Many students outside IISER Pune have been following my course blog on Quantum Optics, so I thought I would share some lectures too. I have recorded some discussion related to statistical optics, and will eventually connect them to quantum optics in a few lectures.
Lecture 1 – Quantum Optics via Statistical Optics
topics discussed: Temporal coherence function Degree of temporal coherence function Coherence time Coherence length Power spectral density Spectral width
There is an important connection between quantum optics and radio astronomy. Hanbury Brown and Twiss in the 1950s devised the intensity interferometer.
Particularly, they were interested in measuring the ‘diameter of discrete radio sources’. The title of their seminal paper reads “A new type of interferometer for use in radio astronomy”. As the authors claimed in their paper: “The principle of the instrument is based upon the correlation between the rectified outputs of two independent receivers at each end of a baseline, and it is shown that the cross-correlation coefficient between these outputs is proportional to the square of the amplitude of the Fourier transform of the intensity distribution across the source.”(Brown and Twiss, 1954)
First, they tested their technique in a laboratory situation and followed it up with a measurement of the diameter of Sirius. Their technique was a game-changer in measuring the diameter of bright stars.
As the intensity interferometers were being developed, the laser was realized in the early 1960s. Unlike conventional light sources, laser light is coherent, and this brings in unique features that can be used to understand the nature of light. In the context of laser optics, intensity interferometers had immediate utility in studying coherence through correlation measurement. It was logical to combine lasers with intensity interferometers and study the correlation. This combination is what led to the discovery of some fascinating aspects of quantum properties of light, including anti-bunching.
If the book by Born and Wolf is considered a classic on the electromagnetic theory of light, the quantum extrapolation is the book by Leonard Mandel and Emil Wolf titled Optical Coherence and Quantum Optics.
This book discusses the interface of statistical optics, optical coherence, and quantum optics. The core argument of the book starts with probability theory and its connection to fluctuations of light and builds optical coherence, polarization, and eventually quantum optical effects of light. It is a well-written treatise on light with a flavor of experiments (Mandel did some pioneering experiments in quantum optics) and theoretical explanation (a hallmark of Wolf).
In the preface of the book, they bring together the importance of intensity interferometers and the discovery of lasers and explain how and why it led to a deeper understanding of quantum optics:
“Prior to the development of the first lasers in the 1960s, optical coherence was not a subject with which many scientists had much acquaintance, even though early contributions to the field were made by several distinguished physicists, including Max von Laue, Erwin Schrodinger and Frits Zernike. However, the situation changed once it was realized that the remarkable properties of laser light depended on its coherence. An earlier development that also triggered interest in optical coherence was a series of important experiments by Hanbury Brown and Twiss in the 1950s, showing that correlations between the fluctuations of mutually coherent beams of thermal light could be measured by photoelectric correlation and two-photon coincidence counting experiments. The interpretation of these experiments was, however, surrounded by controversy, which emphasized the need for understanding the coherence properties of light and their effect on the interaction between light and matter.” (Mandel and Wolf, 1995, p. 1)
This further led to a series of studies on light-matter interaction from a coherence perspective, and included analysis of the fluctuation of light by understanding the randomness and the associated statistics of the fluctuations. Mandel, Wolf, Glauber, E.C.G. Surdarshan and many others across the world laid the foundation and connection between optical coherence and quantum optics. What started as a technical development in radio astronomy turned out to be a vital tool in quantum optics.
Brown, R. Hanbury, and R. Q. Twiss. ‘LXXIV. A New Type of Interferometer for Use in Radio Astronomy’. Philosophical Magazine 45, no. 366 (1954): 663–82. https://doi.org/10.1080/14786440708520475.
Brown, R. Hanbury, and R. Q. Twiss. ‘Correlation between Photons in Two Coherent Beams of Light’. Nature 177, no. 4497 (1956): 27–29. https://doi.org/10.1038/177027a0.
Hanbury Brown, R., and R. Q. Twiss. ‘A Test of a New Type of Stellar Interferometer on Sirius’. Nature 178, no. 4541 (1956): 1046–48. https://doi.org/10.1038/1781046a0.
