Schematic of photon scattering by a two-level emitter in a photonic crystal waveguide (PhC WG). A weak coherent state is coupled into the PhC WG via a shallow etched grating (SEG). In the photon scattering picture, a single-photon wavepacket is mainly reflected by elastic scattering on a two-level emitter, while the two-photon wavepacket can be scattered inelastically in the transmission direction, thus generating the energy-time entangled photon pair. Credit: Physics of nature (2024). DOI: 10.1038/s41567-024-02543-8
A new study in Physics of nature presents 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 necessary condition 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 affects the other. Quantum entanglement is verified by 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 in Denmark. Dr. Liu’s interest in quantum dots grew out of his previous work on traditional sources of entanglement.
He told Phys.org: “During my PhD, I worked on generating entangled light sources using spontaneous parametric conversion (SPDC). However, the intrinsic weak nonlinearity of bulk crystals made it difficult to fully utilize the pump photons. The giant single-photon nonlinearity of quantum dots caught my attention and led me to this research.”
Bell’s inequality
As mentioned earlier, the core of this research is Bell’s inequality. Proposed by physicist John Stewart Bell in 1964, this mathematical expression allows us to distinguish classical behavior from quantum behavior.
In the quantum world, particles can exhibit stronger correlations than 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, which implies quantum entanglement.
Dr. Liu explained: “Bell’s inequality distinguishes between classical and quantum correlations. Any local realistic theory must satisfy the following condition: all measured correlations between particles must be less than or equal to two.”
The researchers used this data to establish the validity of their experiment and determine whether the device they built produced quantum entanglement. The device itself was based on quantum dots and waveguides.
Artificial atoms on a chip
Quantum dots are nanoscale structures that behave like artificial atoms. They are essentially semiconductor chips designed to trap neutral excitons within their structure.
By trapping neutral excitons in a small space, they exhibit quantized energy states as when they are confined in atoms. This is why quantum dots are said to behave like artificial atoms.
These quantum dots work 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 adjusted, 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 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 alternating between high and low refractive index materials. This allows light to be guided through a tubular structure, as thin as a human hair.
Waveguides therefore make it possible to control and manipulate the propagation of light in terms of direction and wavelength, thus 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 solid confinement of the quantum dot,” explains Dr. Liu. “This led not only to a high coupling efficiency of the emitted light into the waveguide (over 90%), but also to a 16-fold Purcell enhancement 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 placed in a resonant optical cavity or near a structured photonic environment.
In simpler terms, Purcell enhancement increases the light emission of quantum emitters by placing them in environments that amplify their interaction with light. It works by changing the number of different ways light can be emitted in the area around the emitter.
Violation of Bell’s inequality
The team also had to deal with rapid dephasing (rapid loss of coherence) induced by thermal vibrations in the crystal lattice. These vibrations disrupt the stable quantum states of the particles, making it harder to maintain and accurately measure their quantum properties.
Their solution was to cool the chip to a freezing temperature of -269°C to minimize unwanted interactions between the quantum dot and phonons in the semiconductor material.
Once their two-level emitter system was set up to produce the entangled photons, the researchers used two unbalanced Mach-Zehnder interferometers to perform the CHSH (Clauser-Horne-Shimony-Holt) Bell inequality test. CHSH is a form of Bell’s inequality.
By carefully adjusting the phases of the interferometer, 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 larger than the locality limit of 2. This result confirmed the violation of Bell’s inequality, thus validating the energy-time entangled state generated via our method,” said Dr. Liu.
This violation is crucial because it confirms the quantum nature of the correlations between photons.
Energy efficiency and the work of the future
One of the remarkable features of their two-level transmitter configuration is its energy efficiency.
The entanglement was generated at pump powers as low as 7.2 picowatts, about 1,000 times lower 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 envisions several exciting directions for future research. “One of them is to explore complex photonic quantum states and many-body interactions via inelastic scattering on multiple two-level emitters,” he suggested. “In addition, further integration of our method into compatible photonic circuits will facilitate more functionalities with a smaller footprint, thereby enhancing versatile photonic quantum applications involving computing, communication, and sensing.”
More information:
Shikai Liu et al, Violation of Bell’s inequality by photon scattering on a two-level emitter, Physics of nature (2024). DOI: 10.1038/s41567-024-02543-8
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