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arXiv:1801.07521 · Physical Review Letters

Multiphoton Interference in the Spectral Domain by Direct Heralding of Frequency Superposition States

Bryn A. Bell, Benjamin J. Eggleton

Published Jul 18, 2018• 7 citations
arXivHTMLPDF

Abstract

Multiphoton interference is central to photonic quantum information processing and quantum simulation, usually requiring multiple sources of nonclassical light followed by a unitary transformation on their modes. We observe interference in the four-photon events generated by a single silicon waveguide, where the different modes are six frequency channels. Rather than requiring a unitary transformation, the frequency correlations of the source are configured such that photons are generated in superposition states across multiple channels, and interference effects can be seen without further manipulation. The frequency correlations of the source also mean that it is effectively acting as multiple pair photon sources, generating photons in different spectral modes, which interfere with each other in a nontrivial manner. This suggests joint spectral engineering is a tool for controlling complex quantum photonic states without the difficulty of implementing spatially separate sources or a large unitary interferometer, which could have practical benefits in various applications of multiphoton interference.

DOI
10.1103/physrevlett.121.033601

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Multiphoton interference is central to photonic quantum information processing and quantum simulation, usually requiring multiple sources of nonclassical light followed by a unitary transformation on their modes. We observe interference in the four-photon events generated by a single silicon waveguide, where the different modes are six frequency channels. Rather than requiring a unitary transformation, the frequency correlations of the source are configured such that photons are generated in superposition states across multiple channels, and interference effects can be seen without further manipulation. The frequency correlations of the source also mean that it is effectively acting as multiple pair photon sources, generating photons in different spectral modes, which interfere with each other in a nontrivial manner. This suggests joint spectral engineering is a tool for controlling complex quantum photonic states without the difficulty of implementing spatially separate sources or a large unitary interferometer, which could have practical benefits in various applications of multiphoton interference.
We demonstrate multiphoton interference using a resource-efficient frequency multiplexing scheme, suitable for quantum information applications that demand multiple indistinguishable and pure single photons. In our source, frequency-correlated photon pairs are generated over a wide range of frequencies by pulsed parametric down conversion. Indistinguishable single photons of a predetermined frequency are prepared using frequency-resolved detection of one photon to control an electro-optic frequency shift applied to its partner. Measured photon statistics show multiplexing increases the probability of delivering a single photon, without a corresponding increase to multiphoton events. Interference of consecutive outputs is used to bound the modal purity and demonstrate the nonclassical nature of the emitted light.
Quantum interference between identical photons lies at the heart of our plan to construct a silicon photonic quantum computer. Several ground-breaking experiments have demonstrated the on-chip interference between photons generated in spiral [1] and ring resonator [2] sources. However, these two-photon experiments have relied on detecting the simultaneous arrival of a pair of photons from either source. In order that such experiments can be scaled-up, we require the multiplexing of probabilistic photon pair sources into an on-demand single photon source [3]. A first step towards this is to demonstrate heralded single photons from different sources will retain the purity and indistinguishability required to interfere with high visibility [4]. In our work we examine photon pair production by spontaneous four-wave mixing in a silicon waveguide source and determine the factors that limit the heralded two-photon interference visibility. We present a novel approach to modelling this generation process using the joint- temporal amplitude and compare our results with experimental data. [1] On-chip quantum interference between silicon photon-pair sources, Nature Photonics 8, 104, (2014). [2] Qubit entanglement between ring-resonator photon-pair sources on a silicon chip, Nature Communications 6, 7948, (2015). [3] Active temporal and spatial multiplexing of photons, Optica 3, 127, (2016) [4] Indistinguishable photon pair generation using two independent silicon wire waveguides, New Journal of Physics 13, 065005, (2011).
Multiphoton quantum interference underpins fundamental tests of quantum mechanics and quantum technologies. Consequently, the detrimental effect of photon distinguishability in multiphoton interference experiments can be catastrophic. Here, we employ correlation measurements in the photonic inner modes, time or frequency, to restore quantum interference between photons differing in their colors or injection times in arbitrary linear optical networks, without the need for additional filtering or post selection. Interestingly, we demonstrate how harnessing the multiphoton inner-mode quantum information enables to unravel symmetries of multiphoton networks and states and the generation of an entire class of multipartite entangled states with a fixed interferometer. These results are therefore of profound interest for future applications of universal inner-mode resolved linear optics across fundamental science and quantum technologies with photons with experimentally different spectral properties.
