Open Source – an example

Open source done with expertise and correct intent looks like the link below.

The world, irrespective of the location, can adapt a lot more to the ‘creative commons’ principle than it has done over the years.

When it comes to knowledge generation and sharing, open source has great value to the world. Think Internet in its early days. The motivation for its propulsion was to connect the nodes of knowledge (www stands for World Wide Web).

Having said that, I acknowledge that commercialization is important, but it has its relevance in certain domains downstream of knowledge, especially where engineering has to interface with the scale, scope and demands of the market. Not at the origins, learning and coupling with the society.

If anything, open source knowledge, harnessed properly with fair markets, may lead to far more commercialization and entrepreneurial opportunities.

For the scale and variety of India, open source has a lot to offer. Are we ready to adopt and adapt?

Intensity Interferometer – connection to coherence

My previous blog discussed some historical papers related to the intensity interferometer and its connection to quantum optics. Here, I explain the basic physics of an intensity interferometer.

In the context of spatial coherence, the coherence theory expresses the degree of spatial coherence as,

$$ \gamma_{12} = \frac{\left\langle U_1(t) U_2^\ast(t) \right\rangle}{\sqrt{\left\langle |U_1|^2 \right\rangle \left\langle |U_2|^2 \right\rangle}} $$

with \( U_i(t) \) representing the fields of sources \( i = 1 \) and \( 2 \).

An intensity interferometer measures the intensity correlation function between such sources. If \( I_1(t) \) is the intensity of source 1 and \( I_2(t) \) is the intensity of source 2, then the intensity correlation function is given by:

$$ \left\langle I_1(t) \cdot I_2(t) \right\rangle $$

where the enclosing brackets denote a time average.

This correlation, measured in the intensity interferometer, is related to the degree of spatial coherence in the following way:

$$ \left\langle I_1 I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left(1 + \left| \gamma_{12} \right|^2 \right) $$

If one ignores the background (the first term in the sum of the above equation) and considers only the fluctuations in the signal (the second term), then the term of relevance will be:

$$ \left\langle \Delta I_1 \Delta I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left| \gamma_{12} \right|^2 $$

The signal in the intensity interferometer is thus proportional to \( \left| \gamma_{12} \right|^2 \).

A conventional interferometer measures a signal that is proportional to \( \left| \gamma_{12} \right| \), which includes the amplitude and phase, whereas an intensity interferometer measures a signal proportional to \( \left| \gamma_{12} \right|^2 \), which is not sensitive to the phase.

Intensity interferometers have certain advantages compared to conventional interferometers (such as the Michelson interferometer). Below is a partial list:

  • Intensity measurements (unlike amplitude or phase) can be done directly using optoelectronic instruments.
  • They do not require precise, sub-wavelength optical alignment, unlike amplitude- or wavefront-dividing interferometers.
  • They can be used with two detectors that are placed far apart, thereby improving the spatial resolution of the measurement (relevant in astronomy).

A constraint of an intensity interferometer is that the intensity of the participating source should be bright.

Reference:

Dravins, Dainis. ‘Intensity Interferometry: Optical Imaging with Kilometer Baselines’. arXiv.Org, 12 July 2016. https://arxiv.org/abs/1607.03490

Pavan’s lectures on Quantum Optics

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

Lecture 2:

Spatial Coherence
Mutual Intensity
Coherence Area
Cross-Spectra Density
Partially Coherent Waves
Interference Equation
Visibility
Interference & Temporal Coherence
Interference & Spatial Coherence

Lecture 3 – Intensity Interferometer: Physics & History

Lecture 4: What is quantum about photons? How to measure it?

Born & Wolf to Mandel & Wolf

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.

This blog is part of my course blog on Quantum Optics.

References:

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.

Mandel, Leonard, and Emil Wolf. Optical Coherence and Quantum Optics. 1st edn. Cambridge University Press, 1995. https://doi.org/10.1017/CBO9781139644105.

Conversation with Sanjit Mitra

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.

References:

‘Sanjit Mitra – IUCAA’ Accessed 26 March 2026. https://www.iucaa.in/en/faculty-research/sanjit.

‘Sanjit Mitra’. n.d. Accessed 26 March 2026. https://web.iucaa.in/~sanjit/home/About_Me.html.

GW @ IUCAA. Accessed 26 March 2026. https://www.gw.iucaa.in/.

LIGO-India. Accessed 26 March 2026. https://www.ligo-india.in/.

‘‪Sanjit Mitra‬ – ‪Google Scholar‬’. n.d. Accessed 26 March 2026. https://scholar.google.com/citations?hl=en&user=1LVFYJ0AAAAJ&view_op=list_works.

‘LISA: Laser Interferometer Space Antenna’. n.d. Accessed 26 March 2026. https://lisa.nasa.gov/.

Long walk to knowledge…

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.

Perhaps this is what a ‘life of a student’ means?

Einstein in conversation with Shankland

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.

Conversation with Sudipta Sarkar

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.

References:

‘IIT Gandhinagar | Sudipta Sarkar’. n.d. Accessed 9 March 2026. https://iitgn.ac.in/faculty/phy/fac-sudipta.

GEORGE GAMOV. n.d. ONE TWO THREE INFINITY. Accessed 13 March 2026. http://archive.org/details/OneTwoThreeInfinity_158.

IIT Gandhinagar. 2022a. Classical Black Hole | Prof Sudipta Sarkar | Lecture 01. 01:18:58. https://www.youtube.com/watch?v=1nKVYasNFh0.

IIT Gandhinagar. 2022b. Towards Relativity: Einstein and His Compass | Sudipta Sarkar | History of Ideas 2.0. 01:05:09. https://www.youtube.com/watch?v=-4gv-S7sLZ0.

Lightman, Alan. n.d. A Sense of the Mysterious: Science and the Human Spirit. Vintage Books.

Miller, Arthur I. 1981. Albert Einstein’s Special Theory of Relativity: Discovery. Addison Wesley Longman Publishing Co.

Pais, Abraham. 2005. Subtle Is the Lord: The Science And the Life of Albert Einstein. Oxford Univ Pr.

‘‪Sudipta Sarkar‬ – ‪Google Scholar‬’. n.d. Accessed 9 March 2026. https://scholar.google.com/citations?user=zXU9ZN4AAAAJ&hl=en.

‘Sudipta Sarkar – INSPIRE’. n.d. Accessed 9 March 2026. https://inspirehep.net/authors/1039819.

TIFR Quantum Space-Time Seminars. 2026. Sudipta Sarkar (IITGandhinagar): Rotating Black Holes Beyond General Relativity. 02:07:12. https://www.youtube.com/watch?v=cRJw9MXVgdc.