Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices

Integrated random projection and dimensionality reduction by propagating light in photonic lattices

It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a photonic lattice with diagonal disorder, which turns out to be a random complex Gaussian matrix. Thus, by collecting the output light from a random subset of the waveguide channels, one can perform an embedding from a higher- to a lower-dimensional space that respects the Johnson-Lindenstrauss lemma and nearly preserves the Euclidean distances. The distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive propagation of light. The proposed scheme can be utilized as a simple and powerful integrated dimension reduction stage that can greatly reduce the burden of a subsequent neural computation stage.

Topological protection versus degree of entanglement of two-photon light in photonic topological insulators

Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states inherit full protection from their single-photon “parents”, a high degree of non-separability may lead to rapid deterioration of the two-photon states after propagation through disorder. In this work, we identify physical mechanisms which contribute to the vulnerability of entangled states in topological photonic lattices. Further, we show that in order to maximize entanglement without sacrificing topological protection, the joint spectral correlation map of two-photon states must fit inside a well-defined topological window of protection.

Topological protection of entangled states is a promising avenue for photonic quantum technologies. Here, Tschernig et al. theoretically analyse the impact of disorder on topological protection of entangled two-photon states in periodic and aperiodic topological insulator lattices.

Probing quantum walks through coherent control of high-dimensionally entangled photons

Control over the duration of a quantum walk is critical to unlocking its full potential for quantum search and the simulation of many-body physics. Here we report quantum walks of biphoton frequency combs where the duration of the walk, or circuit depth, is tunable over a continuous range without any change to the physical footprint of the system-a feature absent from previous photonic implementations. In our platform, entangled photon pairs hop between discrete frequency modes with the coupling between these modes mediated by electro-optic modulation of the waveguide refractive index. Through control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting enhanced ballistic transport or strong energy confinement, to subspaces featuring scattering centers or local traps. We also explore the role of entanglement dimensionality in the creation of energy bound states, which illustrates the potential for these walks to quantify high-dimensional entanglement.

Disorder-Robust Entanglement Transport

We study the disorder-perturbed transport of two noninteracting entangled particles in the absence of backscattering. This situation is, for instance, realized along edges of topological insulators. We find profoundly different responses to disorder-induced dephasing for the center-of-mass and relative coordinates: While a mirror symmetry protects even highly delocalized relative states when resonant with the symmetry condition, delocalizations in the center of mass [e.g., two-particle (N=2) N00N states] remain fully sensitive to disorder. We demonstrate the relevance of these differences to the example of interferometric entanglement detection. Our platform-independent analysis is based on the treatment of disorder-averaged quantum systems with quantum master equations.

Investigation of structural mechanisms of laser-written waveguide formation through third-harmonic microscopy

The mechanisms of laser-induced modification of transparent materials are complex combinations of different processes that depend on the material itself and a range of processing parameters. As such, the mechanisms are still subject to ongoing study. We use a custom-built adaptive third-harmonic generation (THG) microscope to study those mechanisms. New femtosecond-laser-written phenomena are revealed through this method of imaging. This Letter, together with previous reports by Miyamoto Opt. Express24, 25718 (2016)OPEXFF1094-408710.1364/OE.24.025718 and Fernandez J. Phys. D48, 155101 (2015)JPAPBE0022-372710.1088/0022-3727/48/15/155101 suggest that the distribution of the generated plasma during writing is responsible for the newly revealed phenomena.

Localized quantum walks in quasi-periodic Fibonacci arrays of waveguides

New quasi-periodic arrays of waveguides (AWs) constructed with Fibonacci sequences are proposed to realize localized quantum walks (LQWs). The proposed Fibonacci arrays of waveguides (FAWs) are simple and straightforward to make, but have a rich set of properties that are of potential use for applications in quantum communication. Our simulations show that, in contrast with randomly disordered AWs, LQWs in FAWs are highly controllable due to the deterministic disorder nature of quasi-periodic systems. Furthermore, unique LQWs with symmetrical probability distribution can be conveniently realized in the FAWs.

Nearly complete survival of an entangled biphoton through bound states in continuum in disordered photonic lattices

Bound states in the continuum (BICs) of periodic lattices have been the recent focus in a variety of photonic nanostructures. Motivated by the recent results about the photons evolving in BIC structures, we investigate the quantum decay of entangled biphotons through disordered photonic lattices. We report that the persistence of bound states in disordered photonic lattices leads to an interplay between the BIC and disorder-induced Anderson localized states. We reveal a novel effect resulting from such an interplay: a nearly complete quantum survival for the entangled biphoton respecting the antisymmetric exchange symmetry. This is in contrast to the complete vanishment in a periodic photonic lattice.

Probing measurement-induced effects in quantum walks via recurrence

Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a nonunitary projection operation. To probe measurement-induced effects in the state dynamics using a quantum simulator, the challenge is to implement controlled measurements on a small subspace of the system and continue the evolution from the complementary subspace. A powerful platform for versatile quantum evolution is represented by photonic quantum walks because of their high control over all relevant parameters. However, measurement-induced dynamics in such a platform have not yet been realized. We implement controlled measurements in a discrete-time quantum walk based on time-multiplexing. This is achieved by adding a deterministic outcoupling of the optical signal to include measurements constrained to specific positions resulting in the projection of the walker's state on the remaining ones. With this platform and coherent input light, we experimentally simulate measurement-induced single-particle quantum dynamics. We demonstrate the difference between dynamics with only a single measurement at the final step and those including measurements during the evolution. To this aim, we study recurrence as a figure of merit, that is, the return probability to the walker's starting position, which is measured in the two cases. We track the development of the return probability over 36 time steps and observe the onset of both recurrent and transient evolution as an effect of the different measurement schemes, a signature which only emerges for quantum systems. Our simulation of the observed one-particle conditional quantum dynamics does not require a genuine quantum particle but is demonstrated with coherent light.

