Emulation of Coherent Absorption of Quantum Light in a Programmable Linear Photonic Circuit

TL;DR

The work addresses programmable non-Hermitian evolution by emulating coherent absorption of quantum light in a fully programmable linear photonic circuit. It embeds a port-symmetric lossy beam splitter into a three-mode unitary realized with a three-MZI Clements mesh through quasi-unitary dilation, enabling two configurations: Type 1 with fixed internal phase $$\\phi_{rt}=\\pi$$ and Type 2 with equal magnitudes $${|t|=|r|}$$. The experiments with single-photon and NOON inputs demonstrate phase-controlled absorption, phase-dependent state routing, and enhanced phase sensitivity, with maximum total Fisher information $F_{tot}$ reaching 3.4 (surpassing the shot-noise limit of 2 and approaching the Heisenberg limit of 4 for two photons). High Bhattacharyya overlaps ($>0.93$) between experiment and theory corroborate the fidelity of the programmable CPA transformations, supporting applications in quantum state engineering, non-unitary quantum simulations, and multiplexed sensing within scalable photonic processors.

Abstract

Non-Hermitian quantum systems, governed by nonunitary evolution, offer powerful tools for manipulating quantum states through engineered loss. A prime example is coherent absorption, where quantum states undergo phase-dependent partial or complete absorption in a lossy medium. Here, we demonstrate a fully programmable implementation of nonunitary transformations that emulate coherent absorption of quantum light using a programmable integrated linear photonic circuit, with loss introduced via coupling to an ancilla mode [Phys. Rev. X 8, 021017; 2018]. Probing the circuit with a single-photon dual-rail state reveals phase-controlled coherent tunability between perfect transmission and perfect absorption. A two-photon NOON state input, by contrast, exhibits switching between deterministic single-photon and probabilistic two-photon absorption. Across a range of input phases and circuit configurations, we observe nonclassical effects such as anti-coalescence and bunching, along with continuous and coherent tuning of output Fock state probability amplitudes. Classical Fisher information analysis reveals phase sensitivity peaks of 1 for single-photon states and 3.4 for NOON states, the latter exceeding the shot-noise limit of 2 and approaching the Heisenberg limit of 4 for two-photon states. The experiment integrates quantum state generation, programmable photonic circuitry, and photon-number-resolving detection, establishing ancilla-assisted circuits as powerful tools for programmable quantum state engineering, filtering, multiplexed sensing, and nonunitary quantum simulation.

Figures (14)

