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 function of the output state. Interestingly, we find that high values of the disorder tend to preserve quantum properties of some input states when we look at the input waveguide despite the coupling between it and the neighboring waveguides.
We study the transport and quantum walk of nonclassical light in an array of coupled waveguides which have novel properties like very low decoherence and thus making them ideal for storage of quantum information. We show how squeezing gets turned over from one waveguide to another. We further show how input nonclassical light can generate entanglement among different waveguides. Our results involve both first quantization due to array structure and second quantization due to the quantum nature of fields and can also be used to discuss the Talbot effect in the quantum regime.
Optical parametric process occurring in a photonic band-gap planar waveguide is studied from the point of view of nonclassical-light generation. Nonlinearly interacting optical fields are described by the generalized superposition of coherent signals and noise using the method of operator linear corrections to a classical strong solution. Scattered backward-propagating fields are taken into account. Squeezed light as well as light with sub-Poissonian statistics can be obtained in two-mode fields under the specified conditions.
Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. Properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic band-gap structure inside the waveguide. A quantum model of linear operator amplitude corrections to amplitude mean-values provides conditions for an efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. Destructive influence of phase mismatch of the nonlinear interaction can fully …
We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization…
We investigate a decoy-state quantum key distribution (QKD) scheme with a sub-Poissonian single-photon source, which is generated on demand by scattering a coherent state off a two-level system in a one-dimensional waveguide. We show that, compared to coherent state decoy-state QKD, there is a two-fold increase of the key generation rate. Furthermore, the performance is shown to be robust against both parameter variations and loss effects of the system.
The topological trivial band of a lattice can be driven into a topological phase by disorder in the system. This so-called topological Anderson phase has been predicted and observed for uncorrelated static disorder, while in the presence of correlated disorder conflicting results are found. Here we consider a Su-Schrieffer-Heeger (SSH) waveguide lattice in the trivial topological phase, and show that quasi-periodic disorder in the coupling constants can drive the lattice into a topological non-trivial phase. A method to detect the emergence of the topological Anderson phase, based on light dyn…
A model is proposed where two $χ^{(2)}$ nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives rise to quantum violations of the classical limit. These violations are particularly strong when two instabilities are competing, where twin-beam behavior is found as almost complete noise suppression in the difference of the fundamental intensities. Moreover, close to bistable transitions perfect tw…
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…
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 investigate the nonclassical properties of output fields propagated through a contradirectional asymmetric nonlinear optical coupler consisting of a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation. In contrast to the earlier results, all the initial fields are considered weak and a completely quantum mechanical model is used here to describe the system. Perturbative solutions of Heisenberg's equations of motion for various field modes are obtained using Sen-Mandal technique. Obtained solutions are subsequently used to show the existence of singl…
We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicalilty indicators could give further evidence of …
We report the experimental reconstruction of the statistical properties of an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecom wavelengths, with almost perfect photon-number correlations. We used a photon-number-resolving time-multiplexed detector based on a fiber-optical setup and a pair of avalanche photodiodes. By resorting to a germane data-pattern tomography, we assess the properties of the nonclassical light states states with unprecedented precision.
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…
In a numerical study, we investigate the steady-state generation of nonclassical states of light from a coherently driven two-level atom in a one-dimensional waveguide. Specifically, we look for states with a negative Wigner function, since such nonclassical states are a resource for quantum information processing applications, including quantum computing. We find that a waveguide terminated by a mirror at the position of the atom can provide Wigner-negative states, while an infinite waveguide yields strictly positive Wigner functions. Moreover, our investigation reveals a connection between t…
Optical nanostructures have proven to be meritorious for tailoring the emission properties of quantum emitters. However, unavoidable fabrication imperfections may represent a nuisance. Quite remarkably, disorder offers new opportunities since light can be efficiently confined by random multiple scattering leading to Anderson localization. Here we investigate the effect of such disorder-induced cavities on the emission dynamics of single quantum dots embedded in disordered photonic-crystal waveguides. We present time-resolved measurements of both the total emission from Anderson-localized cavit…
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.
