Abstract
Bohr’s complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young’s double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr’s multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.
Highlights
Bohr’s complementarity is one central tenet of quantum physics
A quantitative description of twoslit duality relation was initialized in Wootters and Zurek’s seminal work[6] and formalized by Greenberger, Yasin, Jaeger, and Englert[16,17,18] as D2 þ V2 ≤ 1, where D is the distinguishability of which-path information, and V is the contrast visibility of interference
There are several major open questions remaining: Can Bohr’s duality relation still hold in the multipath interferometric experiment? Are there any good measures of multipath wave and multimode particle properties that are accessible in experiment? Does single photon preserve the inherent dual nature in the multipath delayed-choice scenario? Revealing these unknowns are essential to understand multimode quantum superposition and quantization in complex quantum systems
Summary
Scheme of the generalized multipath delayed-choice experiment. Figure 1a shows a diagram of general d-path. The state of H^d operator is entangled with the state of a control quantify the wave-particle dual nature of a maximal coherent state ρ0 1⁄4 jΨi00hΨj by the delayed choice of measurement M^ m. The chip monolithically integrates an entangled photon-pair source, a d-path MZI, a quantum-controlled d-BS, and a d-mode eraser (note detectors are off chip). The device includes four parts: an entangled photon-pair source, a d-path MZI, a quantum-controlled d-BS, and a d-mode eraser. The which-process information is erased at a d-mode quantum eraser (Fig. 1e), ensuring quantum mechanical indistinguishability between the wave and particle processes These result in the realization of generalized quantumcontrolled H^ d operation or d-BS2. This state-process entanglement approach has been adopted for implementing double-path delayed-choice experiments[13] and for quantum simulations[43].
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