Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays

Konstantinos Poulios, Robert Keil, Daniel Fry, Jasmin D. A. Meinecke, Jonathan C. F. Matthews, Alberto Politi, Mirko Lobino, Markus Gräfe, Matthias Heinrich, Stefan Nolte, Alexander Szameit, and Jeremy L. O’Brien

Phys. Rev. Lett. 112, 143604 – Published 10 April 2014

Abstract

We demonstrate quantum walks of correlated photons in a two-dimensional network of directly laser written waveguides coupled in a “swiss cross” arrangement. The correlated detection events show high-visibility quantum interference and unique composite behavior: 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 nonclassical behavior in a nonplanar structure.

Received 17 July 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.143604

Authors & Affiliations

Konstantinos Poulios¹, Robert Keil², Daniel Fry¹, Jasmin D. A. Meinecke¹, Jonathan C. F. Matthews¹, Alberto Politi^1,*, Mirko Lobino^1,†, Markus Gräfe², Matthias Heinrich^2,‡, Stefan Nolte², Alexander Szameit², and Jeremy L. O’Brien^1,§

¹Centre for Quantum Photonics, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, United Kingdom
²Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany

^*Present address: School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom.
^†Present address: Centre for Quantum Dynamics and Queensland Micro and Nanotechnology Centre, Griffith University, Brisbane QLD 4111, Australia.
^‡Present address: CREOL, The College of Optics and Photonics, University of Central Florida, 4000 Central Florida Blvd., Orlando FL 32816, USA.
^§Jeremy.OBrien@bristol.ac.uk

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Issue

Vol. 112, Iss. 14 — 11 April 2014

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Images

Figure 1
(a) Schematic of the 2D evanescently coupled waveguide array. The coupling constant $C^{(1)}$ is for adjacent waveguides and the second order coupling is denoted as $C^{(2)}$ . (b) Schematic of the interface section of our waveguide circuit, showing the input waveguides fanning from a planar configuration to the 2D, swiss cross configuration.
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Figure 2
Graph structure simulated with a two-photon input state in the swiss cross structure shown in Fig. 1. Each of the 45 vertices corresponds to a two-particle state, with different degrees of connectivity (up to degree 8), and there are 126 links between different vertices corresponding to allowed transitions between two-particle states. Red lines and red vertices correspond to coupling strengths of $C$ and potentials of $β$ , respectively, so they coincide with the ones in the swiss cross structure. For vertices corresponding to a state with two particles in the same waveguide, the on site potential and the coupling are enlarged by a factor of 2 and $\sqrt{2}$ respectively, due to normalisation of the two-particle wavefunction. We mark these vertices and links in green. The two yellow vertices represent the two different two-photon input states in the experiment ( $X 1 - X 4$ and $X 1 - Y 1$ ). Two different complete connecting paths ( $| X 1 X 1 ⟩$ to $| X 4 X 4 ⟩$ and $| X 1 X 1 ⟩$ to $| Y 1 Y 1 ⟩$ ) are labeled as examples.
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Figure 3
Correlation matrices for the two different input combinations. Top row is for inputting the two photons on the same plane in opposite corners ( $X 1$ and $X 4$ ). The measured results for delays leading to (a) distinguishable and (b) indistinguishable photons are presented together with (c) the numerical simulation and (d) the violations (V) of inequality (3) (measured in standard deviations $σ$ , assuming Poissonian statistics for each individual coincidence count and propagating the error—white cells represent no violation), both for the case of indistinguishable photons. The bottom row shows the corresponding results for inputting the two photons in different planes in adjacent corners ( $X 1$ and $Y 1$ ). For both inputs, violations of the inequality for distinguishable photons were not observed, as was expected.
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Figure 4
Quantum interference peak observed when varying the relative free-space delay of the twin photons and monitoring the presence of both photons in the same waveguide using a balanced fiber beam splitter butt-coupled to the output waveguide. This particular peak is for both photons input on the same plane ( $X 1$ , $X 4$ ) and monitoring output waveguide $X 3$ , showing a visibility of $96.8 \pm 2.5 %$ . (Error bars indicate the standard deviation of the underlying Poissonian photon counting statistics.)
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Figure 5
(a) Schematic of the 2D waveguide array when summing correlations over sites within the different branches. (b)–(c) Correlation matrices between the branches for inputting the two photons on the same plane in opposite corners ( $X 1$ and $X 4$ ), showing the (b) distinguishable and (c) indistinguishable case. (d) Violations (V) of inequality (3) (measured in standard deviations $σ$ , assuming Poissonian statistics for each individual coincidence count and propagating the error—white cells represent no violation) for indistinguishable photons. No violations were observed for distinguishable photons, as was expected.
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