We show that a synthetic pseudospin-momentum coupling can be used to design quasi-one-dimensional disorder-resistant coupled resonator optical waveguides (CROW). In this structure, the propagating Bloch waves exhibit a pseudospin-momentum locking at specific momenta where backscattering is suppressed. We quantify this resistance to disorder using two methods. First, we calculate the Anderson localization length $ξ$, obtaining an order of magnitude enhancement compared to a conventional CROW for typical device parameters. Second, we study propagation in the time domain, finding that the loss of…
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 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 present a scheme to generate a continuous variable (CV) multipartite entangled state using an array of plasmonic graphene waveguides that are activated by nonclassical driving microwave modes. Within this scheme, we can exploit the interaction of two light fields coupled to the same microwave mode in each waveguide to produce any type of multipartite Gaussian entangled state. A teleportation network is illustrated using the resultant CV multipartite entangled state. In particular, the proposed setup enables coherent state teleportation across remotely connected nodes with fidelity above a t…
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…
It is generally difficult to study the dynamical properties of a quantum system with both inherent quantum noises and non-perturbative nonlinearity. Due to the possibly drastic intensity increase of an input coherent light in the gain-loss waveguide couplers with parity-time (PT) symmetry, the Kerr effect from a nonlinearity added into the systems can be greatly enhanced, and is expected to create the macroscopic entangled states of the output light fields with huge photon numbers. Meanwhile, the quantum noises also coexist with the amplification and dissipation of the light fields. Under the …
Using the phenomenological expression for the level spacing distribution with only one parameter, $0 \leq β\leq \infty$, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between $β$ and the normalized localization length for the whole transition from strongly localized to extended states. This result allows one to describe all transport properties in the open system entirely in terms of the p…
We show how two-dimensional waveguide arrays can be used to probe the effect of on-site interaction on Anderson localization of two interacting bosons in one dimension. It is shown that classical light and linear elements are sufficient to experimentally probe the interplay between interaction and disorder in this setting. For experimental relevance, we evaluate the participation ratio and the intensity correlation function as measures of localization for two types of disorder (diagonal and off-diagonal), for two types of interaction (repulsive and attractive), and for a variety of initial inp…
We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that the distribution function of the transmitted pulse can be negative for the nonclassical input (i.e., single-photon Fock state). This reveals the quasiprobability nature of photon distribution. Analytical expressions for photon densities in the momentum space as well as in the coordinate space are obtained for the mentioned single-photon Gaussian input. We als…
Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson localization of light has been probed in transmission experiments by measuring the intensity of an external light source after propagation through a disordered medium. However, discriminating between Anderson localization and losses in these experiments remains a major challenge. Here we present an alternative approach where we use quantum emitters embedded in …
A statistical theory of the coupling between a quantum emitter and Anderson-localized cavity modes is presented based on a dyadic Green's function formalism. The probability of achieving the strong light-matter coupling regime is extracted for an experimentally realistic system composed of InAs quantum dots embedded in a disordered photonic crystal waveguide. We demonstrate that by engineering the relevant parameters that define the quality of light confinement, i.e. the light localization length and the loss length, strong coupling between a single quantum dot and an Anderson-localized cavity…
We show that two-photon transport is strongly correlated in one-dimensional waveguide coupled to a two-level system. The exact S-matrix is constructed using a generalized Bethe-Ansatz technique. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.
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 experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhances localization in one type, and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of $δ$-like wavepackets in the presence of disorder. A transition from ballistic wavepacket expansion to exponential (Anderson) localization is observed. We find an intermediate…
Transport regimes of biphoton-state quantum walks in ordered and disordered arrays of nonlinear waveguides
Centro de Investigación en Ciencia e Ingeniería de Materiales, Universidad de Costa Rica（哥斯达黎加大学材料科学与工程研究中心）；Escuela de Física, Universidad de Costa Rica（哥斯达黎加大学物理学院）
In the last decade, there has been remarkable progress on the practical integration of on-chip quantum photonic devices yet quantum state generators remain an outstanding challenge. Simultaneously, the quantum-dot photonic-crystal-resonator platform has demonstrated a versatility for creating nonclassical light with tunable quantum statistics, thanks to a newly discovered self-homodyning interferometric effect that preferentially selects the quantum light over the classical light when using an optimally tuned Fano resonance. In this work, we propose a general structure for the cavity quantum e…
We design and demonstrate on-chip homodyne detection operating in the quantum regime, i.e. able to detect genuine nonclassical features. Our setup exploits a glass-integrated homodyne analyzer (IHA) entirely fabricated by femtosecond laser micromachining. The IHA incorporates on the same chip a balanced waveguide beam splitter and a thermo-optic phase shifter, allowing us to record homodyne traces at different phases and to perform reliable quantum state tomography. In particular, we show that the IHA allows for the detection of nonclassical features of continuous-variable quantum states, such…
