Activities
Hong-Ou-Mandel like effect using classical light
Semiclassical theory of light has been very successful and instrumental in understanding the interaction between light and matter. The first ever semiclassical theory of light and matter interaction is the black-body radiation, in which Planck postulated that electromagnetic energy is absorbed by atoms (strictly speaking, independent oscillators) in chunks. The prefix "semi" is to denote that in such theories, the matter (usually atom or molecules) are described using quantum mechanics whereas electromagnetic radiation or light is treated using the classical Maxwell's equations.
Planck's solution of the black-body problem started a revolution, and the first stroke of genius came from a humble third class patent clerk, Albert Einstein. Using Planck's result, Einstein formulated a corpuscular theory of light in one of the four so called miracle papers of modern physics. Claiming that light interacts with matter in packets of energy, he was able to solve one of the important conundrums of 20th century physics, the photo-electric effect. These packets of energy are know called "photons".
Much of the later part of 20th century saw the development of a quauntum theory of light. Parallely, there were very interesting developments in the semiclassical theories of light-matter interaction. Some of the most notable work done is by Mandel, Sudarshan and Wolf. They developed a semiclassical theory of photo-electric detection. This theory connects the fluctuations in classical electromagnetic fields to the probability of an atom getting excited on which the light falls. If the last statement was too much jargon, let us put it in the form of a concept that is widely seen in college textbooks. In the language of "photons", the theory essentially says that "the number of photons in a beam of light is proportional to its intensity". But it goes beyond that, and relates the fluctuations in classical light beams to the joint probability of photoelectric detections at two separate detectors, what is known in quantum optics as coincidence of photons.
The quantum theory of light on the other hand, built a framework in which light was described using quantum states like number or Fock states and coherent states. This description proved to be very successful in predicting photon statistics in the outcomes of optics experiments. Using the quantum theory of light Hong, Ou and Mandel predicted that two indistinguishable photons entering a 50:50 beam splitter at the same time will always exit the beam splitter from the same port, although each photon had a 50% chance of exiting through either of the two output ports of the beam splitter. This effect is called the Hong-Ou-Mandel effect, named after its authors. The reason for such a behaviour is the two photon interference that occurs when both the photons are inside the beam splitter. This effect is such an important signature of the quantum nature of light that it is used as a diagnostic tool for sources of photons. But can this effect be explained by the semiclassical theory, in which light is treated classically?
According to the semiclassical theory of photoelectric detection, the probability of coincident photodetections is 50% and not zero as is observed in the Hong-Ou-Mandel effect. This led to the belief that no semiclassical theory can explain the Hong-Ou-Mandel effect. In this lab we have shown that a Hong-Ou-Mandel like effect can indeed be simulated using classical pulses if the fluctuations in the classical pulses (in our case the relative phase between the input pulses) are controlled. Find the detailed theory and the experiment in the paper shown below.
Reference
Further in this work we show that although Hong-Ou-Mandel effect is not unique to the quantum description of light, a clear distinction between the quantum and classical can be made via testing for wave-particle complementarity. In this lab, we have designed a novel electrical setup to demonstrate a near 100% Hong-Ou-Mandel like dip in the coincidence probability with classical pulses. The advantage of using an electrical setup is having complete control over the relative phases (the fluctuations) betweent the input pulses. The setup is shown below.
The complementarity setup is shown below.
To compare and distinguish between the classical and quantum using complementarity, we have also done the quantum version of the above experiment. The first setup is for demonstrating the Hong-Ou-Mandel effect and the second is to test for complementarity and compare it with the classical version.
