The quantum of light—the photon—is a little over 100 years old. It was born in 1905 when Einstein merged Planck’s blackbody quantum hypothesis with statistical mechanics and concluded that light itself must be quantized. No one believed him! Fast forward to today, and the photon is a modern workhorse of modern quantum technology. Quantum encryption and communication are performed almost exclusively with photons, and many prototype quantum computers are optics based. Quantum optics also underpins atomic and molecular optics (AMO), which is one of the hottest and most rapidly advancing frontiers of physics today.
Only after the availability of “quantum” light sources … could photon numbers be manipulated at will, launching the modern era of quantum optics.
This blog tells the story of the early days of the photon and of quantum optics. It begins with Einstein in 1905 and ends with the demonstration of photon anti-bunching that was the first fundamentally quantum optical phenomenon observed seventy years later in 1977. Across that stretch of time, the photon went from a nascent idea in Einstein’s fertile brain to the most thoroughly investigated quantum particle in the realm of physics.
The Photon: Albert Einstein (1905)
When Planck presented his quantum hypothesis in 1900 to the German Physical Society , his model of black body radiation retained all its classical properties but one—the quantized interaction of light with matter. He did not think yet in terms of quanta, only in terms of steps in a continuous interaction.
The quantum break came from Einstein when he published his 1905 paper proposing the existence of the photon—an actual quantum of light that carried with it energy and momentum . His reasoning was simple and iron-clad, resting on Planck’s own blackbody relation that Einstein combined with simple reasoning from statistical mechanics. He was led inexorably to the existence of the photon. Unfortunately, almost no one believed him (see my blog on Einstein and Planck).
This was before wave-particle duality in quantum thinking, so the notion that light—so clearly a wave phenomenon—could be a particle was unthinkable. It had taken half of the 19th century to rid physics of Newton’s corpuscules and emmisionist theories of light, so to bring it back at the beginning of the 20th century seemed like a great blunder. However, Einstein persisted.
In 1909 he published a paper on the fluctuation properties of light  in which he proposed that the fluctuations observed in light intensity had two contributions: one from the discreteness of the photons (what we call “shot noise” today) and one from the fluctuations in the wave properties. Einstein was proposing that both particle and wave properties contributed to intensity fluctuations, exhibiting simultaneous particle-like and wave-like properties. This was one of the first expressions of wave-particle duality in modern physics.
In 1916 and 1917 Einstein took another bold step and proposed the existence of stimulated emission . Once again, his arguments were based on simple physics—this time the principle of detailed balance—and he was led to the audacious conclusion that one photon can stimulated the emission of another. This would become the basis of the laser forty-five years later.
While Einstein was confident in the reality of the photon, others sincerely doubted its existence. Robert Milliken (1868 – 1953) decided to put Einstein’s theory of photoelectron emission to the most stringent test ever performed. In 1915 he painstakingly acquired the definitive dataset with the goal to refute Einstein’s hypothesis, only to confirm it in spectacular fashion . Partly based on Milliken’s confirmation of Einstein’s theory of the photon, Einstein was awarded the Nobel Prize in Physics in 1921.
From that point onward, the physical existence of the photon was accepted and was incorporated routinely into other physical theories. Compton used the energy and the momentum of the photon in 1922 to predict and measure Compton scattering of x-rays off of electrons . The photon was given its modern name by Gilbert Lewis in 1926 .
Single-Photon Interference: Geoffry Taylor (1909)
If a light beam is made up of a group of individual light quanta, then in the limit of very dim light, there should just be one photon passing through an optical system at a time. Therefore, to do optical experiments on single photons, one just needs to reach the ultimate dim limit. As simple and clear as this argument sounds, it has problems that only were sorted out after the Hanbury Brown and Twiss experiments in the 1950’s and the controversy they launched (see below). However, in 1909, this thinking seemed like a clear approach for looking for deviations in optical processes in the single-photon limit.
In 1909, Geoffry Ingram Taylor (1886 – 1975) was an undergraduate student at Cambridge University and performed a low-intensity Young’s double-slit experiment (encouraged by J. J. Thomson). At that time the idea of Einstein’s photon was only 4 years old, and Bohr’s theory of the hydrogen atom was still a year away. But Thomson believed that if photons were real, then their existence could possibly show up as deviations in experiments involving single photons. Young’s double-slit experiment is the classic demonstration of the classical wave nature of light, so performing it under conditions when (on average) only a single photon was in transit between a light source and a photographic plate seemed like the best place to look.
