Photons from quantum dot emitters violate Bell inequality in new study

A new study in Physics demonstrates a new method for generating quantum entanglement using a quantum dot, which 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 prerequisite for quantum computing technologies. In this phenomenon, qubits (quantum bits)—the building blocks of quantum computers—are correlated regardless of their physical distance.

This means that if the 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, of the Niels Bohr Institute at the University of Copenhagen in Denmark. Dr. Liu’s interest in quantum dots grew out of his previous 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 fully utilize pump photons. The gigantic nonlinearity at the single-photon level of quantum dots caught my attention and led me to this research.”

The Bell inequality

As mentioned earlier, the core of this research is the Bell inequality. This mathematical expression, proposed 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 correlations exceed this threshold, the nature of the correlations is quantum, implying quantum entanglement.

Dr. Liu explained: “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 determine 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. In essence, 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 confined in atoms. This is why quantum dots behave like artificial atoms.

These quantum dots act as two-level systems, similar to natural atoms, but with the advantage that they are integrated into 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 emitter systems, meaning that they can emit single photons with high efficiency. Under certain conditions, the emitted photons can become entangled.

Coupling with a waveguide

To improve 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 materials with a high and low refractive index. This allows light to be guided through a tube-like structure, which is as thin as a human hair.

Waveguides allow the direction and wavelength of light propagation to be controlled and manipulated, thereby improving the interactions between light and matter.

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

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

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

Simply put, Purcell enhancement increases the emission of light from quantum emitters by placing them in environments that enhance their interaction with light. This works by changing how many different ways light can be emitted in the region around the emitter.

Violation of Bell inequality

The team also had to deal with rapid dephasing (rapid loss of coherence) caused by thermal vibrations in the crystal lattice. These vibrations disrupt the stable quantum states of particles, making it harder to accurately maintain and 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 the phonons in the semiconductor material.

Once their two-level emitter system was in place to produce 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 stages, the researchers measured Franson interference between the emitted photons. Franson interference is a type of interference pattern observed in quantum optics experiments with entangled photons.

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

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

Energy efficiency and future work

One of the most notable features of their dual-emitter setup is its energy efficiency.

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

Dr. Liu foresees several exciting directions for future research. “One way is to explore complex photonic quantum states and many-body interactions using inelastic scattering from multiple two-level emitters,” he suggested. “Moreover, further integration of our method into compatible photonic circuits will enable more functionalities with a small footprint, which will enhance versatile photonic quantum applications in computing, communications, and sensing.”

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