Researchers at the Beijing Academy of Quantum Information Sciences have demonstrated entanglement not just across space, but across time, using a single quantum dot. The team reports violating the Clauser-Horn-Shimony-Holt Bell inequality by creating and manipulating “vacuum–one-photon number superposition states,” where a photon either exists or does not. This approach bypasses the need to generate multiple photons, simplifying the creation of entangled photons from a solid-state source and offering a scalable pathway for future quantum technologies. Bang Wu of the Beijing Academy of Quantum Information Sciences and colleagues detail their findings in a new study.

Quantum Dot Resonance Fluorescence Enables Entanglement

Researchers observed a Bell inequality violation with a parameter S reaching 2. 675(0.050), exceeding the classical limit of 2 by over 13 standard deviations, confirming the non-local nature of the generated quantum state. This result stems from a novel approach exploiting vacuum-one-photon number superposition states created under resonant excitation, bypassing the need for complex multi-photon preparations. The experimental setup centered on a self-assembled InAs quantum dot coupled to a micropillar cavity, resonantly driven by a continuous wave laser; the excitation scheme mirrored that detailed in a prior publication.

Engineered to be almost non-reflective at the cavity resonance, the micropillar minimized background interference, allowing the quantum dot’s response to dominate at low drive levels. The laser driving power was carefully set at n = 0. 01, and this value was important for achieving the observed entanglement.

Normalized second-order correlation measurements, acquired via Franson-type interferometry, revealed clear evidence of time-bin entanglement between detectors $A_{1}$ and $B_{1}$ , with phase settings of 0, π/2, π and 3π/2. Theoretical simulations accurately reproduced the experimental results, validating the team’s pure-state model and providing deeper insight into the nature of atomic resonance fluorescence. As the pump power increased from n = 0. 01 to 9. 81, the $g_{H B T}^{2} (0)$ value also increased, reaching 0. 67(1) due to laser background noise, causing the S parameter to fall below the violation limit of S~ 1. 344(19).

This observation highlights the sensitivity of the system to noise and the importance of maintaining low drive levels for optimal entanglement generation. However, even at lower power, the demonstrated scheme offers advantages over other resonance fluorescence-based approaches, requiring neither complex excitation sequences nor detailed signal post-processing. The resulting system exhibits low power consumption, high brightness and excellent transmission stability, qualities that position it as a promising candidate for practical, integrated quantum communication protocols.

The ability to transform quantum entanglement from proof-of-principle demonstrations to real-world applications relies on such efficiencies. The investigation into the connection between the spectral components of resonance fluorescence and the observed antibunching, coupled with the accurate modeling of experimental results, provides a more complete understanding of the underlying physics. This work suggests a viable route for scalable quantum technologies, building on the precise control over photon-number basis states achieved through resonant excitation of a quantum dot.

Vacuum-One-Photon Superposition States for Qubit Encoding

This achievement hinges on the creation and manipulation of “vacuum–one-photon number superposition states,” where a single photon exists in a superposition of being present or absent. The team’s approach to entanglement uses a unique temporal dimension, testing the Bell inequality with photons whose entanglement isn’t defined by spatial separation, but by the order of their emission. Central to this experiment is the generation of a pure superposition of vacuum and single-photon states, described mathematically as +, where p₀ + p₁ = 1 and the one-photon mode adopts the excitation laser phase.

This precise control over photon number superposition is achieved through resonance fluorescence from a two-level quantum dot, a semiconductor crystal capable of emitting single photons when excited. By resonantly exciting the quantum dot, researchers can prepare these superpositions, encoding quantum information in the very presence or absence of a photon.

The experimental setup involved entangling these vacuum-one-photon states between two spatial modes, labeled Alice and Bob, using a fiber beamsplitter. This initial entanglement created a time-bin entangled state, resembling 1/ +, where ‘e’ and ‘l’ denote early and late time bins, respectively. Alice and Bob then independently measured the entangled photons using asymmetric Mach-Zehnder interferometers. The significance of this work extends beyond simply demonstrating entanglement. It offers a pathway toward solid-state entangled photon sources that bypass the complexities of generating multiple photons.

