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Advances in quantum information science are closely related to our ability to prepare, manipulate, and measure the states of multiple quantum bits (qubits). To this end, quantum gates are the key components by which specific operations over individual and multiple qubits are implemented. In the context of quantum optics, qubits can be encoded in any degree of freedom of a multi-photon state, e.g. polarization, frequency or spatial configuration. The faithful reciprocal exchange of information between two qubits, a so-called SWAP, is one of the fundamental operations that underpin modern quantum architectures. Here, we present a novel method realizing multiple-qubit SWAP operations over several qubits, without relying on any other gates, in an integrated-photonic setting. In principle, our approach allows for the implementation of SWAP operations with unity efficiency regardless of the number of involved qubits. Further, we discuss how this approach can be applied to qudits. Our findings provide a powerful new functional element for the design of compact quantum-photonic circuitry.

We show that it is possible to induced Anderson localization in an optical lattice with no disorder in their couplings or index of refraction but by a disordered artificial gauge field generated by periodic driving.

The possibility of implementing quantum Hamiltonians using linear optical systems and entangled photons has opened the door to employing topologically protected entangled states in optical quantum information processing. In two-dimmensional photonic topologial insulators, single photon edge-states inhabit in the gap between the energy bands supporting the bulk states. Breaking the topological protection requires disorder with sufficient strength to close such a bandgap. For states comprising two indistinguishable photons, the same bandgap does not exists. The reason is because when a linear optical system is excited by two indistinguishable photons, all possible two-photon eigenstates are given by the symmetric combinations of the single-photon eigenstates. Consequently, the corresponding two-photon eigenvalues are given by the combinations of the single-photon eigenvaues λ (2) = λ m + λ n . This fundamental additive property of the single photon eigenenergies removes the bandgap and leads to massive degeneracies of the edge-edge, edge-bulk, and bulk-bulk two-photon states.

We show theoretically that lossy waveguide systems exhibit exceptional points, whose order is enhanced by the photon number resolved detection of their coherent exceptional modes.

We theoretically show that the dynamics of a driven quantum harmonic oscillator subject to non-dissipative noise is formally equivalent to the single-particle dynamics propagating through an experimentally feasible dynamically-disordered photonic network. Using this correspondence, we find that noise assisted energy transport occurs in this network and, if the noise is Markovian or delta-correlated, we can obtain an analytical solution for the maximum amount of transferred energy between all network's sites at a fixed propagation distance. Beyond the Markovian limit, we further consider two different types of non-Markovian noise and show that it is possible to have efficient energy transport for larger values of the dephasing rate., Comment: 12 pages, 4 figures

We investigate theoretically the physical mechanisms that contribute to the vulnerability of highly entangled two-photon edge states propagating in topological insulator photonic lattices. We present clear guidelines for maximizing entanglement without sacrificing topological protection.

Exceptional points are complex-valued spectral singularities that lead to a host of intriguing features such as loss-induced transparency - a counterintuitive process in which an increase in the system's overall loss can lead to enhanced transmission. In general, the associated enhancements scale with the order of the exceptional points. Consequently, it is of great interest to devise new strategies to implement realistic devices capable of exhibiting high-order exceptional points. Here, we show that high-order N-photon exceptional points can be generated by exciting non-hermitian waveguide arrangements with coherent light states. Using photon-number resolving detectors it then becomes possible to observe N-photon enhanced loss-induced transparency in the quantum realm. Further, we analytically show that the number-resolved dynamics occurring in the same nonconservative waveguide arrays will exhibit eigenspectral ramifications having several exceptional points associated to different sets of eigenmodes and dissipation rates.

Quantum theory stipulates that if two particles are identical in all physical aspects, the allowed states of the system are either symmetric or antisymmetric with respect to permutations of the particle labels. Experimentally, the symmetry of the states can be inferred indirectly from the fact that neglecting the correct exchange symmetry in the theoretical analysis leads to dramatic discrepancies with the observations. The only way to directly unveil the symmetry of the states for, say, two identical particles is through the interference of the original state and the physically permuted one, and measure the phase associated with the permutation process, the so-called particle exchange phase. Following this idea, we have measured the exchange phase of indistinguishable photons, providing direct evidence of the bosonic character of photons., Comment: 16 pages, 7 figures

