Category: 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.

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…

Lectures, Notes & Discussion – Topics, Papers, Books etc.

Below are some of the discussions related to my reading and teaching:

  1. Pavan’s lectures on Quantum Optics
  2. Quantum Optics course – thoughts and notes
  3. Horizons – book reco
  4. On Criticism

Raman essay and Open-Access

I see that the essay I wrote on CV Raman and made open access (thanks to Resonance, which published it) has been used by several educators on YouTube, including some in Indian languages. Also, the Google AI overview shows the published essay as the main reference for a search related to Raman’s science communication (see slideshow below).

I am glad to see that making one’s writing open to all has positive effects. Open-access, not just for readers, but also for authors, is beneficial. Especially in India, paywalls for science are a detriment.

My worry is that open-access publishing has been mainly driven by commercial publishers that extract huge funds from the publishing authors. This defeats the purpose of open science, especially when the research of an author is publicly funded. Added to that, Indian researchers and writers cannot afford to pay huge sums for publishing articles and books.

The publication landscape (including journals and books) across the world needs an introspection. Open-access model is effective only when the readers and authors have access to that model. Otherwise, the model becomes a paywall for authors.

History of Maths in India – a good book

In recent years, this has been one of the best books on the history of mathematics in India. The late Prof. Divakaran was a theoretical physicist and a scholar.

This book is also an excellent example of how a scientist can present historical facts and analyse them with rigour and nuance. Particularly, it puts the Indian contribution in the global context and shows how ideas are exchanged across the geography. The writing is jargon-free and can be understood by anyone interested in mathematics.

Unfortunately, the cost of the book ranges from Rs 8800 to Rs 14,000 (depending on the version), which is a shame. Part of the reason why scholarly books, particularly in India, don’t get the traction is because of such high cost. This needs to change for the betterment and penetration of knowledge in a vast society such as India.

There is a nice video by numberphile on Prof. Divakaran and his book:

Meghnad Saha – lest we forget

Meghnad Saha (6 October 1893 – 16 February 1956), of the fame of Saha’s ionization formula, was born this day. In 1993, a postage stamp in India was released commemorating his birth centenary.

Saha was an astrophysicist with a broad knowledge and appreciation of various branches of physics. One of the earliest English translations (1920) of the papers on relativity by Einstein and Minkowski was written by Meghnad Saha and S.N.Bose.

At the beginning of the book, Mahalanobis introduces the topic with a historical introduction. He begins with a thoughtful discussion on experiments that eventually ruled out the presence of ether, and it sets the stage as follows:

“Lord Kelvin writing in 1893 in hig preface to the English edition of Hertz’s Researches on Electric Waves, says many workers and many thinkers have helped to build up the nineteenth century school of plenum, one ether for light, heat, electricity, magnetism; and the German and English volumes containing Hertz’s electrical papers, given to the world in the last decade of the century, will be a permanent monument of the splendid consummation now realised.”

Ten years later, in 1905, we find Einstein declaring that “the ether will be proved to be superflous”. At first sight the revolution in scientific thought brought about in the course of a single decade appears to be almost too violent. A more careful even though a rapid review of the subject will, however, show how the Theory of Relativity gradually became a historical necessity.

Towards the beginning of the nineteenth century, the luminiferous ether came into prominence as a result of the brilliant successes of the wave theory in the hands of Young and Fresnel. In its stationary aspect, the elastic solid ether was the outcome of the search for a medium in which the light waves may “undulate.” This stationary ether, as shown by Young, also afforded a satisfactory explanation of astronomical aberration. But its very success gave rise to a host of new questions all bearing on the central problem of relative motion of ether and matter.“

Saha, in various capacities, took a stance against British colonialism. Although it affected some opportunities, he continued to do science and was recognized for his outstanding contributions. As Rajesh Kochhar mentions:

“Saha had wanted to join the government service, but was refused permission because of his pronounced anti-British stance. For the same reason, the British government would have liked The Royal Society to exclude Saha. It goes to the credit of the Society that it ignored the pressures and the hints, and elected him a fellow, in 1927. This recognition brought him an annual research grant of £300 from the Indian government followed by the Royal Society’s grant of £250 in 1929 (DeVorkin 1994, p. 164).“

