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Experimental Fock-State Capability of Non-Ideal Single-Photon States

Petr Zapletal, Tom Darras, Hanna Le Jeannic, Adrien Cavaillès, Giovanni Guccione, Julien Laurat, Radim Filip

Published Dec 15, 2020• 1 citation
OpenAlex

Abstract

Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behaviour. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether n independent imperfect single photons can ultimately bunch into the Fock state $|n\rangle$. We thereby introduce an experimental Fock-state capability for single-photon sources, which uses phase-space interference for extreme bunching events as a quantifier. In contrast to autocorrelation functions, this operational approach takes into account not only residual multi-photon components but also vacuum admixture and the dispersion of the individual photon statistics. We apply this approach to high-purity single photons generated from an optical parametric oscillator and show that they can lead to a Fock-state capability of at least 14. Our work demonstrates a novel collective benchmark for single-photon sources and their use in subsequent stringent applications.

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Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behaviour. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether n independent imperfect single photons can ultimately bunch into the Fock state ∣n⟩|n\rangle∣n⟩. We thereby introduce an experimental Fock-state capability for single-photon sources, which uses phase-space interference for extreme bunching events as a quantifier. In contrast to autocorrelation functions, this operational approach takes into account not only residual multi-photon components but also vacuum admixture and the dispersion of the individual photon statistics. We apply this approach to high-purity single photons generated from an optical parametric oscillator and show that they can lead to a Fock-state capability of at least 14. Our work demonstrates a novel collective benchmark for single-photon sources and their use in subsequent stringent applications.
Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behavior. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether n independent imperfect single photons can ultimately bunch into the Fock state | n ⟩ . We thereby introduce an experimental Fock-state bunching capability for single-photon sources, which uses phase-space interference for extreme bunching events as a quantifier. In contrast to autocorrelation functions, this operational approach takes into account not only residual multi-photon components but also a vacuum admixture and the dispersion of individual photon statistics. We apply this approach to high-purity single photons generated from an optical parametric oscillator and show that they can lead to a Fock-state capability of at least 14. Our work demonstrates a novel collective benchmark for single-photon sources and their use in subsequent stringent applications.
Linear optical transformations of multiple single-photon inputs are fundamental for the development of photonic quantum technologies. Various nonclassical correlations can already be observed directly in states generated using only single-photon inputs and linear optics transformations. However, some quantum correlations require additional operations, and states that exhibit such correlations are classified as non-Fock states. Here, we demonstrate the generation of a two-photon three-mode non-Fock state that exhibits conditional quantum coherences that can only be achieved by non-Fock states. We determine the fidelity of the non-Fock state based on experimentally observed conditional visibilities that characterize the state and compare the result to the fidelity bounds for different classes of Fock and non-Fock states. Our experimental verification of the non-Fock character of the state provides insights into the technological requirements needed to achieve nonclassical correlations in multiphoton quantum optics.
The generation of high Fock states of light pulses and their superpositions with provable quantum non-Gaussian features is still very challenging, although the power of conditional methods to herald the approximate state from the available Gaussian states is growing. The atom-light interaction in the high- cavity has been considered a viable alternative to the heralded Fock states of the light pulses from nonlinear optics limited to three-photon Fock states for the last decade. Here, by optimizing the realistic protocol combining it with available optical delay elements, we conclusively predict filtering of Fock states up to ten photons with a high success rate of 20 % using a hierarchy of quantum non-Gaussian criteria. Moreover, the filtering protocol enables the preparation of superposition of Fock states, and we analyze this emerging case up to two photons with provable quantum non-Gaussian coherence and high success rate of 50 % . To demonstrate their quality for applications, we evaluate the robustness of such features, the bunching capability in a linear network, and the sensing capability to estimate the magnitude of unknown force, noise, and phase. These assessments outline the essential conditions and application criteria for realistic optical cavity QED interaction on light pulses to outperform photon detection methods.
Quantum interference constitutes one of the sharpest divides between our classical intuition and the weirdness of the quantum world. Whenever there are multiple paths leading to the same outcome, it is the interplay of associated probability amplitudes that determines measurement results. In the double slit experiment, wave-like interference governs the distribution of particles on a detection screen. Extending to multiple particles allows behaviour that cannot be described by a classical wave, such as the bunching of photon pairs in Hong-Ou-Mandel interference. In both these examples, the ability to distinguish the interfering paths leads to degradation of interference and a return to behaviour described by probabilities. Understanding how this transition evolves for larger multiparticle quantum systems is of fundamental interest and also vital for developing photonic quantum technologies that rely on many-photon interference. In this thesis we investigate the role of distinguishability in the interference of three and four independent photons by using polarisation and time delays. For three photons, a new type of collective distinguishing phase appears that goes beyond a pairwise description of the similarity of quantum states. We use nonlinear photon sources and a fibre interferometer to experimentally demonstrate the ability to tune and isolate this phase in interference statistics. Extending to four photons we show that, contrary to intuition from two-photon experiments, the interference of photons prepared in distinguishable states is possible due to a four-particle phase. This is confirmed experimentally using a bulk four-mode interferometer. We then extend our study to include the effects of state impurity in the interference of three photons. New properties of this interference enable diagnosis of realistic experimental imperfections and characterisation tasks impossible using only two photons. Finally, we link discussions of state distinguishability to the group representations underpinning the exchange symmetry of multiparticle wavefunctions.
Quantum state engineering and state characterization is a key task in quantum information processing in both discrete and continuous variable systems in the optical domain. In particular, quantum states with non-Gaussian (i.e., non-positive) Wigner quasiprobability distribution functions are crucial to universal, fault-tolerant quantum computing with continuous variables. In this talk, we present our recent results on single-photon Fock state tomography using Photon-Number-Resolving (PNR) measurements. We generated a highly pure narrow-band single-photon Fock state by heralding cavity-enhanced spontaneous-parametric-downconversion from a PPKTP optical parametric oscillator. The Wigner function was reconstructed with photon statistics obtained using superconducting transition-edge sensors with an overall system efficiency of 58(2)%. We then discuss quantum state engineering for pure displaced single-photon Fock states, optical cat states, and approximate GKP states using coherent states and single-photon states along with linear optics and PNR measurements. We report our experimental progress for the same.
Boson sampling with array of on-demand single photons (discreet variable Fock states) as resource states provides distinct advantages in complexity scaling compared to single photon resource states mimicked by the states (continuous variable) generated in nonlinear photonics. Recent progress in realization of regular ordered array of mesa top single quantum dots (MTSQDs) enabling on-demand generation of many photon resource states with high single photon purity and indistinguishability [1,2] has opened the possibility of implementing chip-scale Boson sampling with single photons. An important question towards scale up of such circuits is how the dephasing and decay timescale of individual on-demand single photons affect the final probability distribution of the N-photon entangled state. In this work we report a framework that provides direct link between the physical sources of decoherence to the outcome of multiphoton correlation measurements. We explicitly incorporate the symmetrization of the N-photon states while accounting for the shape of the individual wave packets and dephasing. Using this framework, we show predictive estimates of the probability of generation of a 4-photon NOON state using an optical circuit initialized with 4 identical single photon wave packets, mimicking the emitted photons from MTSQD single photon sources reported in [2]. Specifically, we show how the probability of generating various 4-photon entangled states depend on the two-photon interference visibility which is determined by the pure dephasing timescale in relation to the radiative decay timescale. The results provide quantitative guidelines to measure 4 photon and higher number of entangled photon states generated in an optical circuit with on demand single photon sources and provide a link between physical processes such as temperature and the output state of the quantum optical circuits.