Multiphoton entanglement plays a critical role in quantum information processing, and greatly improves our fundamental understanding of the quantum world. Despite tremendous efforts in either bulk media or fiber-based devices, nonlinear interactions in integrated circuits show great promise as an excellent platform for photon pair generation with its high brightness, stability and scalability \cite{Caspani2017}. Here, we demonstrate the generation of bi- and multiphoton polarization entangled qubits in a single silicon nanowire waveguide, and these qubits directly compatible with the dense wavelength division multiplexing in telecommunication system. Multiphoton interference and quantum state tomography were used to characterize the quality of the entangled states. Four-photon entanglement states among two frequency channels were ascertained with a fidelity of 0.78±0.020.78\pm0.020.78±0.02. Our work realizes the integrated multiphoton source in a relatively simple pattern and paves a way for the revolution of multiphoton quantum science.
Frequency-time is a degree of freedom suitable for photonic high-dimensional entanglement, with advantages such as compatibility with single-mode devices and insensitivity to dispersion. The engineering control of the frequency-time amplitude of a photon's electric field has been demonstrated on platforms with second-order optical nonlinearity. For integrated photonic platforms with only third-order optical nonlinearity, the engineered generation of the state remains unexplored. Here, we demonstrate a cavity-enhanced photon-pair source on the silicon-on-insulator (SOI) platform that can generate both separable states and controllable entangled states in the frequency domain without post-manipulation. By choosing different resonance combinations and employing on-chip optical field differentiation, we achieve independent control over two functions that affect the joint spectral intensity (JSI) of the state. A semi-analytical model is derived to simulate the biphoton spectral wavefunction in the presence of resonance splitting and pump differentiation, and its parameters can be fully determined through fitting-based parameter extraction from the resonator's measured linear response. The measured spectral purity for the separable state is 95.5±1.2%95.5\pm 1.2\%95.5±1.2%, while the measured JSIs for the entangled states show two- or four-peaked functions in two-dimensional frequency space. The experiments and simulations demonstrate the capacity to manipulate the frequency-domain wavefunction in a silicon-based device, which is promising for applications like quantum information processing using pulsed temporal-mode encoding or long-distance quantum key distribution.
Spatial double-slit experiments have been central to understanding wave-particle duality, demonstrating how single photons interfere in transverse momentum when given two spatially separated alternatives. Analogue demonstrations have shown the corresponding relationship in the time-frequency domain with classical electric fields. Extending this to quantum states of light reveals how different photon states acquire different phases through the same temporal separation, producing distinct spectral interference signatures. In this work, we investigate temporal interference with three different quantum states of light — a single-photon state, a separable two-photon state, and a two-photon NOON state — all on the same physical platform and with the same temporal delay. Experimentally, we prepare ultrafast pulses of photon states in polarization and use the birefringent delay of beta-barium borate (BBO) crystals to introduce a femtosecond temporal separation between the orthogonal polarization components. A polarization projection in a superposition basis then removes the which-time information and produces spectral interference, providing an analogue of the temporal double slit. The photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a Sagnac interferometer, tuned to produce all three quantum states by adjusting the pump polarization, with the NOON state reaching a measured visibility of (88.99 ± 0.21)%. The spectra are recorded through dispersive Fourier transform using a long single-mode fiber and single photon detectors. The measured spectra show that single-photon and separable two-photon states both oscillate at the same rate, consistent with a phase given by the photon frequency multiplied by the temporal delay, with the two-photon spectral pattern being the product of the individual single-photon spectra. The NOON state, in contrast, oscillates twice as fast, governed by the collective phase of the two photons, which depends on the sum of their frequencies rather than on the individual photon spectral modulations, and which reduces to twice the single-photon phase along the equal-frequency diagonal. This doubled phase accumulation makes NOON-state temporal interference directly relevant to quantum-enhanced sensing and metrology. Different polarization projections further allow tuning of the interference patterns across all three states.