Photons from quantum dot emitters violate Bell inequality in new study

A new study in Nature Physics demonstrates a novel method for generating quantum entanglement using a quantum dot, which violates the Bell inequality. This method uses ultra-low power levels and could pave the way for scalable and efficient quantum technologies.

Quantum entanglement is a requirement for quantum computing technologies. In this phenomenon, qubits (quantum bits)—the building blocks of quantum computers—become correlated irrespective of their physical distance.

This means that if the property of one qubit is measured, it impacts the other one. Quantum entanglement is verified through the Bell inequality, a theorem that tests the validity of quantum mechanics by measuring entangled qubits.

Phys.org spoke to the first author of the study, Dr. Shikai Liu, from The Niels Bohr Institute at the University of Copenhagen in Denmark. Dr. Liu's interest in quantum dots stemmed from his earlier work with traditional entanglement sources.

He told Phys.org, "During my Ph.D., I worked on generating entangled light sources using spontaneous parametric down-conversion (SPDC). However, the intrinsic weak nonlinearity of bulk crystals made it difficult to utilize pump photons fully. The giant nonlinearity at the single-photon level from quantum dots caught my attention and led me to this research."

The Bell inequality

As mentioned earlier, the heart of this research is the Bell inequality. Proposed by physicist John Stewart Bell in 1964, this mathematical expression helps distinguish between classical and quantum behavior.

In the quantum world, particles can exhibit correlations that are stronger than what is possible in the classical world. The Bell inequality provides a threshold: If the correlations exceed this threshold, the nature of the correlations is quantum, implying quantum entanglement.

Dr. Liu elaborated, "The Bell inequality distinguishes between classical and quantum correlations. Any local realistic theory must satisfy the condition: All measured correlations between particles must be less than or equal to two."

The researchers used this to establish the validity of their experiment and whether the setup they constructed produced quantum entanglement. The setup itself was based on quantum dots and waveguides.

Artificial atoms on a chip

Quantum dots are nanoscale structures that behave like artificial atoms. Essentially, they are semiconductor chips designed to trap neutral excitons within their structure.

By trapping neutral excitons in a small space, the excitons exhibit quantized energy states as they do when they are confined in atoms. This is why quantum dots are said to behave like artificial atoms.

These quantum dots act as two-level systems, similar to natural atoms, but with the advantage of being integrated into a chip. Additionally, the energy levels can be tuned, determined by the size and composition of the quantum dot.

Quantum dot systems can act as emitter systems, which means they can emit single photons with high efficiency. Under certain conditions, the emitted photons can become entangled.

Coupling with a waveguide

To enhance the efficiency, coherence, and stability of the emitted photons from the quantum dot, the researchers coupled it with a photonic crystal waveguide.

These materials have a periodic structure of alternating high and low refractive index materials. This allows light to be guided through a tube-like structure, which is as thin as a human hair.

Waveguides, therefore, allow the control and manipulation of light propagation in terms of direction and wavelength, thereby enhancing light-matter interactions.

However, achieving efficient coupling between the waveguide and quantum dot poses significant challenges.

"To improve the light-matter interaction, we fabricated a photonic-crystal waveguide that provides strong confinement for the quantum dot," explained Dr. Liu. "This led to not only a high coupling efficiency of emitted light into the waveguide (greater than 90%) but also a Purcell enhancement of 16 by slowing down light in the nanostructure and increasing its interaction time with the quantum dot."

Purcell enhancement refers to the phenomenon where the rate of spontaneous emission of a quantum emitter (such as a quantum dot) is increased when placed in a resonant optical cavity or near a structured photonic environment.

In simpler terms, Purcell enhancement boosts the emission of light from quantum emitters by placing them in environments that amplify their interaction with light. This works by changing how many different ways light can be emitted in the area around the emitter.

Violation of Bell inequality

The team also had to contend with rapid dephasing (quick loss of coherence) induced by thermal vibrations in the crystal lattice. These vibrations disrupt the stable quantum states of particles, making it harder to maintain and measure their quantum properties accurately.

Their solution was to cool the chip to a frigid -269°C to minimize unwanted interactions between the quantum dot and phonons in the semiconductor material.

Once their two-level emitter system was in place for producing the entangled photons, the researchers used two unbalanced Mach-Zehnder interferometers to perform the CHSH (Clauser-Horne-Shimony-Holt) Bell inequality test. The CHSH is a form of the Bell inequality.

By carefully setting up the interferometer phases, the researchers measured Franson interference between the emitted photons. Franson interference is a type of interference pattern observed in quantum optics experiments involving entangled photons.

"The observed S parameter of 2.67 ± 0.16 in our measurements is significantly above the locality bound of 2. This result confirmed the violation of the Bell inequality, thereby validating the energy-time entangled state generated via our method," said Dr. Liu.

This violation is crucial as it confirms the quantum nature of the correlations between the photons.

Energy efficiency and future work

One of the standout features of their two-level emitter setup is its energy efficiency.

The entanglement was generated at pump powers as low as 7.2 picowatts, approximately 1,000 times less than traditional single-photon sources. This ultra-low power operation, combined with the on-chip integration, makes the method highly promising for practical quantum technologies.

Dr. Liu envisions several exciting directions for future research. "One avenue is exploring complex photonic quantum states and many-body interactions through inelastic scattering off multiple two-level emitters," he suggested. "Additionally, further integration of our method into compatible photonic circuits will facilitate more functionalities with a small footprint, enhancing versatile photonic quantum applications involving computing, communication, and sensing."

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