The experiment was performed by finding an optimum exposure of photographic plates in a double slit experiment, then reducing the flux while increasing the exposure time, until the single-photon limit was achieved while retaining the same net exposure of the photographic plate. Under the lowest intensity, when only a single photon was in transit at a time (on average), Taylor performed the exposure for three months. To his disappointment, when he developed the film, there was no significant difference between high intensity and low intensity interference fringes . If photons existed, then their quantized nature was not showing up in the low-intensity interference experiment.
The reason that there is no single-photon-limit deviation in the behavior of the Young double-slit experiment is because Young’s experiment only measures first-order coherence properties. The average over many single-photon detection events is described equally well either by classical waves or by quantum mechanics. Quantized effects in the Young experiment could only appear in fluctuations in the arrivals of photons, but in Taylor’s day there was no way to detect the arrival of single photons.
Quantum Theory of Radiation : Paul Dirac (1927)
After Paul Dirac (1902 – 1984) was awarded his doctorate from Cambridge in 1926, he received a stipend that sent him to work with Niels Bohr (1885 – 1962) in Copenhagen. His attention focused on the electromagnetic field and how it interacted with the quantized states of atoms. Although the electromagnetic field was the classical field of light, it was also the quantum field of Einstein’s photon, and he wondered how the quantized harmonic oscillators of the electromagnetic field could be generated by quantum wavefunctions acting as operators. He decided that, to generate a photon, the wavefunction must operate on a state that had no photons—the ground state of the electromagnetic field known as the vacuum state.
Dirac put these thoughts into their appropriate mathematical form and began work on two manuscripts. The first manuscript contained the theoretical details of the non-commuting electromagnetic field operators. He called the process of generating photons out of the vacuum “second quantization”. In second quantization, the classical field of electromagnetism is converted to an operator that generates quanta of the associated quantum field out of the vacuum (and also annihilates photons back into the vacuum). The creation operators can be applied again and again to build up an N-photon state containing N photons that obey Bose-Einstein statistics, as they must, as required by their integer spin, and agreeing with Planck’s blackbody radiation.
Dirac then showed how an interaction of the quantized electromagnetic field with quantized energy levels involved the annihilation and creation of photons as they promoted electrons to higher atomic energy levels, or demoted them through stimulated emission. Very significantly, Dirac’s new theory explained the spontaneous emission of light from an excited electron level as a direct physical process that creates a photon carrying away the energy as the electron falls to a lower energy level. Spontaneous emission had been explained first by Einstein more than ten years earlier when he derived the famous A and B coefficients , but the physical mechanism for these processes was inferred rather than derived. Dirac, in late 1926, had produced the first direct theory of photon exchange with matter .
Einstein-Podolsky-Rosen (EPR) and Bohr (1935)
The famous dialog between Einstein and Bohr at the Solvay Conferences culminated in the now famous “EPR” paradox of 1935 when Einstein published (together with B. Podolsky and N. Rosen) a paper that contained a particularly simple and cunning thought experiment. In this paper, not only was quantum mechanics under attack, but so was the concept of reality itself, as reflected in the paper’s title “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” .
Einstein considered an experiment on two quantum particles that had become “entangled” (meaning they interacted) at some time in the past, and then had flown off in opposite directions. By the time their properties are measured, the two particles are widely separated. Two observers each make measurements of certain properties of the particles. For instance, the first observer could choose to measure either the position or the momentum of one particle. The other observer likewise can choose to make either measurement on the second particle. Each measurement is made with perfect accuracy. The two observers then travel back to meet and compare their measurements. When the two experimentalists compare their data, they find perfect agreement in their values every time that they had chosen (unbeknownst to each other) to make the same measurement. This agreement occurred either when they both chose to measure position or both chose to measure momentum.
It would seem that the state of the particle prior to the second measurement was completely defined by the results of the first measurement. In other words, the state of the second particle is set into a definite state (using quantum-mechanical jargon, the state is said to “collapse”) the instant that the first measurement is made. This implies that there is instantaneous action at a distance −− violating everything that Einstein believed about reality (and violating the law that nothing can travel faster than the speed of light). He therefore had no choice but to consider this conclusion of instantaneous action to be false. Therefore quantum mechanics could not be a complete theory of physical reality −− some deeper theory, yet undiscovered, was needed to resolve the paradox.
