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arXiv:1103.0604 · New Journal of Physics

Two-photon quantum walks in an elliptical direct-write waveguide array

J O Owens, Matthew A. Broome, Devon N. Biggerstaff, M. E. Goggin, Alessandro Fedrizzi, T Linjordet, Martin Ams, G D Marshall, Jason Twamley, Michael J. Withford, A G White

Published Jul 13, 2011• 138 citations
arXivHTMLPDF

Abstract

Integrated optics provides an ideal testbed 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 characterize 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. This work highlights the feasibility of emulation of coherent quantum phenomena in three-dimensional waveguide structures.

DOI
10.1088/1367-2630/13/7/075003

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Optics InfoBase Conference Papers•Jan 1, 2011•0 citations
Integrated optics provides an ideal testbed 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 characterize 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. This work highlights the feasibility of emulation of coherent quantum phenomena in three-dimensional waveguide structures.
Multiphoton quantum walks in integrated optics comprise 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 the time evolution of such systems is important for characterizing multiparticle 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 arrays of 21 evanescently coupled waveguides fabricated in silicon oxynitride technology. We compare three time evolutions, that follow closely a model assuming unitary evolution, corresponding to three different lengths of the array---in each case we observe quantum interference features that violate classical predictions. The longest array includes reflecting boundary conditions.
Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.
Unlike discrete photonic circuits, which manipulate photons step-by-step using a series of optical elements, arrays of coupled waveguides enable photons to interfere continuously across the entire structure. When composed of a nonlinear material, such arrays can also directly generate quantum states of light within the circuit. To clarify the similarities and distinctions between these two approaches of quantum walks, we conduct here a systematic comparison between linear waveguide arrays, injected with photons produced externally, and nonlinear arrays, where photon pairs are continuously generated via parametric down-conversion. We experimentally validate these predictions using III-V semiconductor nonlinear waveguide lattices with varied geometries, enabling us to tune the depth of the quantum walks over an order of magnitude and reveal the gradual emergence of non-classicality in the output state. Finally, we demonstrate an inverse-design approach to engineer \textit{aperiodic} waveguide arrays, whose optimized coupling profiles generate maximally entangled states such as the biphoton W-state. These results highlight the potential of continuously-coupled photonic systems to harness high-dimensional entanglement within compact architectures.
We theoretically analyze the dynamical evolution of photonic quantum walks on M\"obius strips and other exotic structures in three-dimensional 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 nontrivial array topologies introduce time-dependent symmetries of the two-photon correlations. These properties allow a large degree of control for quantum state engineering of multimode entangled states in these devices.
Abstract Over the last 20 years quantum walks (QWs) have gained increasing interest in the field of quantum information science and processing. In contrast to classical walkers, quantum objects exhibit intrinsic properties like non-locality and non-classical many-particle correlations, which renders QWs a versatile tool for quantum simulation and computation as well as for a deeper understanding of genuine quantum mechanics. Since they are highly controllable and hardly interact with their environment, photons seem to be ideally suited quantum walkers. In order to study and exploit photonic QWs, lattice structures that allow low loss coherent evolution of quantum states are demanded. Such requirements are perfectly met by integrated optical waveguide devices that additionally allow a substantial miniaturization of experimental settings. Moreover, by utilizing the femtosecond direct laser writing technique three-dimensional waveguide structures are capable of analyzing QWs also on higher dimensional geometries. In this context, advances and findings of photonic QWs are discussed in this review. Various concepts and experimental results are presented covering, such as different quantum transport regimes, the Boson sampling problem, and the discrete fractional quantum Fourier transform.