Tag: books

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.

Raman’s pronouncements..

There is a story going around on Facebook related to C.V. Raman and Nehru, and it makes a reference to Raman’s biography. It describes Raman and Nehru’s interaction in a darkened room at Raman Research Institute. Intrigued by the story, I went back and checked some of the biographies of C.V. Raman, and I could not find that story. If someone could find the exact reference, please let me know. (update on 4th March 2026: I dug up the sources further and found this anecdote in chapter 21 of C.V. Raman: A Biography, by Uma Parameswaran, Penguin Books India (2011). Unfortunately, there is no primary or secondary reference associated with the anecdote.)


Among the biographies, Venkatraman’s ‘Journey into the Light’ is comprehensive and mentions Nehru at least 70 times. It does discuss quite a bit about the interaction between these two powerful people and their differences of opinion. It also highlights their common commitment to science and technology. Raman publicly expressed his opinion on the state of science in India. His pronouncements did not go unnoticed, and the press highlighted them. Raman’s biographer, Venkatraman, addresses the issue of Raman’s criticism: “It should not be assumed that Raman was merely making a series of arbitrary and disconnected pronouncements. On the contrary, they were symptoms of a deep concern he had begun to feel about the way science was being promoted. It seemed to him that in the rush for development, scientific excellence and the objectives of science had begun to take a back seat. Sycophancy was on the rise, and ill-equipped people were being propelled into seats they were not ready to occupy. Everyone paid lip sympathy to the universities, but when it came to funding them, they were generally forgotten. What was worse, mediocrity was slowly allowed to become institutionalized. In retrospect, Raman’s utterances, though harsh, implicitly carried a warning that was unfortunately not heeded. And despite all the pious hopes of that period, the linkages between science and technology in India continue to be quite tenuous.” ([Venkataraman, 1989, p. 488])

Having said that, I should mention that almost all of his biographers mention Raman’s confrontation with a variety of people, starting from his Calcutta days till the end of his life. Subsequent scholarship in social sciences has also highlighted Raman’s issue with gender and caste. In contrast to people like Babha, Saha, and Dhawan, Raman was not an institution builder. He had his limitations, but his commitment to science and its role in society is unquestionable.

As I have written before, Raman was not an easy character to study and understand. He contained multitudes. For sure, he was an outstanding experimental physicist. His knowledge of mathematical physics, especially the classical aspect, was very good, and he utilized it extensively in his work. His scientific biographers, both Venkatraman and Ramaseshan, mention that although he had the aptitude to analyze theoretical frameworks, he was more driven by intuition and generally skimmed over the mathematical aspect of his work. This was also observed by Max Born. He also mentored some excellent scientists, such as K.S. Krishnan, Nagendra Nath, Bhagavatham, Pancharatnam, and G.N. Ramachandran, Anna Mani (one of the few women in his lab), to name a few. Probably the most important feature of Raman as an individual was his can-do spirit and his lifelong drive to do science irrespective of the situation.

My broad lesson from all this is to take the positives from the science and the scientific pursuit of a scientist, and yet, remain aware of the flaws in the character of the human being. After all, course correction is from the benefit of hindsight, and its application is in the present and the future.

Raman’s Optics – Historical Overview

Journal of the Optical Society of America is coming up with a special issue on Optics in South Asia. I was invited to write a historical overview of Raman’s work on optics. Below is the snapshot of the pre-print. It should also appear in the axriv in the coming week. Meanwhile, you can access the preprint PDF below.

Also, look out for a research article from my group on multipolar optical binding submitted to the same issue. I will post a link when it appears as a pre-print.

Acknowledgements:

  1. Professor Anurag Sharma, IIT, Delhi, for inviting me to write about Raman;
  2. Other editors of this issue for taking the initiative.
  3. Digital Archive Depository of Raman Research Institute
arxiv – 2026 Main JOSA RDownload

arXiv link here.

Saha and Bose translate Einstein

In physics, the general theory of relativity is one of the most remarkable achievements. It has turned out to be one of the most profound theories in the history of physics. In 1916, Albert Einstein proposed this theory, and it was confirmed in 1919.

Right after this confirmation, around 1920, two Indian gentlemen named Satyendranath Bose and Meghnad Saha translated Einstein’s German work into English. What you are seeing as an image is the remarkable book Principles of Relativity, containing the original papers by Einstein and Minkowski. This translation was done by M.N. Saha and S. N. Bose, who were then at the University College of Science, Calcutta University. It was published in 1920 by the University of Calcutta.

