REALIZING TIGHT-BINDING HAMILTONIANS USING SITE-CONTROLLED COUPLED CAVITY ARRAYS

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Analog quantum simulators rely on programmable and scalable quantum devices to emulate Hamiltonians describing various physical phenomenon.

www.nature.com/ncomms, Aug. 29, 2023 – 

Photonic coupled cavity arrays are a promising alternative platform for realizing such simulators, due to their potential for scalability, small size, and high-temperature operability. However, programmability and nonlinearity in photonic cavities remain outstanding challenges. Here, using a silicon photonic coupled cavity array made up of 8

high quality factor (𝑄

up to∼7.1×104

) resonators and equipped with specially designed thermo-optic island heaters for independent control of cavities, we demonstrate a programmable photonic cavity array in the telecom regime, implementing tight-binding Hamiltonians with access to the full eigenenergy spectrum. We report a ∼50%

reduction in the thermal crosstalk between neighboring sites of the cavity array compared to traditional heaters, and then present a control scheme to program the cavity array to a given tight-binding Hamiltonian. The ability to independently program high-Q photonic cavities, along with the compatibility of silicon photonics to high volume manufacturing opens new opportunities for scalable quantum simulation using telecom regime infrared photons.

Introduction

Achieving analog quantum simulation necessitates the realization of programmable quantum devices1. Due to their inherent driven-dissipative nature, photonic systems are a promising platform for non-equilibrium quantum simulation2. An archetypal photonic quantum simulator consists of an array of programmable non-linear nodes with access to the entire quantized eigenenergy spectra of the Hamiltonians being simulated. While there have been numerous works on analog quantum simulation with microwave photons3,4,5,6,7, optical photons with their extremely weak interaction with the environment, can provide several additional advantages. The higher energy of optical photons allows for the preservation of quantum states even at room temperature, enabling operability at much higher temperatures8, which significantly simplifies the experiments and lowers the resources needed to scale the simulator. Additionally, availability of single photon detectors in the optical domain allows direct measurement of multiparticle correlations9,10 which are a key set of measurements for characterizing the quantum-ness of realized states. Building on recent advancements in nanofabrication, quantum optical systems have shifted from bulky tabletop systems prone to misalignments to fully integrated on chip photonic circuits. These large scale photonic integrated circuits owing to their small size and high speed of operation present opportunities for unprecedented scalability to practical quantum advantage11.

One solution to engineer such quantum systems in optics is via photonic coupled cavity arrays (CCA)12 where coupling between cavities provides a potential map for photons to move around, and strong spatial confinement of light for long durations allows access to onsite non-linearity via coupling with various excitonic materials. For photonic CCAs to be used as quantum simulators, four broad requirements need to be satisfied, namely, (i) scalability: there must exist pathways to scale to a large number of sites; (ii) measurability: there is a need for protocols to perform Hamiltonian tomography with restricted access and have CCAs with addressability to all the eigenstates of the system; (iii) controllability: control over all the terms describing the Hamiltonian is required; and finally (iv) optical non-linearity: need to realize photon-photon interaction to simulate many-body Hamiltonians. The last demand as a precondition, necessitates using high-quality factor (Q) cavities with small mode volumes as constituents of the CCA. Such high-Q cavities are also necessary to probe the entire quantized eigenenergy spectra. Though several experiments showing various physical phenomena using optical CCAs have been previously reported13,14,15, none of these CCAs are programmable and have access to the entire quantized eigenenergy spectra of the Hamiltonian. While careful selection of the operation regime can lead to pathways that allow scalability to multiple sites using photonics16, in the optical regime achieving programmability and measurability of the eigen-spectrum, is very challenging owing to the extremely small physical dimensions involved.

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