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Nature Photonics

Deterministic generation of indistinguishable photons in a cluster state

Dan Cogan, Zu-En Su, Oded Kenneth, D. Gershoni

Published Feb 9, 2023• 132 citations
PDF (CC BY)Publisher

Abstract

Entanglement between particles is a basic concept of quantum sciences. The ability to produce entangled particles in a controllable manner is essential for any quantum technology. Entanglement between light particles (photons) is particularly crucial for quantum communication due to light's non-interactive nature and long-lasting coherence. Resources producing entangled multiphoton cluster states will enable communication between remote quantum nodes, as the inbuilt redundancy of cluster photons allows for repeated local measurements-compensating for losses and probabilistic Bell measurements. For feasible applications, the cluster generation should be fast, deterministic and, most importantly, its photons indistinguishable, which will allow measurements and fusion of clusters by interfering photons. Here, using periodic excitation of a semiconductor quantum-dot-confined spin, we demonstrate a multi-indistinguishable photon cluster, featuring a continuously generated string of photons at deterministic gigahertz generation rates, and an optimized entanglement length of about ten photons. The indistinguishability of the photons opens up new possibilities for scaling up the cluster's dimensionality by fusion, thus building graph states suited for measurement-based photonic quantum computers and all-photonic quantum repeaters.