The book also contains a historical introduction by Mahalanobis, the celebrated statistician, although he was originally trained as a physicist himself. This historical introduction is itself quite remarkable.

If you look at the table of contents of this book, you will find the following:

  1. A historical introduction.
  2. The Electrodynamics of Moving Bodies, which is an important paper and is necessary for understanding what follows.
  3. A short biographical note on Albert Einstein was written by Saha.
  4. The Principle of Relativity, mainly the Minkowski papers, translated by Saha, along with an appendix.
  5. The General Principles of Relativity, Einstein’s epoch-making 1916 paper, translated by S. N. Bose, followed by notes by these gentlemen.

The historical introduction discusses the evolution of ideas that led to the fruition of the general theory of relativity. This turned out to be one of the most important expositions of the general theory of relativity, soon after the emergence of the theory and its subsequent confirmation by Eddington through his famous solar eclipse expedition. This is a remarkable document, and it is available on the Internet Archive.

Quantum Optics course – thoughts and notes

Jan 2026 – Apr 2026 – I am teaching a course on Quantum Optics. Below you will find some random thoughts and notes related to my reading. I will be updating the list as I go along the semester. You can add your comments below.

Lectures:

Pavan’s lectures on Quantum Optics (not the whole course)

Some timelines for reference:

Interactive timeline – includes pre-quantum optics

  1. Anyone interested in physics should know a bit about renormalized QED and the efforts that went behind it… It still remains a benchmark of how experiments and theory work in elevating each other…
    • Hari Dass (erstwhile, IMSc) on FB made an interesting observation:it’s unfortunate that after all those and subsequent developments, a mystery is being built out of renormalisation..it was the price to pay for assuming, without any justification, that the microscopic description held to arbitrarily small distances..wilson,schwinger and even feynman have clarified that the right way to do physics is to start with an effective description with a cutoff, which can be fully quantum in nature, and keep extending it to higher and higher scales with the help of further data, as well as with better theoretical understanding..
  2. “The photon is the only particle that was known as a field before it was detected as a particle.” 
    • This is how Weinberg introduces the birth of quantum field theory. He further adds:  “Thus it is natural that the formalism of quantum field theory should have been developed in the first instance in connection with radiation and only later applied to other particles and fields.”Ref: S. Weinberg (in Quantum Theory of Fields, p.15,  1995)
      • Sudipta Sarkar (IIT G) made an interesting observation in facebook:
        • “In some sense, it did right! Dirac started QFT with the effort to quantise radiation! But formally, it is not easy to write down the quantum version of electrodynamics owing to gauge symmetry. It took quite a bit of time to understand how to manage a quantum theory with massless states!“
        • My reply: “indeed..the reconciliation of symmetry was a bottleneck. I am also amazed by the progress of thought, especially by Dirac, who took the harmonic oscillator problem and treated it the way he did. Historically, the question of quantization of particles was already an established programme, but to quantize the field was indeed a major challenge, and hence ‘second quantization’.“
        • The concept of creation and annihilation operators is an intriguing one because it brings in the thoughts from the commutation relationship that existed in classical physics and transfers that into quantum mechanics. This intellectual connection is mainly attributed to Dirac, and historically, this has been one of the most important connections to be made. The question of field quantization already existed in 1920s, but it is thanks to Dirac who really made this connection in a systematic and mathematically consistent way.
  3. In the context of the quantum harmonic oscillator model of electromagnetic radiation, the shift from canonical variables such as position and momentum to creation and annihilation operators is a fascinating one. Interestingly, this progression further leads to the so-called number operator. It is also a progression from Hermitian to non-Hermitian and again back to a Hermitian operator. In the process of understanding the number operators, one realizes that the ground-state results in the so-called zero-point energy. Taken further, the commutation of the number operator with the electric field of the electromagnetic radiation results in the number-amplitude uncertainty. This further gives an insight into why the field amplitude has a non-zero spread, even for the n = 0 state, and therefore results in the so-called vacuum fluctuations.
    • It can’t get more quantum than this…
  4. An essay on Quantum States in Argand Diagrams: https://historyofscience.in/2026/02/03/quantum-states-in-argand-diagrams-vacuum-coherent-and-squeezed/
  5. The word photon has an interesting and surprising origin – see this paper.
  6. Born & Wolf to Mandel & Wolf – a blog on a famous book and on the connection between radio astronomy and quantum optics.
  7. Intensity Interferometer – connection to coherence
  8. References related to Hong-Ou-Mandel experiments:
    • Original paper
      • Hong, C. K., Z. Y. Ou, and L. Mandel. ‘Measurement of Subpicosecond Time Intervals between Two Photons by Interference’. Physical Review Letters 59, no. 18 (1987): 2044–46. https://doi.org/10.1103/PhysRevLett.59.2044.
    • The references below discuss a few contemporary yet simple approaches toward the HOM experiment. 
      • DiBrita, Nicholas S., and Enrique J. Galvez. ‘An Easier-to-Align Hong–Ou–Mandel Interference Demonstration’. American Journal of Physics 91, no. 4 (2023): 307–15. https://doi.org/10.1119/5.0119906.
      • Bjurlin, Cyrus, and Theresa Chmiel. ‘A Versatile Hong–Ou–Mandel Interference Experiment in Optical Fiber for the Undergraduate Laboratory’. American Journal of Physics 93, no. 2 (2025): 180–86. https://doi.org/10.1119/5.0210869.

