Soul > Part III > Chapter 37 > HOM Interference

The Hong-Ou-Mandel (HOM) interference has been demonstrated to play an important role in quantum information processing (Makino et al., 2015; Wang et al., 2019). This section is a brief introduction to the HOM interference. Subsequent sections will show how quantum entanglement may result from the HOM interference and how the mind may use the same mechanism to process information that ultimately gives rise to conscious perception.

Two Photon Interference

The HOM interference is a two-photon interference which occurs when two identical single-photon waves enter a 1:1 beam splitter. As a photon hits the beam splitter, it will either be reflected or transmitted with equal probability. Two photons, ai and bi, incident on the beam splitter will have four possibilities as shown in Figure 37c.

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Figure 37c. Two photons, ai and bi, incident on a beam splitter. (A) Both photons are transmitted. (B) Both photons are reflected. (C) ai is transmitted but bi is reflected. (D) ai is reflected but bi is transmitted.

Now if we use two photodetectors to observe the output photons, ao and bo. Detectors D1 and D2 are placed for horizontal and vertical outputs, respectively. Each will detect one photon for cases A and B. The detector D1 will register two photons for case C, and no photon for case D, while D2 will register no photon for case C, and two photons for case D. "Coincidence" means that each of the two detectors registers one photon (BraƄczyk, 2017). The coincidence probability equals to 0.5 (cases A and B out of four possible cases) if there is no interaction between two photons. However, experiments have consistently observed lower coincidence probability when the two photons arrive at the beam splitter almost simultaneously. This phenomenon is known as the "HOM dip" or "HOM effect".

The HOM Dip

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Figure 37d. The coincidence probability as a function of relative delay between two incident photons. If the two photons arrive at the beam splitter simultaneously (no delay), the coincidence probability approaches to zero.
[Adapted from: Wikipedia]

The HOM dip is a signature of the HOM interference. It arises from the attractive interaction between two photons. Suppose two photons arrive at the beam splitter with a long relative delay such that they do not interact when they hit the splitter. In this case, the coincidence probability equals to 0.5. As the delay becomes shorter, the two photons may bunch together due to their attractive interaction. Thus, both photons tend to go to the same detector, thereby reducing the coincidence probability. In the extreme case (without any delay), the two photons will bind and almost always go to the same detector, resulting in near zero coincidence probability.

The bottom of the HOM dip reflects coherence between two photons. It occurs when two photons reach a point (e.g., the beam splitter) simultaneously. Of note, as ions pass through two nearby ion channels simultaneously, the photons they emit may also bunch together. This property is crucial for the operation of the mind. Amazingly, the photonic coherence is also critical for the development of quantum computers. The next section will discuss a type of coherence known as "quantum entanglement".

 

Author: Frank Lee
Posted on: 2020-09-15