Saha led a tough life. He not only had to face suppressive British colonial rule but also academic politics and battles (versus Raman, no less). His knowledge of physics, his contributions to Indian science, and his commitment to people (he was a politician too) were significant. Let me end the blog with a few lines from Arnab Rai Choudhuri’s article, which nicely summarizes Saha’s work (specifically his ionization formula), and his scientific life:

“Saha’s tale of extraordinary scientific achievements is simultaneously a tale of triumph and defeat, a tale both uplifting and tragic. Saha showed what a man coming from a humble background in an impoverished colony far from the active centres of science could achieve by the sheer intellectual power of his mind. But his inability to follow the trail which he himself had blazed makes it clear that there are limits to what even an exceptionally brilliant person could achieve in science under very adverse circumstances.“

India and Indian science should remember Meghnad Saha.

Gandhi, Tagore and Celebration of Ideas

One of the books that I have enjoyed reading over the years is  The Mahatma and The Poet – Letters and Debates between Gandhi and Tagore 1915-1941’ compiled and edited by Sabyasachi Bhattacharya. The theme of the book is centered around the intellectual exchanges between M.K. Gandhi and Rabindranath Tagore on a variety of topics, including education, scientific outlook, philosophy and human dignity. Sabyasachi introduces the book with an overview of letters and debates and emphasizes that ‘The intellectual quality of the dialogue between Mahatma Gandhi and Rabindranath Tagore is such that it possesses an enduring interest. In these pages, I have tried to situate their debates, in private letters and in public statements, in the historical context of India’s national life and the cultural and political discourse of those times.’(page 20)

The book has a rich intellectual texture and showcases two minds that are open to ideas and not hesitant to express them. As Sabyasachi mentions that:‘…. the differences between them were real and at the same time they shared a common highground above the terrain of differences. Despite their differences on many crucial questions, they were willing to learn from each other.’(page 34) It shows what two engaging minds can reveal not only about themselves, but also about the place and time in which they live and operate. In there, we learn something that was a hallmark of Gandhi’s life: he was open to criticism and changed his mind in the light of evolving times and thoughts, as Sabyasachi indicates with an example:

‘Gandhi was equally open to candid criticism. It is possible that in some respects his outlook evolved, in response to the debates with Tagore. Consider, for instance, his: approach in Hind Swaraj: “I believe that the civilization India has evolved is not to be beaten in the world. Nothing can equal the seeds sown by our ancestors…. India remains immovable and that is her glory…. India has nothing to learn from anybody else and this is as it should be.” One can compare that with his later pronouncements, most notably his reply to Tagore in 1921, a truly memorable statement: “I do not want my house to be walled in all sides and my windows to be stuffed. I want the culture of all the lands to be blown about my house as freely as possible. But I refuse to be blown off my feet by any.’ (page 36)

A snapshot from the book: The Mahatma And The Poet.

Gandhi is many things to many people, some positive and some negative. For me, what stands out is his ability to utilize philosophical ideas such as ahimsa (non-violence) and satyagraha (pursuit of truth) for a political goal and effectively communicate it to a large population in that era. He may well have failed in this era, but he remains an excellent benchmark for human dignity across the world, even today. In that sense, he represents ‘the swadeshi’ in all of us and yet appeals to the whole world, just as Tagore does.

The book (freely available online) is a great read; it is a visit not only to the past, but also into the depths of two human minds, and perhaps into the depths of oneself. After all, ideas too need celebration.  

Sir MV on Education

In India, “National Engineers’ Day is celebrated every year on September 15 to honor the birth anniversary of Sir Mokshagundam Visvesvaraya, one of India’s greatest engineers”. Sir MV, as he was known, is one of the 20th-century Indians I admire. He was a forward-looking statesman who contributed immensely to building India (literally and figuratively). MV was a well-read and well-travelled person for his era, and wrote a few books and memos that are still pertinent to the current developments in India and the world.

Reconstructing India (1920)

One of his books, Reconstructing India (1920), reveals his thoughts on how and why India needs to reconstruct itself based on knowledge in science, technology and humanities. The title page is shown below, and the book is free to read online, thanks to the Internet Archive.