Sanjit Mitra is a Senior Professor at IUCAA, Pune, and explores gravitational wave astronomy. Serving as the science spokesperson, Laser Interferometer Gravitational-Wave Observatory (LIGO)-India and project coordinator, his research focuses on stochastic backgrounds, detector noise, and CMB analysis.
In this episode, we discuss the science and technology behind LIGO and its Indian expansion.
I have been studying quantum mechanics for almost 30 years now. Every time I go back to study and understand something, it reminds me of a quote by Nelson Mandela: “There is nothing like returning to a place that remains unchanged to find the ways in which you yourself have altered” ~ Long Walk to Freedom (1994)
On further contemplation, I find the same with other branches of physics and certain aspects of mathematics, too.
14th of March is Einstein’s birthday. There is so much written about Einstein, and every time you read about him or a text written by him, there is always something interesting to learn. Recently, I came across a wonderful paper by Shankland, who compiled his conversation with Einstein over a period of ten years and published it in 1962 in the American Journal of Physics. Below are three excerpts from the paper to give you a taste of the conversation. I would urge you to read the conversation in full, and it is a delight.
(Shankland 1963, 1)
“When I asked him how he had learned of the Michelson-Morley experiment, he told me that he had become aware of it through the writings of H. A. Lorentz, but only after 1905 had it come to his attention! “Otherwise,” he said, “I would have mentioned it in my paper.” He continued to say the experimental results which had influenced him most were the observations on stellar aberration and Fizeau’s measurements on the speed of light in moving water. “They were enough,” he said. I reminded him that Michelson and Morley had made a very accurate determination at Case in 1886 of the Fresnel dragging coefficient with greatly improved techniques and showed him their values as given in my paper. To this he nodded agreement, but when I added that it seemed to me that Fizeau’s original result was only qualitative, he shook his pipe and smiled, “Oh it was better than that!” He thought Zeeman’s later precise repetition of this experiment was very beautiful. He seemed really delighted when I mentioned to him how elegant I had found (as a student) his method of obtaining the Fresnel dragging coefficient from his composition of velocities law of special relativity.” (Shankland 1963, 2)
“I asked Professor Einstein how long he had worked on the Special Theory of Relativity before 1905. He told me that he had started at age 16 and worked for ten years; first as a student when, of course, he could only spend part-time on it, but the problem was always with him. He abandoned many fruitless attempts, “until at last it came to me that time was suspect!” Only then, after all his earlier efforts to obtain a theory consistent with the experimental facts had failed, was the development of the Special Theory of Relativity possible. This led him to comment at some length on the nature of mental processes in that they do not seem at all to move step by step to a solution, and he emphasized how devious a route our minds take through a problem. “It is only at the last that order seems at all possible in a problem.”” (Shankland 1963, 2)
“Our conversation then returned to the Michelson-Morley experiment and the Special Theory of Relativity. I could not help feeling that this elegant special theory, the product of his youthful efforts, held the place nearest to his heart. I asked him if he felt that writing out the history of the ;v[ichelson-Morley experiment would be worthwhile. He said, “Yes, by all means, but you must write it as Mach wrote his Science of Mechanics.” Then he gave me his ideas on historical writing of science. “Nearly all historians of science are philologists and do not comprehend what physicists were aiming at, how they thought and wrestled with their problems. Even most of the work on Galileo is poorly done.” A means of writing must be found which conveys the thought processes that lead to discoveries. Physicists have been of little help in this because most of them have no “historical sense.” Mach’s Science of Mechanics, however, he considered one of the truly great books and a model for scientific historical writing. He said, “Mach did not know the real facts of how the early workers considered their problems,” but Einstein felt that Mach had sufficient insight so that what he says is very likely correct anyway.” (Shankland 1963, 4)
There is a lot more to explore in the wonderful conversation paper. Link below.
Shankland, R. S. 1963. ‘Conversations with Albert Einstein’. American Journal of Physics 31 (1): 47–57. https://doi.org/10.1119/1.1969236.
