Violation of Bell-type Inequality in the Hanbury Brown-Twiss (HBT) Toy-Model: Quantum Correlations beyond Local-Realism

Light has long been understood as a wave, rippling through space like a disturbance in a pond. For decades, scientists described its behavior using the familiar laws of classical physics, treating it as a continuous electromagnetic field. However, a deeper layer of reality emerged in the mid-twentieth century when researchers realized that light also behaves as a stream of discrete particles called photons. This dual nature gave rise to the field of quantum optics, which explores how light interacts with matter at the most fundamental level. One of the most famous experiments in this field is the Hanbury Brown and Twiss effect, a technique originally designed to measure the size of distant stars. By placing two detectors far apart and measuring how the brightness of starlight fluctuates in unison, astronomers discovered that light possesses a statistical personality that classical physics could not fully explain. This effect revealed that photons can arrive in groups or avoid each other, behaviors that hint at a deeper, stranger connection between particles. Today, the question remains: can these optical setups reveal a more profound kind of connection known as non-locality, where particles influence each other instantly across space, defying the idea that everything must be explained by local, hidden causes?

In a recent study, researchers at the Indian Institute of Science Education and Research Mohali set out to investigate this question using a simplified version of the famous star-measuring experiment. The original setup for the Hanbury Brown and Twiss effect is complex, involving eight different paths that light can take as it travels from two sources to two detectors. To make the mathematics manageable without losing the essential physics, the team constructed a streamlined model using only four paths. They imagined two sources of light, each sending out a special kind of quantum state known as a two-mode squeezed vacuum. These states are not ordinary light; they are carefully prepared quantum resources where the properties of the light are linked in a way that classical physics cannot replicate. The researchers directed these beams through a series of mirrors, beam splitters, and polarizers, mimicking the journey of light in the original experiment but within a controlled, theoretical framework. The goal was to see if the correlations between the light arriving at the two detectors could break a specific mathematical rule known as a Bell-type inequality. This rule acts as a boundary line: if the measurements stay within the line, the results could be explained by a classical world where everything is determined by local, hidden factors. If the measurements cross the line, it proves that the light is exhibiting genuine quantum non-locality.

The team found that their simplified model did indeed cross that boundary. When they analyzed the data generated by their four-mode system, the correlations between the detectors violated the inequality, demonstrating that the light was behaving in a way that no classical description could account for. This violation occurred specifically when the light sources were prepared in a squeezed state, a condition where the uncertainty in the light's properties is reduced below the standard quantum limit. The researchers observed that the effect was strongest when both sources were squeezed in a matching way, but they also discovered something surprising: even if one source was squeezed and the other remained a standard, classical-like state, the system still produced a violation. This suggests that the optical components in the setup, acting like a mixer, were able to entangle the two separate beams, weaving them into a single, non-local quantum state. The study also looked at what happens when the light is not perfectly pure but has some thermal noise, simulating a warmer environment. They found that the non-local connection persisted even at finite temperatures, though the strength of the violation gradually faded as the temperature rose.

These results confirm that the Hanbury Brown and Twiss setup is not just a tool for measuring star sizes or counting photons, but a powerful platform for testing the very foundations of reality. By stripping the experiment down to its bare essentials, the researchers showed that the strange, non-local features of quantum mechanics are robust enough to survive in a simplified optical arrangement. The work highlights that the boundary between the classical world we see and the quantum world that underpins it is not a rigid wall but a permeable line that can be crossed with the right kind of light. While the study relied on theoretical calculations rather than a physical bench-top experiment, the mathematical rigor of the model provides a clear roadmap for future investigations. It suggests that even in a system with just four paths of light, the universe can reveal its most counterintuitive secrets, proving that the quantum nature of light is not a fragile curiosity but a fundamental feature of how the world works.