Fully integrated quantum frequency processor on a silicon chip

Abstract

Frequency-bin encoding has recently emerged as a powerful approach for photonic quantum information processing, offering high dimensionality, gate-parallelization, and compatibility with existing telecommunication infrastructure. However, its scalable deployment has so far been hindered by the lack of an integrated platform capable of unifying quantum state generation, coherent frequency mixing, and programmable spectral control.\\ Here, we report the first fully integrated quantum frequency processor, monolithically integrating on the same silicon photonic chip a microresonator-based biphoton quantum frequency comb source, a pump-rejection filter, high-speed phase modulators, and a four-channel, line-by-line pulse shaper. We demonstrate key functionalities, such as tunable frequency beamsplitters with success probabilities exceeding $94\%$ and fidelities above $99.9\%$, as well as the ability to synthesize more general single-qubit gates. Finally, we generate and coherently manipulate high-dimensional frequency-bin entangled states entirely on chip, showcasing control over two-photon quantum walks and performing the first on-chip frequency-bin quantum state tomography of a Bell-state with a fidelity of $95.7(3)\%$. By integrating all key functional elements on the same $4\times7\,\textrm{mm}^2$ chip, with the possibility of scaling to a larger number of modes, our work marks an important step toward large-scale frequency-domain photonic processors for both classical and quantum applications.

Figures (6)