Bohr, on the other hand, did not hold “reality” so sacred. In his rebuttal to the EPR paper, which he published six months later under the identical title , he rejected Einstein’s criterion for reality. He had no problem with the two observers making the same measurements and finding identical answers. Although one measurement may affect the conditions of the second despite their great distance, no information could be transmitted by this dual measurement process, and hence there was no violation of causality. Bohr’s mind-boggling viewpoint was that reality was nonlocal, meaning that in the quantum world the measurement at one location does influence what is measured somewhere else, even at great distance. Einstein, on the other hand, could not accept a nonlocal reality.
The Intensity Interferometer: Hanbury Brown and Twiss (1956)
Optical physics was surprisingly dormant from the 1930’s through the 1940’s. Most of the research during this time was either on physical optics, like lenses and imaging systems, or on spectroscopy, which was more interested in the physical properties of the materials than in light itself. This hiatus from the photon was about to change dramatically, not driven by physicists, but driven by astronomers.
The development of radar technology during World War II enabled the new field of radio astronomy both with high-tech receivers and with a large cohort of scientists and engineers trained in radio technology. In the late 1940’s and early 1950’s radio astronomy was starting to work with long baselines to better resolve radio sources in the sky using interferometery. The first attempts used coherent references between two separated receivers to provide a common mixing signal to perform field-based detection. However, the stability of the reference was limiting, especially for longer baselines.
In 1950, a doctoral student in the radio astronomy department of the University of Manchester, R. Hanbury Brown, was given the task to design baselines that could work at longer distances to resolve smaller radio sources. After struggling with the technical difficulties of providing a coherent “local” oscillator for distant receivers, Hanbury Brown had a sudden epiphany one evening. Instead of trying to reference the field of one receiver to the field of another, what if, instead, one were to reference the intensity of one receiver to the intensity of the other, specifically correlating the noise on the intensity? To measure intensity requires no local oscillator or reference field. The size of an astronomical source would then show up in how well the intensity fluctuations correlated with each other as the distance between the receivers was changed. He did a back of the envelope calculation that gave him hope that his idea might work, but he needed more rigorous proof if he was to ask for money to try out his idea. He tracked down Richard Twiss at a defense research lab and the two working out the theory of intensity correlations for long-baseline radio interferometry. Using facilities at the famous Jodrell Bank Radio Observatory at Manchester, they demonstrated the principle of their intensity interferometer and measured the angular size of Cygnus A and Cassiopeia A, two of the strongest radio sources in the Northern sky.
One of the surprising side benefits of the intensity interferometer over field-based interferometry was insensitivity to environmental phase fluctuations. For radio astronomy the biggest source of phase fluctuations was the ionosphere, and the new intensity interferometer was immune to its fluctuations. Phase fluctuations had also been the limiting factor for the Michelson stellar interferometer which had limited its use to only about half a dozen stars, so Hanbury Brown and Twiss decided to revisit visible stellar interferometry using their new concept of intensity interferometry.
To illustrate the principle for visible wavelengths, Hanbury Brown and Twiss performed a laboratory experiment to correlate intensity fluctuations in two receivers illuminated by a common source through a beam splitter. The intensity correlations were detected and measured as a function of path length change, illustrating an excess correlation in noise for short path lengths that decayed as the path length increased. They published their results in Nature magazine in 1956 that immediately ignited a firestorm of protest from physicists .
In the 1950’s, many physicists had embraced the discrete properties of the photon and had developed a misleading mental picture of photons as individual and indivisible particles that could only go one way or another from a beam splitter, but not both. Therefore, the argument went, if the photon in an attenuated beam was detected in one detector at the output of a beam splitter, then it cannot be detected at the other. This would produce an anticorrelation in coincidence counts at the two detectors. However, the Hanbury Brown Twiss (HBT) data showed a correlation from the two detectors. This launched an intense controversy in which some of those who accepted the results called for a radical new theory of the photon, while most others dismissed the HBT results as due to systematics in the light source. The heart of this controversy was quickly understood by the Nobel laureate E. M Purcell. He correctly pointed out that photons are bosons and are indistinguishable discrete particles and hence are likely to “bunch” together, according to quantum statistics, even under low light conditions . Therefore, attenuated “chaotic” light would indeed show photodetector correlations, even if the average photon number was less than a single photon at a time, the photons would still bunch.
