A single-phonon directional coupler

TL;DR

This work demonstrates an integrated GHz-phonon directional coupler comprising two single-phonon sources, two single-mode waveguides, and a central four-port coupler, achieving tunable 50:50 phononic beam splitting in a compact 210 μm footprint. Coherent phonon wavepackets and single-phonon Fock-state measurements validate beam-splitting behavior both classically and quantum mechanically, with a transfer-matrix model yielding a measured reflection of about $R\approx0.43$ for a 50:50 device. The experiments further reveal non-classical correlations via $g^{(2)}_{om}$ measurements exceeding the classical limit, confirming quantum-coherent phonon routing and equal retrieval probabilities into both output ports. Together, these results establish a foundational platform for scalable on-chip phononic circuits and hybrid quantum networks, enabling deterministic phonon routing, interference, and potential integration with superconducting qubits or quantum dots.

Abstract

Integrated photonics has revolutionized fields such as telecommunications, quantum optics, and metrology by enabling compact, scalable circuits through highly confined optical modes. Within the field of quantum acoustics, phonons have emerged as a compelling alternative, offering advantages such as lower energy, smaller mode volume, and low propagation speeds, which make them ideal for interfacing diverse quantum systems. Developing integrated phononic circuits is thus essential for unlocking the full potential of quantum acoustics and advancing technologies such as quantum computing and hybrid systems. In this work, we demonstrate the first 4-port directional coupler for quantum mechanical excitations - a key building block for phononic circuits. By tuning the coupling region length, we achieve phononic beam splitters with controllable splitting ratios. We validate quantum-level performance by sending a single-phonon Fock state through the device. This work represents a foundational advance toward scalable, integrated phononic platforms for both classical and quantum applications.

Figures (10)

• Figure 1: a) Sketch of the phononic directional coupler device, which includes two uncoupled phononic waveguides (green) coupled together in the central region (purple). The orange pulses represent classical wavepackets. A wavepackets generated in one of the waveguide splits into two identical wavepackets after transmission through the coupler with a 50:50 spitting ratio. b) Band structure simulation of the in-plane breathing mode of the unit cell structure (inset) of the directional coupler, showing normal mode splitting of the symmetric (green line) and anti-symmetric (red line) supermodes due to the coupling. c) The splitting between the two modes is clearly visible in the zoom-in around 4.9GHz. The oscillating anti-symmetric and symmetric supermodes are shown on the top and bottom, respectively. d) Simulated optomechanical single photon coupling rate of the full structure. The mechanical mode of the optomechanical cavity is hybridized by a series of Fabry-Pérot modes of the waveguide and each mode is split into a doublet of symmetric (green) and anti-symmetric normal modes (more details are given in SI \ref{['SI:sim']}. e) Scanning electron microscope (SEM) images of the fabricated device with false color highlighting of the different parts -- the phononic and photonic mirrors (blue), the optomechanical cavities (red), the phononic waveguide (green), the phononic directional coupler (purple). For a 50:50 splitting, the coupler length is about 26μ m, and the total device length is about 210μ m. Due to space constraints, only a short section of the waveguides is shown.
• Figure 2: a,b) Optical response of device A (left) and B (right). The devices have optical resonances in the C-band at telecom wavelengths. c,d) Mechanical spectrum of device A (left) and B (right) measured using OMIT. We observe a series of Fabry-Pérot modes spaced by $\Delta \nu_{\rm FRS}$ and split by the normal-mode splitting $\Delta \nu_{\rm NMS}$ due to the directional coupler. The green shaded area indicates the spectral region used to investigate the dynamics of phononic wavepackets (see text for more details).
• Figure 3: a) Different permutations of exciting and reading the two cavities. b) Normalized phononic population in different cavities with respect to the excited population at t = 0 (first letter: excited cavity, second letter: read-out cavity), using a coherent state phononic wavepacket. The number on the top corresponds to the round trip number of the phononic packet with the respective time range highlighted in blue. c) Blue, orange, green, red color bars: integrated counts of phononic population around the first, second and third round-trip time, normalized to the amplitude of the peak at zero delay in the excitation waveguide. Grey color bars: result of the global fit described in the main text, from which we extract a reflection coefficient $R=0.43$. d) The reflection coefficient of the phononic directional coupler as a function of the coupling length, measured on different devices.
• Figure 4: The second order cross-correlation $g^{(2)}_{om}$ between the Stokes and anti-Stokes scattered photons from the write and read pulses -- we measure $g^{(2)}_{om,AA} = 3.8^ {+0.8}_{-0.5}$, $g^{(2)}_{om,AB} = 3.1^ {+0.8}_{-0.5}$, $g^{(2)}_{om,BA} = 3.2^ {+0.7}_{-0.5}$ and $g^{(2)}_{om,BB} = 3.5^ {+0.5}_{-0.5}$ -- all values are above the classical threshold of 2 (dashed line) by more than two standard deviations. Error bars indicate one standard deviation.
• Figure S1: Simulation of the whole structure for a device with 50 unit cell of directional coupler and about 80µ m total length (shorter than the measured device in the main text, for a faster simulation time). Left: calculated single photon optomechanical coupling rate for symmetric (green) and anti-symmetric (red) modes - for each Fabry-Pérot mode, the symmetric and anti-symmetric modes form a doublet split by $\Delta \nu_{\rm NMS}$ due to the phononic coupling between the top and bottom waveguides. Right: mechanical mode profiles corresponding to one of the doublets. The whole structure is reported in segments for space reason.