Indistinguishable and/or entangled photons propagating in waveguide arrays (WAs) represent a promising platform whose utility ranges from research on fundamental aspects of quantum mechanics all the way to applications in quantum sensing and quantum information processing. Quantum simulators of decoherence reveal that while decoherence processes inevitably destroy single-particle coherence and any form of multiparticle entanglement, quantum correlations based on particle indistinguishability do endure. Further, by judiciously combining multi-photon states with the idea of synthetic dimensions in WAs yields the notion of a synthetic atom and in turn this provides entirely novel perspectives on the dynamics of such multi-photon states. Similarly, simple beam splitters fed with indistinguishable photons, can be used to perform discrete fractional Fourier transforms or can be tuned to realize exceptional points of any order. The latter setup facilitates efficient quantum-enhanced sensors.

Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in non-Hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. Here, we present the first study on the emergence of topological edge states in two-dimensional Haldane lattices exhibiting balanced gain and loss. In line with recent studies on other Chern insulator models, we show that edge states can be observed in the so-called broken $\mathcal{P}\mathcal{T}$-symmetric phase, that is, when the spectrum of the gain-loss-balanced system's Hamiltonian is not entirely real. More importantly, we find that such topologically protected edge states emerge irrespective of the lattice boundaries, namely zigzag, bearded or armchair.

Topological physics exploits concepts from geometry and topology to implement systems capable of guiding waves in an unprecedented fash- ion. These ideas have led to the development of photonic topological insulators, which are optical systems whose eigenspectral topology allows the creation of light states that propagate along the edge of the system without any coupling into the bulk or backscattering even in the presence disorder. Indeed, topological protection is a fully coherent effect, and it is not clear to what extent topological effects endure when the wavefronts become partially coherent. Here, we study the interplay of topological protection and the degree of spatial coherence of classical light propa- gating in disordered photonic topological insulators. Our results reveal the existence of a well-defined spectral window in which partially coher- ent light is topologically protected. This opens up the design space to a wider selection of light sources, possibly yielding smaller, cheaper and more robust devices based on the topological transport of light.

We present the first study on the emergence of topologically-protected edge states in a two-dimensional Haldane honeycomb lattice with balanced gain and loss.

We study fundamental limitations to topological protection induced by increasing the amount of entanglement in nonseparable two-photon states. We identify the physics underlying such vulnerability and the conditions for robust protection of two-photon states.

It is widely accepted that photons are bosons. To the best of our knowledge, we present the first-ever test of this fundamental assumption of quantum electrodynamics and discuss the influence of experimental imperfections.

Activating transitions between internal states of physical systems has emerged as an appealing approach to create lattices and complex networks. In such a scheme, the internal states or modes of a physical system are regarded as lattice sites or network nodes in an abstract space whose dimensionality may exceed the systems' apparent (geometric) dimensionality. This introduces the notion of synthetic dimensions, thus providing entirely novel pathways for fundamental research and applications. Here, we analytically show that the propagation of multi-photon states through multi-port waveguide arrays gives rise to synthetic dimensions where a single waveguide system generates a multitude of synthetic lattices. Since these synthetic lattices exist in photon-number space, we introduce the concept of pseudo-energy and demonstrate its utility for studying multi-photon interference processes. Specifically, the spectrum of the associated pseudo-energy operator generates a unique ordering of the relevant states. Together with generalized pseudo-energy ladder operators, this allows for representing the dynamics of multi-photon states by way of pseudo-energy term diagrams that are associated with a synthetic atom. As a result, the pseudo-energy representation leads to concise analytical expressions for the eigensystem of $N$ photons propagating through $M$ nearest-neighbor coupled waveguides. In the regime where $N>2$ and $M>2$, non-local coupling in Fock space gives rise to hitherto unknown all-optical dark states which display intriguing non-trivial dynamics., Two-column layout, 11 pages, 8 figures

The quantum theory of electromagnetic radiation predicts characteristic statistical fluctuations for light sources as diverse as sunlight, laser radiation, and molecule fluorescence. Indeed, these underlying statistical fluctuations of light are associated with the fundamental physical processes behind their generation. In this contribution, we experimentally demonstrate that the manipulation of the quantum electromagnetic fluctuations of two-mode squeezed vacuum states leads to a family of quantum-correlated multiphoton states with tunable mean photon numbers and degree of correlation. Our technique relies on the use of conditional measurements to engineer the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. The experimental generation of nonclassical multiphoton states by means of photon subtraction unveils novel mechanisms to control fundamental properties of light. As a remarkable example, we demonstrate the engineering of a quantum state of light with up to ten photons, exhibiting nearly Poissonian photon statistics, that constitutes an important step towards the generation of entangled lasers. Our technique enables a robust protocol to prepare quantum states with multiple photons in high-dimensional spaces and, as such, it constitutes a novel platform for exploring quantum phenomena in mesoscopic systems.