Lattice topology dictates photon statistics

Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.

Photonic Loschmidt echo in binary waveguide lattices

Time reversal is one of the most intriguing yet elusive wave phenomena of major interest in different areas of classical and quantum physics. Time reversal requires in principle to flip the sign of the Hamiltonian of the system, leading to a revival of the initial state (Loschmidt echo). Here it is shown that Loschmidt echo of photons can be observed in an optical setting without resorting to reversal of the Hamiltonian. We consider photonic propagation in a binary waveguide lattice and show that, by exchanging the two sublattices after some propagation distance, a Loschmidt echo can be observed. Examples of Loschmidt echoes for single photon and NOON states are given in one- and two-dimensional waveguide lattices.

Hybrid laser written waveguides in fused silica for low loss and polarization independence

Photonic integrated circuits (PICs) written with an ultrashort pulsed laser provide advantages in a range of applications, such as photon-based quantum information processing, where low insertion loss and low polarization dependence are critical concerns. Here we demonstrate the inscription of hybrid waveguides in fused silica at a pulse repetition rate of 1MHz that fulfill both these criteria. The mechanisms for propagation and coupling losses are identified and decoupled, with separate sections of the waveguide minimizing for each and an adiabatic mode conversion between the two. Moreover, differing sources of birefringence were revealed to be non-parallel for the waveguides, such that structures can be designed where these competing sources cancel to remove any polarization dependence.

Topologically robust transport of entangled photons in a 2D photonic system

We theoretically study the transport of time-bin entangled photon pairs in a two-dimensional topological photonic system of coupled ring resonators. This system implements the integer quantum Hall model using a synthetic gauge field and exhibits topologically robust edge states. We show that the transport through edge states preserves temporal correlations of entangled photons whereas bulk transport does not preserve these correlations and can lead to significant unwanted temporal bunching or anti-bunching of photons. We study the effect of disorder on the quantum transport properties; while the edge transport remains robust, bulk transport is very susceptible, and in the limit of strong disorder, bulk states become localized. We show that this localization is manifested as an enhanced bunching/anti-bunching of photons. This topologically robust transport of correlations through edge states could enable robust on-chip quantum communication channels and delay lines for information encoded in temporal correlations of photons.

Engineering integrated photonics for heralded quantum gates

Scaling up linear-optics quantum computing will require multi-photon gates which are compact, phase-stable, exhibit excellent quantum interference, and have success heralded by the detection of ancillary photons. We investigate the design, fabrication and characterisation of the optimal known gate scheme which meets these requirements: the Knill controlled-Z gate, implemented in integrated laser-written waveguide arrays. We show device performance to be less sensitive to phase variations in the circuit than to small deviations in the coupler reflectivity, which are expected given the tolerance values of the fabrication method. The mode fidelity is also shown to be less sensitive to reflectivity and phase errors than the process fidelity. Our best device achieves a fidelity of 0.931 ± 0.001 with the ideal 4 × 4 unitary circuit and a process fidelity of 0.680 ± 0.005 with the ideal computational-basis process.

Ensemble-Averaged Quantum Correlations between Path-Entangled Photons Undergoing Anderson Localization

We measure ensemble-averaged quantum correlations of path-entangled photons, propagating in a disordered lattice and undergoing Anderson localization. These result in intriguing patterns, which show that quantum interference leads to unexpected dependencies of the location of one particle on the location of the other. These correlations are shared between localized and nonlocalized components of the two-photon wave function, and, moreover, yield information regarding the nature of the disorder itself. Such effects cannot be reproduced with classical waves, and are undetectable without ensemble averaging.

Experimental observation of N00N state Bloch oscillations

Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation.

Bloch oscillations consist of periodic spreading and relocalization of particle wave functions, but have been so far observed only in separable states. Here the authors observe them for two-photon N00N states in integrated photonic circuits, revealing transitions from particle bunching to anitbunching.

Quantum walk coherences on a dynamical percolation graph

Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. Here, we present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical time-multiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear non-Markovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proof-of-principle experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media.

Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits

Chip-based photonic quantum computing is an emerging technology that promises much speedup over conventional computers at small integration volumes. Particular interest is thereby given to polarisation-encoded photonic qubits, and many protocols have been developed for this encoding. However, arbitrary wave plate operation on chip are not available so far, preventing from the implementation of integrated universal quantum computing algorithms. In our work we close this gap and present Hadamard, Pauli-X, and rotation gates of high fidelity for photonic polarisation qubits on chip by employing a reorientation of the optical axis of birefringent waveguides. The optical axis of the birefringent waveguide is rotated due to the impact of an artificial stress field created by an additional modification close to the waveguide. By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations. Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides. The implemented gates are tested with classical and quantum light.