Franson Interferometry Verifies Time-Bin Entanglement

Researchers surpassed previous limitations by generating time-bin entanglement directly from vacuum-one-photon superposition states, eliminating the need for post-selection of multi-photon components that typically reduce efficiency. This approach allowed for a clear violation of the Clauser-Horn-Shimony-Holt Bell inequality, providing direct evidence of genuine entanglement between separate nodes. The team achieved a S parameter of 2. 675 ± 0. 01, with $g_{H B T}^{2} (0)$ ~0. 037(3)). Baseline coincidence counts, measured as a function of phase, further supported these findings, demonstrating the coherence of the vacuum-one-photon superposition states within the Franson interferometer.

The experimental data closely matched simulations using the same calculation method, validating the pure-state model employed to explain the results. Analysis of raw data revealed how the coherence of vacuum-one-photon number superposition states manifests in the Franson interferometry.

Figures show baseline coincidence counts as a function of $φ_{A}$ for different $φ_{B}$ values, measured at a laser driving power of n = 0. 01. These measurements, alongside the experimental second-order correlation, provide a detailed view of the entanglement process. While the system’s performance is affected by laser background noise, leading to a decrease in the S parameter at higher pump powers, the initial results demonstrate an efficiency using solid-state-based photon sources.

The high brightness of this source allows for scaling nonlocal tests by extending time-bin entanglement across multiple spatial modes. Researchers suggest replacing the fiber beam splitter with a tritter or a 1-to-3 fiber coupler to create a tripartite entangled qutrit state.

Bell Inequality Violation Confirms Quantum Correlation

This approach allows for the creation of time-bin entanglement, where the entangled particles exist in different temporal modes, and was verified through Franson-type interferometry. The experimental setup revealed a visibility of 92. 8 ± 2. 6% in the observed time-entangled state, indicating a strong correlation between the entangled photons.

This result is particularly notable given that the source exhibits a brightness exceeding previous implementations of similar entangled states by more than two orders of magnitude, even under the weakest excitation conditions. Analysis of the data revealed a crossover point where Bell inequality violation ceased, occurring when the unwanted laser component of the collected light constituted approximately 43% of the total average photon number.

However, at low driving levels, the system demonstrated a clear ability to generate and maintain entanglement, exhibiting a behavior not observable in non-resonantly excited single-photon sources. “This difference in phase dependence enables continuous tuning of the correlation between detectors $A_{1}$ and $B_{1}$ ,” the researchers explain.

The ability to observe the strongest bunching at (φ_A,φ_B) = (π,π) further validates the unique characteristics of this entanglement source. The team concludes that their work experimentally demonstrates the harnessing of vacuum-one-photon number superposition states to fundamentally test the CHSH Bell inequality, confirming the generation of time-entanglement in a Franson-like interferometer.

InAs Quantum Dot Source Simplifies Photon Generation

This advance bypasses complex multi-photon generation techniques, streamlining the creation of entangled photons for quantum technologies. The experimental setup relies on a precise control of the quantum light source, composed of the InAs quantum dot coupled to the micropillar cavity. High-resolution radio frequency spectra, measured with a Fabry-Pèrot interferometer, confirm the resonant excitation of the quantum dot. Auto-correlation function measurements, $g^{2} (τ)$ , revealed a value at an average photon number of 0.

Fiber collimators, quarter-wave plates, mirrors, piezoelectric transducers, beam splitters, and polarizing beam splitters direct the photons to superconducting nanowire single photon detectors labeled $A_{1}$ , $A_{2}$ , $B_{1}$ and $B_{2}$ . The crossover point for this violation, where the S parameter falls below 2, occurs at a $g_{H B T}^{2} (0)$ value of approximately 0. 2. This design simplifies the process of preparing and manipulating the vacuum-one-photon states, which typically requires sophisticated quantum state engineering and conditional preparation. The source’s high brightness is particularly notable given the challenges of generating these superposition states.