Photons from quantum dot emitters violate Bell’s inequality in new study

A new study in Nature Physics demonstrates a new 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 interconnected regardless of their physical distance.

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

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

He told Phys.org, “During my PhD, I worked on generating entangled light sources using spontaneous parametric downconversion (SPDC). However, the weak intrinsic nonlinearity of bulk crystals made it difficult to use full of pump photons. The giant nonlinearity at the one-photon level from quantum dots caught my attention and led me to this research.”

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 possible in the classical world. The Bell inequality provides a threshold: If the correlations cross 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 realistic local theory must satisfy the condition: All measured correlations between particles must be less than or equal to two.”

The researchers used this to determine the validity of their experiment and whether the structure they built 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. Basically, they are semiconductor chips designed to trap neutral exciters within their structure.

By trapping neutral excitons in a small space, the excitons exhibit quantized energy states as they do when confined to 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 on a chip. Furthermore, the energy levels can be tuned, determined by the size and composition of the quantum dot.

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

Coupling with a waveguide

To increase the efficiency, coherence and stability of the photons emitted by the quantum dot, the researchers coupled it to a photonic crystal waveguide.

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

So waveguides allow the control and manipulation of light propagation in direction and wavelength, thereby enhancing light-matter interactions.

However, achieving efficient coupling between waveguide and quantum dot presents 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 not only to a high coupling efficiency of the emitted light into the waveguide (more than 90%), but also to a Purcell enhancement of 16 by slowing down the light in the nanostructure and increasing its interaction time with the quantum dot .”

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

In simpler terms, the Purcell enhancement enhances the light emission 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 the Bell inequality

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

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

After their two-level emitter system was set up to produce entangled photons, the researchers used two unbalanced Mach-Zehnder interferometers to perform the CHSH (Clauser-Horne-Shimony-Holt) inequality test. CHSH is a form of Bell’s inequality.

By carefully setting the stages of the interferometer, the researchers measured the 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 well above the locality limit of 2. This result confirmed the violation of the Bell inequality, thus validating the time-entangled state of energy created through our method,” said Dr. Liu.

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

Energy efficiency and future work

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

The entanglement was created at pump powers of up to 7.2 picowatts, roughly 1000 times less than traditional single-photon sources. This ultra-low power operation, combined with on-chip integration, makes the method very promising for practical quantum technologies.

Dr. Liu foresees some exciting directions for future research. “One route is exploring complex quantum photonic states and many-body interactions through inelastic scattering outside multiple two-level emitters,” he suggested. “Furthermore, further integration of our method into compatible photonic circuits will facilitate more functionalities with a small footprint, enhancing versatile quantum photonic applications spanning computing, communication and sensing.”

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