We address the problem of the persistence of entanglement of quantum light under mode transformations, where orthogonal modes define the parties between which quantum correlations can occur. Since the representation of a fixed photonic quantum state in different optical mode bases can substantially influence the entanglement properties of the said state, we devise a constructive method to obtain families of states with the genuine feature of remaining entangled for any choice of mode decomposition. In the first step, we focus on two-photon states in a bipartite system and optimize their entanglement properties with respect to unitary mode transformations. Applying a necessary and sufficient entanglement witness criteria, we are then able to prove that the class of constructed states is entangled for arbitrary mode decompositions. Furthermore, we provide optimal bounds to the robustness of the mode-independent entanglement under general imperfections. In the second step, we demonstrate the power of our technique by showing how it can be straightforwardly extended to higher-order photon numbers in multipartite systems, together with providing a generally applicable and rigorous definition of mode-independent separability and inseparability for mixed states.

We show that by injecting N indistinguishable photons in a waveguide beam-splitter, one can create lattice-like structures in the photon number space, which are equivalent to coupled systems that perform discrete fractional Fourier operations.

Direct laser writing of surface waveguides with ultrashort pulses is a crucial achievement towards all-laser manufacturing of photonic integrated circuits sensitive to their environment. In this Letter, few-cycle laser pulses (with a sub-10 fs duration) are used to produce subsurface waveguides in a non-doped, non-coated fused silica substrate. The fabrication technique relies on laser-induced microdensification below the threshold for nanopore formation. The optical losses of the fabricated waveguides are governed by the optical properties of the superstrate. We have measured losses ranging from less than 0.1~dB/mm (air superstrate) up to 2.8~dB/mm when immersion oil is applied on top of the waveguide.

We experimentally demonstrate that the simultaneous subtraction of photons from a two-mode squeezed vacuum state leads to the generation of entangled states with increasingly larger average photon number.

Quantum walks in dynamically-disordered networks have become an invaluable tool for understanding the physics of open quantum systems. In this work, we introduce a novel approach to describe the dynamics of indistinguishable particles in noisy quantum networks. By making use of stochastic calculus, we derive a master equation for the propagation of two non-interacting correlated particles in tight-binding networks affected by off-diagonal dynamical disorder. We show that the presence of noise in the couplings of a quantum network creates a pure-dephasing-like process that destroys all coherences in the single-particle Hilbert subspace. Remarkably, we find that when two or more correlated particles propagate in the network, coherences accounting for particle indistinguishability are robust against the impact of noise, thus showing that it is possible, in principle, to find specific conditions for which many indistinguishable particles can traverse dynamically-disordered systems without losing their ability to interfere. These results shed light on the role of particle indistinguishability in the preservation of quantum coherence in dynamically-disordered quantum networks., Comment: 15 pages, 4 figures

The femtosecond laser direct-writing (FLDW) of waveguide circuits in glasses has seen interest from a number of fields over the previous 20 years. It has evolved from a curiosity to a viable platform for the rapid prototyping of small scale circuits. The field of quantum information science has exploited this capability and in the process advanced the fabrication technique. In this review the technological aspects of the laser inscription method relevant to quantum information science will be discussed. A range of demonstrations which have been enabled by laser written circuits will be outlined; these include novel circuits, simulations, photon sources and detection. This places the FLDW technique among the few integrated optical platforms to have produced individually every component required for scalable quantum computation.

We experimentally demonstrate that the simultaneous subtraction of photons from a two-mode squeezed vacuum state leads to the generation of entangled states with increasingly larger average photon number.

We demonstrate generation of entangled photon-subtracted states and manipulation of their quantum fluctuations. The flexibility of our technique allows us to explore Hong-Ou-Mandel interferometry with mesoscopic states that resemble systems of entangled lasers.

We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations is discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.