• Figure 1: Integrated quantum frequency processor. (a) Photograph of the $4 \times 9 \, \mathrm{mm}^2$ chip, indicating the fiber-array unit (FAU) for optical input–output coupling, the external PCB wire-bonded to the on-chip heater pads (wire bonds), and the RF probes in the signal–ground–signal (SGS) configuration. (b) Schematic of the integrated silicon photonic quantum frequency processor. SOURCE: microresonator-based photon-pair source, PF: Mach–Zehnder–based pump-rejection filter, IN PM: input fast phase modulator, WS: four-channel line-by-line waveshaper, OUT PM: output fast phase modulator. Waveguides are shown in blue, heaters in yellow, Germanium absorbers in green, and the p–n junctions of the modulators are indicated in red and purple. The pump(calibration) light is injected through the IN-1(IN-2) port, while photon pairs(filtered pump) are extracted from the OUT-1(OUT-2) port. (c) High-level schematic of the processor operation. From top to bottom, the on-chip generated input frequency bins first undergo mode mixing in the IN PM, then acquire programmable spectral phases $\{\Phi_j\}_{j=1}^{4}$ imparted by the four-channel WS, and are finally mixed again by the OUT PM. (d) Top: dual-ring WS-unit working principle. The DEMUX ring (DR) drops a selected frequency bin (green), which is phase-shifted by $\Phi$ and subsequently multiplexed back into the common bus waveguide by the MUX ring (MR). DC-voltages and separate dither tones $\Omega_{D(M)}$ are applied to the heaters for wavelength tuning and calibration purposes. Bottom: programmable channel operations, each associated with different light paths and relative resonance detuning $\Delta\lambda_{D(R)}$ of the DR(MR) ring with respect to the target channel wavelength (dashed green line). (e) Spectral response of a WS channel at $\Phi=\pi$ and of one resonances of the resonator source. Both spectra are reported as a function of the wavelength detuning $\Delta\lambda$ from the center wavelength of the WS channel. (f) Measured amplitude of the Fourier transform $\tilde{I}$ at frequency $2(\Omega_M+\Omega_D)$ of the time-dependent signal intensity $I(t)$ at the output of a WS channel during the calibration phase. See Methods section for more details on the calibration procedure. (g) Calibration of the phase $\Phi$ of a WS channel. This is done by measuring the time-dependent intensity $I(t)$ transmitted by the WS channel and by computing the real part of the Fourier transform $\tilde{I}$ at frequency $\Omega_M-\Omega_D$ as a function of the heater power $P$. The data is fit with the sinusoidal relation $\sim\sin \left ( \frac{2\pi P}{P_{2\pi}} +\Phi_0\right )$, shown as a solid line. The 95$\%$ confidence bounds from the fit are indicated with shaded regions.
• Figure 2: Implementation of frequency beamsplitters ($R_y$ rotations) with a tunable splitting ratios and $R_z$ rotations. (a) Schematic of the processor configuration used to implement frequency beamsplitters with a tunable splitting ratio. An external probe laser is injected either into FB 2 or FB 3, or into a coherent superposition of the two. After the IN PM, programmable spectral phases $\{\Phi\}_{j=1}^4$ are applied to four modes before they enter the OUT PM. The spectral response at the output of the processor is recorded by an optical spectrum analyzer (OSA). (b) Measured output spectra when the processor is programmed to realize a 50/50 beamsplitter. The four spectral phases $\{\Phi\}_{j=1}^4$ applied by the WS are shown in the top inset of the leftmost panel. From left to right: input (shaded vertical line) in FB 2, input in FB 3, input in a coherent superposition of FBs 2 and 3 with relative phase $\gamma=0$, and with a relative phase $\gamma=\pi$. (c) Top: tunable beamsplitter reflectivity $\mathcal{R}$ and transmittivity $\mathcal{T}$ as a function of the relative phase $\alpha$ applied between the FBs 2 and 3. The shaded regions represent the 95$\%$ confidence bounds predicted by the best fit using Eq.(\ref{['eq:RandT']}). Bottom: success probability $\mathcal{P}$ of the transformation and fidelity $\mathcal{F}$ with respect to the target operation. Errors on $\alpha$ are derived from the power-to-phase calibration of $\Phi(P)$ shown in Fig. \ref{['fig:set-up']}(g). The y-error bars are shown and are included within the marker size. (d) Top: reconstructed scattering matrix (squared magnitude and phase) of the 50/50 beamsplitter, corresponding to the operation $R_y(\theta=\pi/2)$. The equivalent transformation, illustrated using dual-rail encoding, is sketched to the left of the matrices. The spectral phases applied to the four FBs are indicated inside the colored circles (see correspondence with panel (a)). Bottom: reconstructed scattering matrix of the transformation $R_y(\theta=\pi/2)R_z(\lambda=\pi/2)$.
• Figure 3: On-chip coherent manipulation of high-dimensional frequency-bin entangled states and quantum state tomography. (a) Schematic of the processor configuration used to implement high-dimensional quantum walks. A programmable spectral phase is applied to four idler (blue) modes, labeled from 1 to 4. Signal and idler modes are independently mixed at the OUT PM. Frequency-resolved signal–idler coincidence events are recorded off chip using superconducting nanowire single photon detectors (SNSPD). (b) JSIs in a restricted $4\times4$ subspace in three different processor configurations. From left to right: the initial JSI of the source, after the correlated quantum walk, and after the anticorrelated quantum walk. The recorded coincidence counts are here reported normalized to the maximum of each subspace. (c) Processor configuration used to implement on-chip two-qubit quantum state analysis. Two signal and two idler comb lines are isolated by guard-band modes. Spectral phases are applied to the idler FBs to control the measurement projectors, while the OUT PM enables projections onto superposition bases. (d) On-chip Bell state analysis. The measured coincidences (green) and single counts (blue and red) are reported as a function of the relative phase $\Delta\Phi = \Phi_1-\Phi_0$ introduced between the FBs by two WS channels. The green curve (solid line) is a sinusoidal fit of the data, where 95$\%$ confidence bounds are shown as shaded regions. (e) Reconstructed magnitude (height of the bars) and phase (color of the bars) of the density matrix through quantum state tomography of the two-qubit state, which closely approximates the maximally entangled Bell state $|{\Phi^{+}}\rangle$.
• Figure 4: Detailed experimental setup. (a) Setup at the input of the silicon chip, showing the main optical and electrical (DC bias, dither tones and RF signal) connections. (b) Configuration of the chip and setup used for gate synthesis and WS calibration (PHASE operation). (c) Configuration of the chip and setup used for quantum walks and quantum state tomography demonstrations. ISO: fiber isolator, EOM: electro-optic modulator, WS: bulk off-chip waveshaper, FPC: fiber polarization controller, BPF: band pass filter, S: Source, PF: pump filter, QFP: quantum frequency processor, OSA: optical spectra analyzer, PD: photodiode, DWDM: dense wavelength division multiplexing, TF: tunable narrowband pass-band filter, SNSPD: superconducting nanowire single photon detector.
• Figure 5: Additional WS characterizations and simulations. (a) Experimental spectra of a single WS unit varying the applied phase shift $\Phi$. (b) Simulated real part of the Fourier components at $\Omega_M - \Omega_D$ as a function of the phase-shift $\Phi$ applied by the WS-unit. The shown amplitude is normalized to the maximum of the curve. (c) Simulated magnitude of the Fourier component at $2(\Omega_D + \Omega_M)$ for for different phases. For (b) and (c), the corresponding experimental results are reported in the main text.