Topological phonon transport in an optomechanical system

The study investigates whether and how on-chip optomechanical arrays can realize topologically protected phonon transport, enabling robust propagation of thermal phonons along edge channels immune to backscattering. Advances in cavity optomechanics have enabled manipulation of mechanical motion down to the single-phonon level, while microfabrication has produced small-scale optomechanical circuits. Theoretical proposals suggest that larger-scale optomechanical arrays could realize topologically protected phonon transport via mechanisms like the Valley Hall effect. Realizing such transport at the nanoscale would enable robust hypersonic acoustic circuits and potentially control heat-carrying phonons. The work aims to experimentally observe topological phonon transport using a multiscale optomechanical crystal (OMC) platform with site-resolved optical read-out, demonstrating reduced backscattering and robust edge propagation in the 0.3 GHz band.

Background encompasses developments in cavity optomechanics for controlling and measuring mechanical motion and in optomechanical circuits enabling nonreciprocity and synthetic gauge fields. Prior topological mechanical systems have been implemented across platforms (pendula, fluids, solid elastic plates) and at the nanoscale (on-chip nanoelectromechanical metamaterials). The Valley Hall effect provides a route to robust, counter-propagating, valley-polarized edge states in time-reversal symmetric systems with Dirac cones. The snowflake phononic crystal has been proposed theoretically as a nanoscale platform for topological phononics. Challenges include downscaling to hypersonic frequencies and achieving robust edge transport with minimal backscattering, motivating the multiscale OMC approach that decouples photonic and phononic engineering while enabling sensitive, site-resolved read-out.

Device design and fabrication: A multiscale OMC is implemented by superimposing two commensurate triangular lattices in a 220 nm-thick SOI silicon membrane: a phononic snowflake lattice (lattice spacing a_m = 16.02 µm) and a smaller-scale photonic crystal lattice of cylindrical holes (a = 450 nm). After etching and release, connected triangular silicon membranes form the phononic crystal; each triangular membrane embeds a photonic crystal hosting a localized high-Q optical nanocavity for site-resolved read-out. Only downward-pointing triangles contain optical cavities; upward-pointing triangles remain unperturbed photonic crystals. Topological band engineering: The even (Mz-symmetric) in-plane vibrational modes of the snowflake phononic crystal host isolated Dirac cones centered near ~0.3 GHz with ~70 MHz linear dispersion. A bulk bandgap is opened by breaking Mz symmetry via reducing photonic-crystal hole sizes in upward-pointing triangles by a factor of 0.78, yielding a simulated gap of ~18 MHz. Finite-element method (FEM) simulations are used to obtain phononic band structures, mode shapes, and optomechanical couplings. A large unit-cell vacuum optomechanical coupling g0 ≈ 2×33.7 kHz is achieved for a higher-frequency mode exhibiting breathing motion around the optical cavity. Topological domains and domain walls: Two domains with opposite valley Chern numbers are created by mirror operation Mz of the symmetry-broken design. Interfaces (domain walls) between domains host helical, valley-polarized edge states. Due to anisotropy (elongated cavity design and silicon crystal anisotropy), edge-state dispersion depends on domain wall orientation; horizontal walls support in-gap edge states only across part of the gap. A Dirac Hamiltonian with anisotropic parameters is fit to simulations to capture edge-state properties. Optomechanical read-out: A tunable external-cavity diode laser is locked at a blue detuning of 340 MHz from the optical nanocavity resonance to enhance sensitivity near the Dirac frequency. An optical fiber taper with a dimple evanescently couples light to individual nanocavities, enabling site-resolved addressing across the >800-cavity array. Mechanical motion is imprinted as phase modulation on the cavity field and transduced to intensity modulation in transmission, then amplified by an EDFA and detected on a high-speed photoreceiver. The RF noise power spectral density (NPSD) is measured on a spectrum analyzer, yielding a local, optomechanically weighted mechanical NPSD proportional to a coarse-grained local density of states. Thermal motion with amplitudes ~10 fm is detected. Calibration procedures account for read-out variations between sites. Geometries tested: (1) Triangular topological mechanical cavity formed by enclosing a domain 2 region within domain 1, creating a closed domain wall; (2) Two tree-shaped topological cavities with identical total domain-wall circumference (96 unit cells) and seven 60° corners but differing segment lengths; (3) A trivial waveguide cavity created by a line defect pulling a band into the bulk gap as a control. Data analysis: Frequency- and position-resolved NPSD is compared with FEM-informed scattering matrix calculations assuming perfect transmission at corners. Group-velocity dispersion and frequency-dependent g0^(1D) are included. Sensitivity to backscattering is assessed by modeling corner transmission |t|^2 with values 1.0, 0.95, and 0.6. Fabrication-disorder-induced backscattering is estimated via simulations with 10 nm standard deviation in selected geometrical parameters of snowflake and cylindrical holes, yielding a round-trip reflection estimate for the triangular cavity. Theoretical model: An effective two-band anisotropic Dirac Hamiltonian captures valley Hall physics with parameters fitted near the K valley (e.g., m = 2π×10.8 MHz, m′/4 = −2π×5.4 MHz, v_xm = 2π×12.5 MHz, v_ym = 2π×14.9 MHz). Valley Chern numbers C = ±1/2 for the two domains predict counter-propagating valley-polarized edge states consistent with FEM.

