Quantum transport simulations in a programmable nanophotonic processor

Journal name:
Nature Photonics
Year published:
Published online


Environmental noise and disorder play critical roles in quantum particle and wave transport in complex media, including solid-state and biological systems. While separately both effects are known to reduce transport, recent work predicts that in a limited region of parameter space, noise-induced dephasing can counteract localization effects, leading to enhanced quantum transport. Photonic integrated circuits are promising platforms for studying such effects, with a central goal of developing large systems providing low-loss, high-fidelity control over all parameters of the transport problem. Here, we fully map the role of disorder in quantum transport using a nanophotonic processor: a mesh of 88 generalized beamsplitters programmable on microsecond timescales. Over 64,400 experiments we observe distinct transport regimes, including environment-assisted quantum transport and the ‘quantum Goldilocks’ regime in statically disordered discrete-time systems. Low-loss and high-fidelity programmable transformations make this nanophotonic processor a promising platform for many-boson quantum simulation experiments.

At a glance


  1. A quantum transport simulator.
    Figure 1: A quantum transport simulator.

    a, Schematic of programmable nanophotonic processor. Dark lines are silicon nanowire waveguides; circles are programmable MZIs. Inset: thermal phase modulators control the splitting ratio and differential output phase. Time (τ) is defined from left to right. Space (i) is defined from top to bottom. b,c, Example graphs implementable with the processor's Hamiltonian (labelled dark circles represent waveguide positions or nodes): nearest-neighbour graph implemented in this work (b), where the coupling between waveguides depends on whether the time step is even or odd; binary tree graph allowed by the processor Hamiltonian (c). d, Dynamic disorder is implemented by choosing {φi} such that there are no spatiotemporal correlations. Disorder strength is described via the cd parameter. e, Static disorder is implemented by choosing {φi} to be constant in time, but uncorrelated in space. f, Arrested transport of a quantum particles in strong, statically disordered system to external sites can be optimized by introducing dynamic disorder.

  2. Programmable nanophotonic processor.
    Figure 2: Programmable nanophotonic processor.

    a, Processor composed of 88 MZIs, 26 input modes, 26 output modes and 176 phase shifters; gold wirebond filaments are visible. b, Zoom in of the white inset in a, showing individual interferometer and thermo-optic phase shifters (θ,φ). c, Phase versus voltage curve for all internal and external phase shifters on the chip. d, Transmission spectrum for an MZI with careful input polarization filtering. The extinction ratio was measured to be 0.9999998 ± 1.3 × 10–8. e, Set-up used in this experiment. The processor accepts only transverse-electric polarized light, requiring a bank of polarization rotators to couple to the chip modes. Polarization rotator fibres are connected to the input glass photonic integrated circuit, which serves as both a waveguide pitch reducer and as a spot-size converter. The output of the PNP is sent to an array of detectors and read out using a microcontroller. The processor is electronically programmed using a 240-channel biasing system and operated using a microcontroller. f, Nonlinear optimization protocol used to generate the Massachusetts Institute of Technology logo shown in g, across the 26 output modes of the processor |ψ(i,11)|2.

  3. Convergence and the full noisy transport space.
    Figure 3: Convergence and the full noisy transport space.

    a, Programming routine for transport experiments. PNP is initialized, environmental noise is introduced, and the output distribution is measured. This process is repeated N times to develop robust statistics. b, A measurement of a single instance of disorder coordinate (0,1). With one instance, it is difficult to determine what disorder coordinate could have generated this distribution. c, Convergence of the mean output distribution with iteration number. N ≥ 10 is necessary to achieve a fidelity f exceeding 98%. d, 〈|ψ(i,11)|2〉 for 400 combinations of (cd,cs) with both disorder coordinates varying on [0,1]. Modes labelled i = 7 → 20 are shown; i < 7 and i > 20 are relatively constant for all levels of disorder, as predicted via simulation. The mean fidelity for all modes and all disorder coordinates is 99.8 ± 0.036%. Particle-like, incoherent transport occurs on the right edge of these plots. Coherent, ballistic transport occurs in the bottom left corner. eg, Measurements of 〈|ψ(i,11)|2N=100 at disorder coordinates (0,0), (1,1) and (0,1). Fits to the Laplace and Gaussian distributions are shown in red in f and g, respectively.

  4. Environment-assisted quantum transport and the Goldilocks regime.
    Figure 4: Environment-assisted quantum transport and the Goldilocks regime.

    a, Conceptual drawing of the phase landscape for a strong, statically disordered system where particle is localized to initial site at i14. By adding dynamic disorder (shown as red vibrations), it is possible to optimize transport of the particle to sites further away. b, Slice through cs = 0.6 and all cd, corresponding to a randomized phase span of 1.2π. The y axis represents quantum transport efficiency η and the x axis is dynamic disorder strength. Red and blue lines are experimental data and simulation data for the phase configuration used in the experiment, respectively. The green line represents simulation with N = 2 × 104—the asymptotic distribution. These data show environment-assisted quantum transport in a discrete-time system. Standard errors are plotted as a transparent band around the mean.


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Author information


  1. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    • Nicholas C. Harris,
    • Gregory R. Steinbrecher,
    • Mihika Prabhu,
    • Jacob Mower &
    • Dirk Englund
  2. Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

    • Yoav Lahini
  3. Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    • Darius Bunandar
  4. Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    • Changchen Chen &
    • Franco N. C. Wong
  5. Elenion Technologies, 171 Madison Avenue, Suite 1100, New York, New York 10016, USA

    • Tom Baehr-Jones &
    • Michael Hochberg
  6. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    • Seth Lloyd


N.C.H. designed the photonic integrated circuit and experimental set-up and performed the experiments. N.C.H. laid out the design mask, with assistance from G.S. on metal routing. N.C.H. and M.P. calibrated the system. N.C.H., Y.L., G.S., S.L. and D.E. conceived the experiment. D.B. assisted with the theory. C.C. and F.N.C.W. assisted with multiphoton experiments. T.B.-J. and M.H. fabricated the system. All authors contributed to writing the paper.

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