• Figure 1: Schematic overview of the coherent perfect absorption experiment.(a) Schematic of the theoretical synthesis workflow: a $2\times2$ non-unitary scattering matrix is embedded into a $3\times3$ unitary via quasiunitary extension and decomposed into a Mach-Zehnder interferometer mesh using the Clements scheme. $R_{ij}$ represents the additional complex numbers resulting from the quasiunitary decomposition step. (b) Conceptual comparison between free-space and integrated photonic implementations of coherent absorption. In both cases, the input is a quantum superposition state over two spatial modes (a single-photon state or a two-photon NOON state), prepared via a bulk 50:50 beam splitter in the free-space setup or an on-chip MZI in the integrated photonic platform. In the free-space case, this state interacts with a static, lossy beam splitter, with absorption governed by the relative phase of the input state. The integrated version emulates this process using a programmable 3-mode interferometer (MZI$_1$–MZI$_3$), enabling tunable control over $|r|$, $|t|$, $\phi_{rt}$, and A of the emulated beam splitter. All other on-chip MZIs are configured as passive waveguides to route light without affecting the circuit. Detection is performed via heralding (single-photon state case) or photon-number-resolving coincidence counting (NOON state case).
• Figure 2: Experimental setup and photonic circuit layout. (a) Schematic of the experimental setup. Photon pairs are generated via type-II spontaneous parametric down-conversion (SPDC) in a PPKTP crystal pumped by a 785 nm CW laser. Light is coupled in and out of the chip using edge couplers. Fiber-based polarization controllers are used before the input to ensure efficient coupling to the TE mode, and after the chip to rotate the output light to the polarization for which the detectors show maximum efficiency. Output photons are detected using superconducting nanowire single-photon detectors (SNSPDs) (in a 2.6 K cryostat), and coincidence counts are recorded with a Swabian Time Tagger. (b) Functional layout of the $8 \times 8$ programmable photonic chip used in the experiment. The mesh comprises three active subnetworks: (i) a single-MZI unit for preparing single-photon superposition or NOON states, (ii) a central three-mode programmable interferometer implementing the CPA transformation, and (iii) a photon-number-resolving array of MZIs for state analysis. (c) On-chip Hong-Ou-Mandel interference corresponding to NOON state preparation, fitted using a triangular function $y = a - b|x - x_0|$, shows a visibility of $0.939$. This interference dip is obtained by tuning the relative delay between the photon pair paths using a prism mounted on a translational stage on one SPDC output path.
• Figure 3: Single-photon state experiment results. (a–c) Normalized counts measured at signal (S1, S2) and ancilla (Anc) ports as functions of input phase $\phi$, with the intrinsic absorption coefficient $|A|^2$ represented by the colour scale, for Type 1 ($\phi_{rt} = \pi$) beam splitter. Panels show: (a) individual signal ports; (b) Signals sum (S1+S2) vs. Anc; (c) corresponding Fisher information per output mode for different absorption settings (See Eq. \ref{['eq:fisher_max']}). (d–f) Same as above for Type 2 symmetric beam splitter ($|t| = |r|$), with (d) signal outputs; (e) Signals sum vs. Anc; (f) Fisher information. Each data point corresponds to coincidence counts between the circuit outputs and a heralding detector triggered by the twin photon from the SPDC source. All data for both beam splitter configurations are normalized by the total coincidences across all outputs and corrected for variations in detector efficiency and coupling efficiency of the chip’s output waveguides to the corresponding fibers. Error bars represent one standard deviation, calculated as $\sqrt{N}$ from Poisson counting statistics, with proper propagation through the normalization procedure. (g) Phase-dependent visibility of signal outputs vs. absorption; (h) relative phase shift between S1 and S2 intensities. The lines denote theoretical predictions; symbols are experimental data. The theoretical data are obtained by applying the CPA unitary transformation matrix $S_\text{total}$ to the input state vector and computing output intensities.
• Figure 4: Beam splitter with $\pi$-shifted reflection (Type1) – NOON state experiment. (a–d) Experimentally measured and normalized counts, and theoretically predicted probabilities for various output Fock states, plotted as a function of the input state phase $\phi$, with $|A|^2$ represented by the colour scale. Probabilities are normalized to the total coincidence counts across all output states and corrected for variations in detector efficiency and coupling efficiency of the chip’s output waveguides to the corresponding fibers. The lines denote theoretical predictions; symbols are experimental data. The theoretical data are obtained by applying the CPA unitary transformation matrix $S_\text{total}$ to the input state vector and computing output intensities. Error bars represent one standard deviation, calculated as $\sqrt{N}$ from Poisson counting statistics, with proper propagation through the normalization procedure. (e) Bhattacharyya overlap coefficients between experimental and theoretical distributions across $\phi$ and $|A|^2$, evaluated in the Fock basis, demonstrating high-fidelity implementation of the beam splitter transformations. (f) Maximum classical Fisher information extracted for each output Fock state at different $|A|^2$ values (See Eq. \ref{['eq:fisher_max']}).
• Figure 5: Symmetric beam splitter (Type 2) – NOON state experiment. (a–d) Experimentally measured and normalized counts, and theoretically predicted probabilities for various output Fock states, plotted as a function of input state phase $\phi$, with $|A|^2$ represented by the colour scale. Probabilities are normalized to the total coincidence counts across all output states and corrected for variations in detector efficiency and coupling efficiency of the chip’s output waveguides to the corresponding fibers. The lines denote theoretical predictions; symbols are experimental data. The theoretical data are obtained by applying the CPA unitary transformation matrix $S_\text{total}$ to the input state vector and computing output intensities. Error bars represent one standard deviation, calculated as $\sqrt{N}$ from Poisson counting statistics, with proper propagation through the normalization procedure. (e) Bhattacharyya overlap coefficients between experiment and theory across $\phi$ and $|A|^2$, evaluated in the Fock basis, demonstrating high-accuracy implementation of the beam splitter transformations. (f) Maximum classical Fisher information extracted for each output Fock state at different $|A|^2$ values (See Eq. \ref{['eq:fisher_max']}).