Sudipta Sarkar is a Professor of Physics at IIT Gandhinagar, specializing in gravitation, black hole thermodynamics, gravitational waves, and quantum field theory in curved spacetime. He is also interested in the history of science, particular history of relativity and connected ideas.
In this conversation, we discussed his intellectual journey and the research questions that he has been interested in.
Anthony James Leggett (26 March 1938 – 8 March 2026)
pic credit: Britannica
I was informed that Anthony Leggett passed away…he made physics wonderful by asking profound questions, as below:
“……there is no good reason to accept thisdivision of the world into a microscopic regime where QM reigns and a macroscopic one governed by classical physics; QM is a very ‘totalitarian’ theory, and if it applies to an individual and electrons, then it should prima facie equally apply to the macroscopic objects made up of them, including any devices which we have set up as measuring apparatus….” [1]
This image is a modern perception of ‘bias for action’ and is extensively used in advertisements. It frames thinking and doing as mutually exclusive tasks. In doing so, it takes a potshot at thinking as an activity.
Why is thinking not popular? Probably because taking time to think delays a decision. In commercial terms, it means the consumer does not ‘buy’ instantaneously, and hence affects the commerce.
But why not consider ‘doing’ as a good thing? Indeed, doing is important, and that is how the world moves. But the point here is to criticize ‘doing without thinking’. The world has many examples of this kind of ‘action without thinking’. The argument is that we can adapt as we go forward with the action. The problem with this approach is that it does not work without a reversibility clause. It works fine for actions that can have reversible consequences. If such a clause is absent, then you are forced to work on new problems that you are not prepared for.
One of the important issues to be addressed in recent (AI-driven) times is: how can research scholars acquire knowledge and simultaneously contribute to and communicate with society? Related to this question is: What is the role of scholarship in contemporary times?
Below are three thoughts that I wrote mainly with young researchers in mind. I am hoping that it may find use even among others.
1) Pursuit and utility of knowledge is the primary task of a scholar, and managing the perception of that knowledge is secondary. This means a scholar should use a majority of their time, resources and energy in enhancing scholarly knowledge, and in cases where there is utility, applying that knowledge in the outside ‘noisy’ world. This is your personal knowledge based on your efforts and experiences, and cannot be replaced instantaneously. This also brings uniqueness. Once you have this, you can venture into creating a realistic perception of your knowledge. Remember that learning and researching, to a large extent, are under your control; whereas how the outside world perceives your knowledge is not. Therefore, it would be prudent to pay more attention to learning and doing rather than creating a perception. Note that I am not saying that perception is unimportant. All I am saying is that perception is secondary in importance.
2) One of the key learnings in research and education is that the world is always open to good knowledge and ideas, be it in academia or industry. People are always interested in interacting with and hiring people with a sound knowledge base. It may take a while for somebody to discover your knowledge, but if you have a strong foundation and then go out to the world and interact with it, it is very difficult for the world to ignore you. This means that, having done good work, you should be able to share that work with the outside world. This can be a research paper or an engineering prototype, or any form of science, art or talent that you have. The crucial point here is to first do the hard work and then venture into the sharing of that work.
3) In your work, do not compromise on rigor. If you are a researcher, your first commitment should be towards addressing your scholarly peers or the specialized industry and then broadening your communication. Within scholarly communication, you will have to address questions within the research community. This means you will be basing your work on a large body of knowledge and subjecting yourself to internal and external criticism. This is where rigor comes in handy. Here, rigor does not mean unclear communication. It means to have thought through the questions, nuances and complications of a problem and have a broad and balanced view of the research problem. The general audience sometimes perceives rigorous scholarly communication as filled with jargon and complications. Therefore, it is always better to create two versions of your work: one for your peers and one for the general audience. In the age of AI, the second version is easier to create. Remember that your expertise will be vital in creating the second version for the general audience. That is where you can bring your authenticity and creativity. This can also broaden the scope of your knowledge without compromising your scholarship.
These are a few fleeting thoughts. You can criticize, edit, expand and adapt it to make your own version of it. After all, that is how knowledge moves forward 😊