The bunching of photons in light is a second order effect that moves beyond the first-order interference effects of Young’s double slit, but even here the quantum nature of light is not required. A semiclassical theory of light emission from a spectral line with a natural bandwidth also predicts intensity correlations, and the correlations are precisely what would be observed for photon bunching. Therefore, even the second-order HBT results, when performed with natural light sources, do not distinguish between classical and quantum effects in the experimental results. But this reliance on natural light sources was about to change fundmaentally with the invention of the laser.
Invention of the Laser : Ted Maiman (1959)
One of the great scientific breakthroughs of the 20th century was the nearly simultaneous yet independent realization by several researchers around 1951 (by Charles H. Townes of Columbia University, by Joseph Weber of the University of Maryland, and by Alexander M. Prokhorov and Nikolai G. Basov at the Lebedev Institute in Moscow) that clever techniques and novel apparati could be used to produce collections of atoms that had more electrons in excited states than in ground states. Such a situation is called a population inversion. If this situation could be attained, then according to Einstein’s 1917 theory of photon emission, a single photon would stimulate a second photon, which in turn would stimulate two additional electrons to emit two identical photons to give a total of four photons −− and so on. Clearly this process turns a single photon into a host of photons, all with identical energy and phase.
Charles Townes and his research group were the first to succeed in 1953 in producing a device based on ammonia molecules that could work as an intense source of coherent photons. The initial device did not amplify visible light, but amplified microwave photons that had wavelengths of about 3 centimeters. They called the process microwave amplification by stimulated emission of radiation, hence the acronym “MASER”. Despite the significant breakthrough that this invention represented, the devices were very expensive and difficult to operate. The maser did not revolutionize technology, and some even quipped that the acronym stood for “Means of Acquiring Support for Expensive Research”. The maser did, however, launch a new field of study, called quantum electronics, that was the direct descendant of Einstein’s 1917 paper. Most importantly, the existence and development of the maser became the starting point for a device that could do the same thing for light.
The race to develop an optical maser (later to be called laser, for light amplification by stimulated emission of radiation) was intense. Many groups actively pursued this holy grail of quantum electronics. Most believed that it was possible, which made its invention merely a matter of time and effort. This race was won by Theodore H. Maiman at Hughes Research Laboratory in Malibu California in 1960 . He used a ruby crystal that was excited into a population inversion by an intense flash tube (like a flash bulb) that had originally been invented for flash photography. His approach was amazingly simple −− blast the ruby with a high-intensity pulse of light and see what comes out −− which explains why he was the first. Most other groups had been pursuing much more difficult routes because they believed that laser action would be difficult to achieve.
Perhaps the most important aspect of Maiman’s discovery was that it demonstrated that laser action was actually much simpler than people anticipated, and that laser action is a fairly common phenomenon. His discovery was quickly repeated by other groups, and then additional laser media were discovered such as helium-neon gas mixtures, argon gas, carbon dioxide gas, garnet lasers and others. Within several years, over a dozen different material and gas systems were made to lase, opening up wide new areas of research and development that continues unabated to this day. It also called for new theories of optical coherence to explain how coherent laser light interacted with matter.
Coherent States : Glauber (1963)
The HBT experiment had been performed with attenuated chaotic light that had residual coherence caused by the finite linewidth of the filtered light source. The theory of intensity correlations for this type of light was developed in the 1950’s by Emil Wolf and Leonard Mandel using a semiclassical theory in which the statistical properties of the light was based on electromagnetics without a direct need for quantized photons. The HBT results were fully consistent with this semiclassical theory. However, after the invention of the laser, new “coherent” light sources became available that required a fundamentally quantum depiction.
