
We investigate the formation of photon bound states in a system of interacting photons inside nanoscale wires. The photons interact through the exchange of vibrational modes induced along the waveguide mainly due to radiation pressure. The problem of many-body photons is treated in using the formalism of contour Green's functions under the T-matrix approximation. The complex pole of the T-matrix is a signature for the appearance of photon-molecules. The analysis of such singularity provides the critical temperature at which the T-matrix approximation breaks down and photon-molecules appear. Fo…
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general no…
It is of fundamental interest in controlling the light-matter interaction for a long time in the field of quantum information processing. However, usual excitation with the propagating photon can hardly excite a localized state of light while keeping the atom under a subradiant decay in an atom-waveguide system. Here, we propose a model of coupling between a giant atom and the dynamically-modulated coupled-resonator waveguide and find that a bound state, where the light shows the localization effect and atom exhibits a subradiant decay time, can be excited by a propagating photon. An analytica…
At the quantum many-body level, atom-light interfaces generally remain challenging to solve for or understand in a non-perturbative fashion. Here, we consider a waveguide quantum electrodynamics model, where two-level atoms interact with and via propagating photons in a one-dimensional waveguide, and specifically investigate the interplay of atomic position disorder, multiple scattering of light, quantum nonlinear interactions and dissipation. We develop qualitative arguments and present numerical evidence that such a system exhibits a many-body localized~(MBL) phase, provided that atoms are l…
The Maryland model was introduced more than 30 years ago as an integrable model of localization by aperiodic order. Even though quite popular and rich of fascinating mathematical properties, this model has so far remained quite artificial, as compared to other models displaying dynamical localization like the periodically-kicked quantum rotator or the Aubry-Andre$^{\prime}$ model. Here we suggest that light propagation in a polygonal optical waveguide lattice provides a photonic realization of the Maryland model and enables to observe a main prediction of this model, namely fragility of wave l…
We have studied a hybrid system of a one-dimensional coupled-cavity waveguide with a two-level system inside, which subject to a external periodical field. Using the extended Hilbert space formalism, the time-dependent Hamiltonian is reduced into an equivalent time-independent one. Via computing the Floquet-Green's function, the Zeno-anti-Zeno crossover is controlled by the driven intensity and frequency, and the detuning between the cavity and the two-level system.
This is a theory for the effect of localization on the super-Poissonian noise of radiation propagating through an absorbing disordered waveguide. Localization suppresses both the mean photon current I and the noise power P, but the Fano factor P/I is found to remain unaffected. For strong absorption the Fano factor has the universal value 1+3f/2 (with f the Bose-Einstein function), regardless of whether the waveguide is long or short compared to the localization length.
We study theoretically the competition between directional asymmetric coupling and disorder in a one-dimensional array of quantum emitters chirally coupled through a waveguide mode. Our calculation reveals highly nontrivial phase diagram for the eigenstates spatial profile, nonmonotonously depending on the disorder and directionality strength. The increase of the coupling asymmetry drives the transition from Anderson localization in the bulk through delocalized states to chirality-induced localization at the array edge. Counterintuitively, this transition is not smeared by strong disorder but …
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.
Decoherence for a one-dimensional coupled-resonator waveguide with a two-level system inside one of resonators, induced by their interaction with corresponding environments, is investigated. Each environment is modeled as a continuum of harmonic oscillators. By finding the eigenstates of the hybrid system, which is the dressed state of the hybrid system, we calculate the lifetime of one excitation, which characterizes the existence of quantum coherence in such hybrid system and the basic quantum nature.
We study a waveguide QED system with a rectangular waveguide and a two-level system (TLS) inside, where the transverse modes TMmn define the quantum channels of guided photons. It is discovered that the loss of photons in the TM11 channel into the others can be overcome by replacing it with a certain coherent superposition of TMmn channels, which is named as the controllable channel (CC) as the photons in CC can be perfectly reflected or transmitted by the TLS, and never lost into the other channels. The dark state emerges when the photon is incident from one of the scattering-free channels (S…
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.
Random scattering of photons in disordered one-dimensional solids gives rise to an exponential suppression of transmission, which is known as Anderson localization. Here, we experimentally study Anderson localization in a superconducting waveguide quantum electrodynamics system comprising eight individually tunable qubits coupled to a photonic continuum of a waveguide. Employing the qubit frequency control, we artificially introduce frequency disorder to the system and observe an exponential suppression of the transmission coefficient in the vicinity of its subradiant dark modes. The localizat…
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the rest-energy and the potential energy. Moreover, a geometrical optics model of the propagation illustrates how the width as a function of distance determines the velocity and accelerations of the particle. The model entails the disappearance of action-at-a-distance problem, and that interactions are conveyed via the potential, i.e. by photons.
The driven-dissipative nature of light-matter interaction inside a multimode, dye-filled microcavity makes it an ideal system to study nonequilibrium phenomena, such as transport. In this work, we investigate how light is efficiently transported inside such a microcavity, mediated by incoherent absorption and emission processes. In particular, we show that there exist two distinct regimes of transport, viz. conductive and localized, arising from the complex interplay between the thermalizing effect of the dye molecules and the nonequilibrium influence of driving and loss. The propagation of li…
Propagation of light through dielectrics lies at the heart of optics. However, this ubiquitous process is commonly described using phenomenological dielectric function $\varepsilon$ and magnetic permeability $μ$, i.e. without addressing the quantum graininess of the dielectric matter. Here, we present a theoretical study where we consider a one-dimensional ensemble of atoms in a subwavelength waveguide (nanoguide) as fundamental building blocks of a model dielectric. By exploring the roles of the atom-waveguide coupling efficiency, density, disorder, and dephasing, we establish connections amo…
We demonstrate that a flat-band state in a quasi-one-dimensional rhombic lattice is robust in the presence of external drivings along the lattice axis. The lattice was formed by periodic arrays of evanescently coupled optical waveguides, and the external drivings were realized by modulating the paths of the waveguides. We excited a superposition of flat-band eigenmodes at the input and observed that this state does not diffract in the presence of static as well as high-frequency sinusoidal drivings. This robust localization is due to destructive interference of the analogous wavefunction and i…
We report on the coherent internal-state control of single crystalline nanodiamonds, containing on average 1200 nitrogen-vacancy (NV) centers, embedded in three-dimensional direct-laser-written waveguides. We excite the NV centers by light propagating through the waveguide, and we show that emitted fluorescence can be efficiently coupled to the waveguide modes. We find an average coupling efficiency of 21.6% into all guided modes. Moreover, we investigate optically-detected magnetic-resonance spectra as well as Rabi oscillations recorded through the waveguide-coupled signal. Our work shows tha…
We propose an efficient light-matter interface at optical frequencies between a single photon and a superconducting qubit. The desired interface is based on a hybrid architecture composed of an organic molecule embedded inside an optical waveguide and electrically coupled to a superconducting qubit placed near the outside surface of the waveguide. We show that high fidelity, photon-mediated, entanglement between distant superconducting qubits can be achieved with incident pulses at the single photon level. Such a low light level is highly desirable for achieving a coherent optical interface wi…
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,…