The book, as mentioned by MV in the preface, was written just after the First World War, and contemplates problems faced by India in light of geopolitical developments. In the 17 chapters of the book, divided into 4 parts, MV discusses specific issues faced by India, and proposes that political and administrative reforms can help India become a progressive society.

The largest part of the book is on economic reconstruction, in which he proposes contemporary methods (for the 1920s) to improve various sectors of manufacturing, including agricultural technology and communication media.

The third part of the book is on social reforms, and in there, he has a dedicated chapter on Education, which caught my attention, and I found it relevant even for today’s India.

Education, Humanities, and STEM

It is important that students of science and technology have a good exposure to some aspects of the humanities, including economics, history and philosophy. The pursuit and ability to choose good problems in science and technology critically depend on the social and economic structure in which they are practiced in universities and research institutions. MV anticipated this and highlights it as:

“Secondary and university education, though producing many able recruits for subordinate positions in the Civil Service, does not provide the men needed to carry on the work of agriculture, engineering, commerce and technology. The provision for training in economics and history is inadequate, and the study of those subjects is even discouraged. An attempt is actually made to teach economics in such a way as to render India’s emergence from a state of dependency difficult.”

Even in 2025, I would suggest that STEM students pay attention to economics, as it anchors them to understand the need and functions of a society, and therefore, their work can be calibrated accordingly. This is not to discourage open-ended research, but to understand how natural sciences are connected to the societal thoughts and needs. It gives us a broader understanding of the context, which is so important while understanding the evolution of ideas.

Comparative Education Systems

There is always a lot to learn from various societies and cultures. In order to do so, one needs comparative analysis. This helps one to choose some good elements from a society that can be emulated elsewhere. MV compares and comments on the 1900s British educational system in contrast to the German and Japanese counterparts. Note that India in the 1920s was still a British colony, and in a way, MV is critical of the system in which he himself was educated and trained. As he notes:

“Britain herself has had to pay a heavy price for her hand-to-mouth policy in regard to education. The educational chaos still existing there compares unfavourably with the great yet orderly progress made by Germany and Japan, both of which countries, after weighing and testing the educational systems of the world, absorbed the best of all.”

These were words written long before the Second World War, and give us a glimpse of how German and Japanese systems were functioning in the 1920s and had a lot to offer to the world. Of course, history took its own path, and German and Japanese society had other ideas.

Incidentally, I am writing this piece sitting in Leipzig (eastern Germany), and I am amazed by its architectural marvels that date back centuries. Indeed, German society had (and has) a lot to offer to the world. As MV indicates above, we need to absorb the best that is on offer. In doing so, we also need to reject that which is not good for any society.

Liberal Education and Financial Support

He further adds how liberal education adds value to a society, and calls not only the government but also the people to recognize the importance of financial support for education.

“Both the Government and the people must recognize that only by pursuing a liberal educational policy, and making generous financial provision for schools and colleges can they lift India out of her present low condition and ensure rapid progress.”

These words still hold good, and as a society, India has to re-emphasize modern education that helps us become not only better doctors and engineers, but also better human characters that can add value to the “modern” world.

Call to Action

In the final part of the book, MV makes a passionate appeal to the people of India, calling them to take action and move towards becoming a progressive nation:

“Do the people of India propose to profit by the lessons which world experience has to teach them, or will they be content to allow matters to drift and themselves grow weaker and poorer year by year?
This is the problem of the hour. They have to choose whether they will be educated or remain ignorant; whether they will come into closer touch with the outer world and become responsive to its influences, or remain secluded and indifferent; whether they will be organized or disunited, bold or timid, enterprising or passive ; an industrial or an agricultural nation ; rich or poor ; strong and respected, or weak and dominated by forward nations. The future is in their own hands.”

Indeed, the future is in our hands, and these words written more than 100 years ago still resonate loudly. We need more engineers like Sir MV. The reason he was so effective was that he combined thinking and doing. Importantly, the lesson we can learn from MV’s life and by reading this book, is that an open mind can grasp good ideas at any time and anywhere. Implementing those ideas is an equally important challenge, and MV was up to this in his own way. Are we, as Indians, open to this prospect and engineer our future?