• First experimental observation of topological phonon transport in an on-chip optomechanical device at room temperature using a multiscale OMC with site-resolved optical read-out across >800 cavities.
• Demonstrated robust edge transport with substantial reduction of backscattering in a 0.325–0.34 GHz band; topological bandwidth ~15 MHz (e.g., robust regime ~327–337 MHz), exceeding prior nanoscale implementations in carrier frequency and bandwidth.
• Clear contrast between transport regimes: standing-wave fringes (backscattering) at lower frequencies (321–327 MHz) vs. fringe-free running waves (backscattering-immune) at higher frequencies (327–337 MHz) along domain walls.
• Spectral measurements on slanted and horizontal edges agree closely with FEM- and scattering-matrix-based theory assuming perfect corner transmission; inclusion of group-velocity dispersion and frequency-dependent optomechanical coupling g0^(1D) reproduces peak-height behavior.
• Tree-shaped topological cavities with identical circumference (96 unit cells) and seven 60° corners but different segment lengths yield nearly identical spectra outside the crossover region, indicating negligible segment-dependent standing waves and thus minimal backscattering.
• Quantified robustness: modeling shows that even 5% corner reflection would visibly split peaks; measured spectra show no such deviations, implying transmission |t|^2 > 0.95 at corners (figure-of-merit). Disorder simulations (10 nm rms geometry variations) predict round-trip reflection |r|^2 ~ 1% for the triangular cavity; actual lithography disorder expected 2–4 nm.
• Bulk bandgap (measured in domain 1 bulk) spans ~316–338 MHz, consistent with FEM; designed symmetry breaking opens a simulated gap of ~18 MHz within the Dirac cone region.
• Detected thermal vibrations down to ~10 fm amplitude via cavity-enhanced optomechanical read-out; laser detuning set 340 MHz blue of cavity resonance for sensitivity near Dirac frequency.
• Control (trivial) cavity exhibits strong backscattering: irregular peak spacing and location differences between slanted and horizontal edges, consistent with coexisting forward and backward modes within the same valley facilitating backscattering.
• Orientation-dependent edge dispersion observed (horizontal vs slanted domain walls) in agreement with anisotropic Dirac model; horizontal-edge states span only part of the bulk gap, limiting the usable topological bandwidth.

The results directly address the central question of realizing robust, topologically protected phonon transport in nanoscale optomechanical systems. By engineering valley Chern domains in a multiscale OMC and using cavity-enhanced, site-resolved optical read-out, the study visualizes and quantifies backscattering-immune edge propagation of thermal phonons. The agreement between measurements and theory that assumes perfect corner transmission, the geometry-insensitive spectra across tree devices, and the inferred high transmission (|t|^2 > 0.95) through seven sharp corners collectively demonstrate topological protection consistent with the Valley Hall mechanism. The frequency-resolved data also illuminate practical limits: anisotropy and proximity to Brillouin zone boundaries for horizontal edges allow backscattering in a crossover region, constraining the topological bandwidth. These findings validate the multiscale OMC approach as a scalable platform for topological phononics with integrated optical access, providing a pathway to robust hypersonic phononic circuits and heat/phonon flow control on-chip.

A multiscale optomechanical crystal platform was realized that decouples photonic and phononic engineering, enabling site-resolved optical interrogation of topological phonon edge states. The experiment demonstrates robust, low-backscattering transport of thermal phonons near 0.3 GHz over ~15 MHz bandwidth, with corner transmission exceeding 95% and minimal sensitivity to geometric segment variations. This establishes an on-chip route to topological phononic circuits leveraging the full optomechanical toolbox (cooling, lasing, sensitive read-out, and nonclassical state generation). Future directions include: expanding to higher hypersonic frequencies (potentially up to ~100 GHz) by inverting photonics/phononics scales; implementing unidirectional (Chern) edge channels for thermal diodes, topological phonon amplification, and lasing; active optical reconfiguration of topological circuits (e.g., switchable links); and leveraging topological phononic circuits for quantum acoustodynamics, interfacing with dopants or superconducting qubits for quantum information processing and storage.

• Anisotropy from device geometry and silicon crystal breaks C3 symmetry, causing orientation-dependent edge-state dispersion; horizontal domain walls host edge states over only part of the bandgap, limiting the effective topological bandwidth.
• Sharp domain walls reduce valley localization, enabling backscattering near Brillouin zone boundaries (crossover region), thereby constraining bandwidth; smoother domain walls could mitigate this.
• The effective Dirac model’s validity condition is not strictly satisfied, leading to deviations from the idealized behavior.
• Measurements probe thermal motion at room temperature; quantum-regime characterization is not addressed here.
• Fabrication disorder, while small (estimated 2–4 nm), still induces finite (though low) reflection; simulations with 10 nm disorder estimate ~1% round-trip reflection in the triangular cavity.
• The demonstrated protection relies on the Valley Hall mechanism (time-reversal symmetric), which does not yield strictly unidirectional transport; chiral (Chern) edge channels would be required for nonreciprocal one-way guiding.