A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For classical light, the photonic system realizes an optical analogue of coherent population trapping in the continuum encountered in atomic physics, where destructive interference between different light leakage channels leads to the appearance of a trapped state embedded in the continuum. For nonclassical light, two-photon interference effects are predicted, …
In this paper, we develop the notion of the linear atomic quantum coupler. This device consists of two modes propagating into two waveguides, each of them includes a localized and/or a trapped atom. These waveguides are placed close enough to allow exchanging energy between them via evanescent waves. Each mode interacts with the atom in the same waveguide in the standard way, i.e. as the Jaynes-Cummings model (JCM), and with the atom-mode in the second waveguide via evanescent wave. We present the Hamiltonian for the system and deduce the exact form for the wavefunction. We investigate the ato…
In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by the second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through nondegenerate optical parametric interaction. Main attention is paid to generation and transmission of nonclassical light, based on a discussion of squeezing phenomenon, normalized second-order correlation function, and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are consider…
Few-photon transport via waveguide-coupled local quantum systems has attracted extensive theoretical and experimental studies. Most of the study has focused on atomic or atomic-like local quantum systems due to their strong light-matter interaction useful for quantum applications. Here, we study few-photon transport via a waveguide-coupled multimode optical cavity with second-order bulk nonlinearity. We develop a Feynman diagram approach and compute the scattering matrix of the one- and two-photon transport. Based on the calculated scattering matrix, we show highly nonclassical photonic effect…
A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting the concept of polariton as the system natural eigenstate. We apply a bosonization procedure, which was presented separately by P. W. Anderson and V. M. Agranovich, to transform excitation spin-half operators into interacting bosons, and which shown here to confirm the hard-core boson model. We derive polariton-polariton kinematic interactions and study them by solving the scattering problem. In using the excitation-photon detuning as a control parameter, we examine the regime …
We study the generation of strongly correlated photons by coupling an atom to photonic quantum fields in a one-dimensional waveguide. Specifically, we consider a three-level or four-level system for the atom. Photon-photon bound states emerge as a manifestation of the strong photon-photon correlation mediated by the atom. Effective repulsive or attractive interaction between photons can be produced, causing either suppressed multiphoton transmission (photon blockade) or enhanced multiphoton transmission (photon-induced tunneling). As a result, nonclassical light sources can be generated on dem…
The recent observation of the dynamical Casimir effect in a modulated superconducting waveguide, coronating thirty years of world-wide research, empowered the quantum technology community with a powerful tool to create entangled photons on-chip. In this work we show how, going beyond the single waveguide paradigm using a scalable array, it is possible to create multipartite nonclassical states, with the possibility to control the long-range quantum correlations of the emitted photons. In particular, our finite-temperature theory shows how maximally entangled $NOON$ states can be engineered in …
Disorder-Induced Exponential Scaling of Subradiant Decay Rates
School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, and Wuhan institute of quantum technology（华中科技大学物理学院和量子科学与工程学院，以及武汉量子技术研究院）
We present a method to map the evolution of photonic random walks that is compatible with nonclassical input light. Our approach leverages a newly developed flexible waveguide platform to tune the jumping rate between spatial modes, allowing the observation of a range of evolution times in a chip of fixed length. In a proof-of-principle demonstration we reconstruct the evolution of photons through a uniform array of coupled waveguides by monitoring the end-face alone. This approach enables direct observation of mode occupancy at arbitrary resolution, extending the utility of photonic random wa…
When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and analytical modeling, we uncover a set of surprising features that characterize discrete speckle in one- and two-dimensional lattices known to exhibit transverse Anderson localization. Firstly, the finge…
This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig-Penney models with different types of perturbations. Main attention is payed to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to …
Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices. These can be implemented by femtosecond laser waveguide writing, recently adopted for quantum applications. In particular, multiarm interferometers include "tritter" and "quarter" as basic elements, corresponding to the generalization of a beam splitter to a 3- and 4-port splitter, respectively. By injecting Fock states in the input ports of such interferomete…
We investigate the quantum properties for the codirectional three-mode Kerr nonlinear coupler. We investigate single-, two- and three-mode quadrature squeezing, Wigner function and purity. We prove that this device can provide richer nonclassical effects than those produced by the conventional coupler, i.e. the two-mode Kerr coupler. We show that it can provide squeezing and the quadrature squeezing exhibiting leaf-revival-collapse phenomenon in dependence on the values of the interaction parameters. In contrast to the conventional Kerr coupler two different forms of cat states can be simultan…