We theoretically show that multiport photonic lattices emulating driven quantum harmonic oscillators give rise to Aharonov–Anandan geometric phase, which is proportional to the associated dynamic phase irrespective of the initial state. Consequently, the non-adiabatic geometric phase can be directly measured without the need of complex setups to remove the dynamic phase. Further, we propose the observation of such geometric phases in multiport photonic lattices via integrated interferometry. Our work provides insights into the potential development of integrated photonic platforms for modulation-based topological photonics.

Single-photon W-states — coherent superpositions of all qubits with equal probability amplitudes — involving up to 16 spatial modes are generated by means of evanescently-coupled waveguide technology. A scheme capable of exploiting the maximal entanglement of W-states is proposed for the efficient generation of random numbers.

Exceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, corresponding eigenmodes become degenerate. Classical and quantum photonic systems with EPs have attracted tremendous attention due to their unusual properties, topological features, and an enhanced sensitivity that depends on the order of the EP, i.e. the number of degenerate eigenmodes. Yet, experimentally engineering higher-order EPs in classical or quantum domains remains an open challenge due to the stringent symmetry constraints that are required for the coalescence of multiple eigenmodes. Here we analytically show that the number-resolved dynamics of a single, lossy, waveguide beamsplitter, excited by $N$ indistinguishable photons and post-selected to the $N$-photon subspace, will exhibit an EP of order $N+1$. By using the well-established mapping between a beamsplitter Hamiltonian and the perfect state transfer model in the photon-number space, we analytically obtain the time evolution of a general $N$-photon state, and numerically simulate the system's evolution in the post-selected manifold. Our results pave the way towards realizing robust, arbitrary-order EPs on demand in a single device., Comment: 5 pages, 2 figures

We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold---which we referred to as a metal-insulator phase transition---between an exponential growth and a low photon production. The low photon production is due to Bloch-like oscillations that produce a strong localization of the initial vacuum state, thus preventing higher generation of photons. To break localization of the vacuum state, and enhance the photon generation, we impose a dephasing mechanism, based on dynamic disorder, into the driving frequency of the mirror. Additionally, we explore the effects of finite temperature on the photon production. Concurrently, we propose a classical analogue of the dynamical Casimir effect in engineered photonic lattices, where the propagation of classical light emulates the photon generation from the quantum vacuum of a single-mode tunable cavity.

We report on the experimental observation of Bloch Oscillations of nonlocal quantum states. Our on-chip photonic lattice could serve as a platform for quantum simulation of the dynamics of bosonic, anyonic and fermionic particles.

We present a linear photonic approach to implement two-qubit SWAP gates based on engineered arrangements of evanescently coupled waveguides. Our scheme puts forward an alternative to implement two-qubit SWAP gates without using C-Not gates.

Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most prominent adversary of quantum coherence is noise arising from the interaction of the associated dynamical system with its environment. Under certain conditions, however, the existence of noise may drive quantum and classical systems to endure intriguing nontrivial effects. Along these lines, here we demonstrate, both theoretically and experimentally, that when two indistinguishable particles co-propagate through quantum networks affected by noise, the system always evolves into a steady state in which coherences between certain separable states perpetually prevail. Furthermore, we show that the same steady state with surviving quantum coherences is reached irrespectively of the configuration in which the particles are prepared.

In this work we experimentally demonstrate the realization of the discrete fractional Fourier transforms (DFrFT) in both the classical and quantum realm. Our approach is fully integrated and free of bulk optical components.

We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs.

We propose that waveguide array-based photonic topological insulators can be used to protect the entanglement of quantum states in photonic quantum walks. The promise of the field of ‘topological photonics’ lines in the use of the physics of the quantum Hall effect and topological insulators, usually associated with electrons passing through solid-state materials, to provide robustness to complex photonic structures. In the quantum Hall effect, incredibly robust Hall conductivity — quantized transport — arose from the presence of scatter-free edge states permeating the entire structure. In other words, when a wavepacket moving along the edge encounters disorder of any kind, it simply passes through it unimpeded. The robustness of transport is associated with a ‘topological invariant’ of the band structure: this is a quantity that can be calculated from the bulk band structure of the periodic lattice in question by calculating an associated Berry phase where the Bloch wave vector acts as the adiabatic parameter. Recently a great deal of effort has been directed towards the realization of photonic topological structures — photonic crystals (whether in the form of waveguide arrays, coupled-resonator-optical-waveguide structures, microwave photonic crystal slabs, among others) with quantum Hall-like protected transport along the edge. Here we show that we can use a waveguide-array based photonic topological insulator to protect photonic quantum information — namely we can preserve the character of ‘NOON’ states (and other entangled states) as they propagate through such a lattice. NOON states are notoriously fragile entities and are entirely destroyed by any type of scattering: photonic topological protection could act as a novel mechanism for preserving these fragile quantum states in complex geometries.