Prof. Supradeepa from IISc made an important observation related to the non-Poissonian distribution and anti-bunching as follows: When I taught quantum optics earlier this semester, there was an interesting discussion with students which I had not had given thought previously. I have seen the terms anti-bunching and g2(0) < 1 sometimes interchanged. But the idea is that g2(0) < 1 is only non-poissonian while, the stronger condition that g2(0) < g2(\tau) is also needed to have anti-bunching. An easy to calculate example was fock states with |n> for n > 1. g2(tau) = 1-1/n, so these states are non-poissonian because g2(0)<1, but not anti-bunched.

My reply: This is an important point, and Fox’s book has a small discussion related to this non-equivalence: sub-Poisson distribution and anti-bunching can overlap, but need not be the same. As you mentioned, g2(0) < 1 and g2(0) < g2(\tau) have to be satisfied. The criteria for a single-photon source are much stricter than those for a sub-Poisson light source. In my lecture, I do mention this as seen in the picture…

Hedi Born’s picture

This is Hedi Born (wife of Max Born) sending a picture with a note to Lokasundari Ammal (CV Raman’s wife) in 1937.

Max Born and his family spent some time at IISc, Bangalore, in 1935-36.

Amazing to see how communication channels have changed, but the human urge to communicate remains the same..

picture source: (Venkataraman, G.; Journey into Light: Life and Science of C.V. Raman. Indian Academy of Sciences, 1989. p. 364)

Conversation with Chaitanya Athale

Chaitanya is a professor of biology at IISER Pune and works on quantifying biology at the cellular scale. His lab focuses on cytoskeleton and cell shape research and explores synthetic biological roots to address a variety of questions at the cellular scale.

In this freewheeling conversation, we talked about quantitative biology in his lab, reading, the German language, his recent comic-themed book, and a bit on philosophy of biology as we explored his intellectual journey. Also, don’t miss the 3D model he shows to explain his research.

References with links:

‘Chaitanya Athale – IISER Pune’. Accessed 3 January 2026. https://www.iiserpune.ac.in/research/department/biology/people/faculty/regular-faculty/chaitanya-athale/6.

‘Dr. Chaitanya Athale – Lab – Cytoskeleton and Cell Shape Research – Synthetic Biology’. Accessed 3 January 2026. https://sites.iiserpune.ac.in/~cathale/.

‘‪Chaitanya Athale – ‪Google Scholar’. Accessed 3 January 2026. https://scholar.google.com/citations?user=Volq2gEAAAAJ&hl=en.

Chaitanya Athale | LinkedIn’. Accessed 3 January 2026. https://www.linkedin.com/in/chaitanyaa/?originalSubdomain=in.

Arias, Alfonso Martinez. The Master Builder: How the New Science of the Cell Is Rewriting the Story of Life. Basic Books, 2023.

 ‘Athale Lab: CyCelS 💉💉💉💉🚲🤿⛵ (@AthaleLab) / X’. 9 January 2025. https://x.com/athalelab.