DOI
10.1038/s41566-022-01152-2

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Entanglement between particles is a basic concept of quantum sciences. The ability to produce entangled particles in a controllable manner is essential for any quantum technology. Entanglement between light particles (photons) is particularly crucial for quantum communication due to light's non-interactive nature and long-lasting coherence. Resources producing entangled multiphoton cluster states will enable communication between remote quantum nodes, as the inbuilt redundancy of cluster photons allows for repeated local measurements-compensating for losses and probabilistic Bell measurements. For feasible applications, the cluster generation should be fast, deterministic and, most importantly, its photons indistinguishable, which will allow measurements and fusion of clusters by interfering photons. Here, using periodic excitation of a semiconductor quantum-dot-confined spin, we demonstrate a multi-indistinguishable photon cluster, featuring a continuously generated string of photons at deterministic gigahertz generation rates, and an optimized entanglement length of about ten photons. The indistinguishability of the photons opens up new possibilities for scaling up the cluster's dimensionality by fusion, thus building graph states suited for measurement-based photonic quantum computers and all-photonic quantum repeaters.
Measurement-based quantum communication relies on the availability of highly entangled multi-photon cluster states. The inbuilt redundancy in the cluster allows communication between remote nodes using repeated local measurements, compensating for photon losses and probabilistic Bell-measurements. For feasible applications, the cluster generation should be fast, deterministic, and its photons - indistinguishable. We present a novel source based on a semiconductor quantum-dot device. The dot confines a heavy-hole, precessing in a finely tuned external weak magnetic field while periodically excited by a sequence of optical pulses. Consequently, the dot emits indistinguishable polarization-entangled photons, where the field strength optimizes the entanglement. We demonstrate Gigahertz rate deterministic generation of >90% indistinguishable photons in a cluster state with more than 10 photons characteristic entanglement-length.
Cluster states are key resources for measurement-based quantum information processing. Photonic cluster and graph states, in particular, play indispensable roles in quantum network and quantum metrology. We demonstrate a semiconductor quantum dot based device in which the confined hole spin acts as a needle in a quantum knitting machine producing continuously and deterministically at sub-Gigahertz repetition rate single indistinguishable photons which are all polarization entangled to each other and to the spin in a one dimensional cluster state. By projecting two nonadjacent photons onto circular polarization bases we disentangle the spin from the photons emitted in between. This way we demonstrate a novel way for producing deterministic and continuous all-photonic cluster states. We use polarization tomography on four sequentially detected photons to demonstrate and to directly quantify the robustness of the cluster's entanglement and the determinism in its photon generation.
We propose a complete architecture for deterministic generation of entangled multiphoton states. Our approach utilizes periodic driving of a quantum-dot emitter and an efficient light-matter interface enabled by a photonic crystal waveguide. We assess the quality of the photonic states produced from a real system by including all intrinsic experimental imperfections. Importantly, the protocol is robust against the nuclear spin bath dynamics due to a naturally built-in refocusing method reminiscent to spin echo. We demonstrate the feasibility of producing Greenberger-Horne-Zeilinger and one-dimensional cluster states with fidelities and generation rates exceeding those achieved with conventional ``fusion'' methods in current state-of-the-art experiments. The proposed hardware constitutes a scalable and resource-efficient approach towards implementation of measurement-based quantum computing and quantum communication.
Quantum technologies witness rapid contemporary developments transitioning from abstract scientific ideas and fundamental demonstrations, into systems of sufficient quality and scale, enabling real applications. Photonic quantum technologies are playing a pivotal role in these developments, since photons are robust, easily controlled, detect and measured, thus qualify as flying carriers of quantum information and entanglement distributers. The efforts to develop photonic quantum technologies benefit from the maturity of the classical optical technologies. It was shown that even a source of heralded three entangled photons is sufficient for building large scale quantum computers using otherwise classical optical elements. Here, we demonstrate a novel semiconductor quantum dot based device, which deterministically generate at GHz rates, indistinguishable single photons in a robust Greenberger-Horne-Zeilinger (GHZ) state of more than a dozen photons. The device utilizes novel natural spin echo concept, provided by the opposite precession directions of the negative and positive carriers' spins in the excited and ground levels of the periodically excited dot, respectively. The excitation rate is finely tuned to nullify the phase acquired by both spins' precession. Our record long GHZ state producing device can yet be feasibly improved to provide higher-rate, brighter and more robust deterministic GHZ source, significantly reducing the overhead requirements for photonic quantum technologies.
Deterministic sources of multi-photon entanglement are highly attractive for quantum information processing but are challenging to realize experimentally. In this paper, we demonstrate a route towards a scaleable source of time-bin encoded Greenberger-Horne-Zeilinger and linear cluster states from a solid-state quantum dot embedded in a nanophotonic crystal waveguide. By utilizing a self-stabilizing double-pass interferometer, we measure a spin-photon Bell state with (67.8±0.4)%(67.8\pm0.4)\%(67.8±0.4)% fidelity and devise steps for significant further improvements. By employing strict resonant excitation, we demonstrate a photon indistinguishability of (95.7±0.8)%(95.7\pm0.8)\%(95.7±0.8)%, which is conducive to fusion of multiple cluster states for scaling up the technology and producing more general graph states.
Photonic cluster states are fundamental resource for measurement-based quantum computing (MBQC), which is a promising approach for scalable quantum computing. These highly entangled states enable computation with applying local measurements rather than gate operations, which makes them essential for fault-tolerant quantum computing. Generation of the photonic cluster states requires high-quality entanglement and stability, which can be done by making use of cavity quantum electrodynamics (cavity QED), which is embedding quantum dots (QDs) into photonic microcavities. This method enables controlled single-photon emission and the entanglement of them, helping with key challenges in generating photonic cluster states. Enhancing the generation of the photonic cluster state requires improvement in the quality factor (Q-factor) and therefore, cooperativity of cavity and QD systems. A high Q-factor helps with reduction in photon loss and decoherence, ensuring more stable and high-fidelity quantum states. It also enables better light-matter interactions, improving cluster state quality. Cooperativity, which is a measure for the light-matter coupling strength relative to dissipation, directly impacts photon emission efficiency. Optimization of these parameters improves entanglement generation, which is essential for producing high-quality photonic cluster states. Therefore, optimized cavities are essential for improving the generation of the photonic cluster states. Scalability is also an important parameter for the generation of the large-scale cluster states used in quantum computing. In this paper, after reviewing MBQC, cluster states, and the generation of the photonic cluster states, we investigate the deterministic generation of the photonic cluster state resource for the purpose of MBQC, and highlights the importance of the inverse design techniques for this goal.