We demonstrate that superpositions of coherent and displaced Fock states, also referred to as generalized Schr\"odinger cats cats, can be created by application of a nonlinear displacement operator which is a deformed version of the Glauber displacement operator. Consequently, such generalized cat states can be formally considered as nonlinear coherent states. We then show that Glauber-Fock photonic lattices endowed with alternating positive and negative coupling coefficients give rise to classical analogs of such cat states. In addition, it is pointed out that the analytic propagator of these deformed Glauber-Fock arrays explicitly contains the Wigner operator opening the possibility to observe Wigner functions of the quantum harmonic oscillator in the classical domain., Comment: 17 pages, 5 figures

Beyond the adiabatic limit, the Aharonov-Anandan phase is a generalized description of Berry's phase. In this regime, systems with time-independent Hamiltonians may also acquire observable geometric phases. Here we report on a measurement of the Aharonov-Anandan phase in photonics. Different from previous optical experiments on geometric phases, the implementation is based on light modes confined in evanescently coupled waveguides rather than polarization-like systems, thereby physical models in more than two-dimensional Hilbert spaces are achievable. In a tailored photonic lattice, we realize time-independent quantum-driven harmonic oscillators initially prepared in the vacuum state and achieve a measurement of the Aharonov-Anandan phase via integrated interferometry.

We show that light evolution occurring in waveguide arrays with a particular n-functional square root dependence of coupling coefficients can be used to produce classical analogues of nonlinear quantum coherent states. Using operator algebras we obtain closed-form expressions describing the optical field dynamics in such structures. In addition, by numerically monitoring the Mandel's parameter, we obtain the conditions necessary to generate sub-Poissonian and super-Poissonian classical intensity distributions in the proposed photonic lattices.

We study theoretically the surface plasmon electromagnetic field in the plane of the interface along which it propagates. Arbitrary surface plasmon fields are expressed by a linear superposition of elementary surface plasmon modes, thus obtaining an expression for the in-plane components similar to the angular spectrum model, which establishes the formal foundations of a two-dimensional surface plasmon optics. From this representation, we obtain the general description for surface plasmon modes be having as in-plane diffraction free beams. These new modes with their corresponding phase parameters are used to study surface plasmon self-imaging phenomenon and the synthesis of surface plasmon singularity regions (caustics) of surface plasmon fields, proposing experimental means to observe both.

The Aharonov-Anandan phase is a generalization of the Berry phase and so far its observation in photonics has been elusive. Here work we report on measurements of Aharonov-Anandan phases using driven harmonic oscillator photonic lattices.

In this work we demonstrate, theoretically and experimentally, that two-photon probability amplitudes describing propagation of light in any two-photon state are governed by an evolution equation identical to a 2D tight-binding equation.

We experimentally demonstrate a fully integrated photon-counting device based on a divide-and-conquer technique using linear optics in combination with standard on-off detectors.

Bloch Oscillations (BOs) of quantum particles manifest themselves as periodic spreading and re-localization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit BOs are deeply rooted into the very foundations of quantum mechanics, all experimental observations of this phenomenon so far have only contemplated dynamics of one or two particles initially prepared in separable local states, which is well described by classical wave physics. Evidently, a more general description of genuinely quantum BOs will be achieved upon excitation of a Bloch-oscillator lattice system by nonlocal states, that is, containing correlations in contradiction with local realism. Here we report the first experimental observation of BOs of two-particle Einstein-Podolsky-Rosen states (EPR), whose associated N-particle wave functions are nonlocal by nature. The time evolution of two-photon EPR states in Bloch-oscillators, whether symmetric, antisymmetric or partially symmetric, reveals unexpected transitions from particle antibunching to bunching. Consequently, the initial state can be tailored to produce spatial correlations akin to bosons, fermions or anyons. These results pave the way for a wider class of photonic quantum simulators., Comment: 21 pages, 6 figures

We report on the experimental realization of quantum and classical discrete fractional Fourier transforms using photonic lattices. Our approach is fully integrated and free of bulk optical components.