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…
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 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 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 presence of disorder and inhomogeneities in quantum networks has often been unexpectedly beneficial for both quantum and classical resources. Here, we experimentally realize a controllable inhomogenous Quantum Walk dynamics, which can be exploited to investigate the effect of coherent disorder on the quantum correlations between two indistinguishable photons. Through the imposition of suitable disorder configurations, we observe two photon states which exhibit an enhancement in the quantum correlations between two modes of the network, compared to the case of an ordered Quantum Walk. Diffe…
Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can be emulated with classical light. This rises a question: which aspects of the model are truly nonclassical? We address it by carrying out a photonic experiment based on a pre- and post-selection paradox. The paradox implies that if somebody could choose to ask, either if the particle is at position x = 0 at even time steps, or at position x = d (d > 1) at o…
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 …
The question of witnessing or quantifying nonclassicality of quantum systems has been addressed in various ways. For a given system or theory, we propose identifying it with the incompatibility of admissible states. We quantify the nonclassicality of quantum systems using the Hilbert-Schmidt norm of the commutator of two states. As a particular application of this measure, we study the classicalization of a discrete-time quantum walk with a noisy coin.
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.
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…
Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically implemented. To this end we design, model and experimentally fabricate, using the femtosecond laser direct-write technique, a 3D tubular waveguide array within glass to implement a photonic quantum walk on a circle. The boundary conditions of a QRW on a circle naturally suggests a 3D waveguide implementation - allowing much simpler device design than what could be achieved using a 2D waveguide archi…
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 demonstrate quantum walks of correlated photons in a 2D network of directly laser written waveguides coupled in a 'swiss cross' arrangement. The correlated detection events show high-visibility quantum interference and unique composite behaviour: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal non-classical behaviour in a non-planar structure.
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…
That quantum correlations can be generated over time between the spin and the position of a quantum walker is indisputable. The creation of bipartite entanglement has also been reported for two-walker systems. In this scenario, however, since the global state lies in a fourpartite Hilbert space, the question arises as to whether genuine multipartite entanglement may develop in time. Also, since the spatial degrees of freedom can be viewed as a noisy channel for the two-spin part, one may wonder how other nonclassical aspects, such as Bell nonlocality, Einstein-Podolsky-Rosen steering, quantum …
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 …
Integrated optics provides an ideal test bed for the emulation of quantum systems via continuous-time quantum walks. Here we study the evolution of two-photon states in an elliptic array of waveguides. We characterise the photonic chip via coherent-light tomography and use the results to predict distinct differences between temporally indistinguishable and distinguishable two-photon inputs which we then compare with experimental observations. Our work highlights the feasibility for emulation of coherent quantum phenomena in three-dimensional waveguide structures.
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…
We analyze the process of simultaneous photon pair generation and quantum walks realized by spontaneous parametric down conversion of a pump beam in a quadratic nonlinear waveguide array. We demonstrate that this flexible platform allows for creating quantum states with different spatial correlations. In particular, we predict that the output photon correlations can be switched from photon bunching to antibunching controlled entirely classically by varying the temperature of the array or the spatial profile of the pump beam.
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior than that of classical random walks such as ballistic propagation or localization due to disorder. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially …
Continuous-time quantum walks (CTQW) have shown the capability to perform efficiently the spatial search of a marked site on many kinds of graphs. However, most of such graphs are hard to realize in an experimental setting. Here we study CTQW spatial search on a planar triangular lattice by means of both numerical simulations and experiments. The experiments are performed using three-dimensional waveguide arrays fabricated by femtosecond laser pulses, illuminated by coherent light. We show that the retrieval of the marked site by the quantum walker is accomplished with higher probability than …
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence in the quantum ``coin'' which drives the walk. We find exact analytical expressions for the time dependence of the first two moments of position, and show that in the long-time limit the variance grows linearly with time, unlike the unitary walk. We compare this to the results of direct numerical simulation, and see how the form of the position distribution…
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…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple quantum ``coins'' in order to diminish the effects of interference between paths. We find solutions to this system in terms of the single coin random walk, and compare the asymptotic limit of these solutions to numerical simulations. We find exact analytical expressions for the time-dependence of the first two moments, and show that in the long time limit th…
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 …
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers an alternate route to simulating such nonclassical behavior in a more robust platform. However, in photonic implementations to date, an increase to the depth of a continuous quantum walk requires modifying the footprint of the system. Here we report continuous walks of a two-photon quantum frequency comb with entanglement across multiple dimensions. The coupl…
We investigate the viability of coupled waveguides as basic units of quantum circuits. In particular, we study the dynamics of entanglement for the single photon state, and single mode squeezed vacuum state. We further consider the case of entangled inputs in terms of the two mode mode squeezed vacuum states and the two photon NOON state. We present explicit analytical results for the measure of entanglement in terms of the logarithmic negativity. We also address the effect of loss on entanglement dynamics of waveguide modes. Our results indicate that the waveguide structures are reasonably ro…
Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity…
We theoretically analyze the dynamical evolution of photonic quantum walks on Möbius strips and other exotic structures in 3D integrated photonics. Our flexible design allows discrete observations of continuous time quantum walks of photons in a variety of waveguide arrays. Furthermore, our design allows one to inject photons during the evolution, allowing the possibility of interacting with the photons as they are 'walking'. We find that non-trivial array topologies introduce novel time-dependent symmetries of the two-photon correlations. These properties allow a large degree of control for q…
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…
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…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum telep…
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…
Integrated optical devices will play a central role in the future development of nonlinear quantum photonics. Here we focus on the generation of high-gain nonclassical light within them. Starting from the solid foundation provided by Maxwell's equations, we then move to applications by presenting a unified formulation that allows for a comparison of stimulated and spontaneous experiments in ring resonators and nanophotonic waveguides, and leads directly to the calculation of the quantum states of light generated in high-gain experiments.
We study the far field spatial distribution of the quantum fluctuations in the transverse profile of the output light beam generated by a type II Optical Parametric Oscillator below threshold, including the effects of transverse walk-off. We study how quadrature field correlations depend on the polarization. We find spatial EPR entanglement in quadrature-polarization components: For the far field points not affected by walk-off there is almost complete noise suppression in the proper quadratures difference of any orthogonal polarization components. We show the entanglement of the state of symm…
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…
Multi-photon quantum walks in integrated optics are an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light without an exponential overhead in resources. The ability to observe time evolution of such systems is important for characterising multi-particle quantum dynamics---notably this includes the effects of boundary conditions for walks in spaces of finite size. Here we demonstrate the coherent evolution of quantum walks of two indistinguishable photons using planar…
We show how to generate and control the correlations in a set of two distant quantum emitters coupled to a one-dimensional dissipative plasmonic waveguide. An external laser field enhances the dimer's steady-state correlations and allows an active control (switching on/off) of nonclassical correlations. The plasmon-assisted dipolar-interacting qubits exhibit persistent correlations, which in turn can be decoupled and made to evolve independently from each other. The setup enables long-distance ($\sim 1\, μ$m) qubit control that works for both resonant and detuned emitters. For suitable emitter…
