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

A new study in Natural physics demonstrates a new method for generating quantum entanglement using a quantum dot that violates Bell’s 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 regardless of their physical distance.

This means that if a property of one qubit is measured, it will affect the other. Quantum entanglement is verified using Bell’s 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, of The Niels Bohr Institute at the University of Copenhagen, Denmark. The interest of Dr. Liu’s work on quantum dots was based on his earlier work with traditional sources of entanglement.

He told Phys.org: “During my PhD, 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 fully exploit photons. The giant single-photon nonlinearity from quantum dots caught my attention and led me to this research.”

Bell’s inequality

As mentioned earlier, the heart of this research is Bell’s inequality. This mathematical term, coined by physicist John Stewart Bell in 1964, 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. Bell’s inequality provides a threshold: If the correlation exceeds this threshold, the nature of the correlations is quantum, implying quantum entanglement.

Dr. Liu elaborated: “Bell’s inequality distinguishes between classical and quantum correlations. Any local realistic theory must satisfy a 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 setup they constructed created quantum entanglement. The setup itself was based on quantum dots and waveguides.

Artificial atoms on a chip

Quantum dots are nanoparticles that behave like artificial atoms. Basically, these are semiconductor chips designed to trap neutral excitons in their structure.

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

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

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

Connection to the waveguide

To increase the efficiency, coherence and stability of the photons emitted 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 tubular structure that is as thin as a human hair.

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

However, achieving efficient coupling between the waveguide and the 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 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) increases when it is placed in a resonant optical cavity or in the vicinity of a structured photonic medium.

Put simply, the Purcell enhancement increases the light emission from quantum emitters by placing them in an environment that enhances their interaction with light. It works by changing how many different ways the light can be emitted in the area around the emitter.

Violation of Bell’s 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 maintain and accurately measure their quantum properties.

Their solution was to cool the chip to a freezing -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 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 adjusting the phases of the interferometer, the scientists 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 limit of site 2. This result confirmed the violation of Bell’s inequality, thereby confirming the energy-time entanglement state generated by our method,” said Dr. Liu.

This violation is crucial because 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 generated at a pump power of only 7.2 picowatts, approximately 1000 times less than traditional single-photon sources. This ultra-low-power operation combined with on-chip integration makes the method highly promising for practical quantum technologies.

Dr. Liu envisions several exciting directions for future research. “One route is to probe complex photonic quantum states and many-body interactions through inelastic scattering from multiple two-level emitters,” he suggested. “Additionally, further integration of our method into compatible photonic circuits will facilitate more functions with a small footprint, thereby enhancing versatile photonic quantum applications spanning computing, communication, and sensing.”

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