Roy Glauber was a theoretical physicist who received his PhD working with Julian Schwinger at Harvard. He spent several years as a post-doc at Princeton’s Institute for Advanced Study starting in 1949 at the time when quantum field theory was being developed by Schwinger, Feynman and Dyson. While Feynman was off in Brazil for a year learning to play the bongo drums, Glauber filled in for his lectures at Cal Tech. He returned to Harvard in 1952 in the position of an assistant professor. He was already thinking about the quantum aspects of photons in 1956 when news of the photon correlations in the HBT experiment were published, and when the laser was invented three years later, he began developing a theory of photon correlations in laser light that he suspected would be fundamentally different than in natural chaotic light.
Because of his background in quantum field theory, and especially quantum electrodynamics, it was a fairly easy task to couch the quantum optical properties of coherent light in terms of Dirac’s creation and annihilation operators of the electromagnetic field. Related to the minimum-uncertainty wave functions derived initially by Schrödinger in the late 1920’s, Glauber developed a “coherent state” operator that was a minimum uncertainty state of the quantized electromagnetic field . This coherent state represents a laser operating well above the lasing threshold and predicted that the HBT correlations would vanish. Glauber was awarded the Nobel Prize in Physics in 2005 for his work on such “Glauber” states in quantum optics.
Single-Photon Optics: Kimble and Mandel (1977)
Beyond introducing coherent states, Glauber’s new theoretical approach, and parallel work by George Sudarshan around the same time , provided a new formalism for exploring quantum optical properties in which fundamentally quantum processes could be explored that could not be predicted using only semiclassical theory. For instance, one could envision producing photon states in which the photon arrivals at a detector could display the kind of anti-bunching that had originally been assumed (in error) by the critics of the HBT experiment. A truly one-photon state, also known as a Fock state or a number state, would be the extreme limit in which the quantum field possessed a single quantum that could be directed at a beam splitter and would emerge either from one side or the other with complete anti-correlation. However, generating such a state in the laboratory remained a challenge.
In 1975 by Carmichel and Walls predicted that resonance fluorescence could produce quantized fields that had lower correlations than coherent states . In 1977 H. J. Kimble, M. Dagenais and L. Mandel demonstrated, for the first time, photon antibunching between two photodetectors at the two ports of a beam splitter . They used a beam of sodium atoms pumped by a dye laser.
This first demonstration of photon antibunching represents a major milestone in the history of quantum optics. Taylor’s first-order experiments in 1909 showed no difference between classical electromagnetic waves and a flux of photons. Similarly the second-order HBT experiment of 1956 using chaotic light could be explained equally well using classical or quantum approaches to explain the observed photon correlations. Even laser light (when the laser is operated far above threshold) produced classic “classical” wave effects with only the shot noise demonstrating the discreteness of photon arrivals. Only after the availability of “quantum” light sources, beginning with the work of Kimble and Mandel, could photon numbers be manipulated at will, launching the modern era of quantum optics. Later experiments by them and others have continually improved the control of photon states.
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- 1905 – A. Einstein (1905). “Generation and conversion of light with regard to a heuristic point of view.” Annalen Der Physik 17(6): 132-148.
- 1909 – A. Einstein (1909). “On the current state of radiation problems.” Physikalische Zeitschrift 10: 185-193.
- 1909 – G.I. Taylor: Proc. Cam. Phil. Soc. Math. Phys. Sci. 15 , 114 (1909) Single photon double-slit experiment
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- 1916 – Einstein, A. (1916). “Strahlungs-Emission un -Absorption nach der Quantentheorie.” Verh. Deutsch. Phys. Ges. 18: 318.. Einstein predicts stimulated emission
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- 1926 – Lewis, G. N. (1926). “The conservation of photons.” Nature 118: 874-875.. Gilbert Lewis named “photon”
- 1927 – D. Dirac, P. A. M. (1927). “The quantum theory of the emission and absorption of radiation.” Proceedings of the Royal Society of London Series a-Containing Papers of a Mathematical and Physical Character 114(767): 243-265.
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- 1956 – R. Hanbury-Brown, R.W. Twiss: Nature 177 , 27 (1956) Photon bunching
- 1963 – R. J. Glauber: Phys. Rev. 130 , 2529 (1963) Coherent states
- 1963 – E. C. G. Sudarshan: Phys. Rev. Lett. 10, 277 (1963) Coherent states
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- 1967 – B. R. Mollow, R. J. Glauber: Phys. Rev. 160, 1097 (1967); 162, 1256 (1967) Parametric converter
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- 1975 – Carmichael, H. J. and D. F. Walls (1975). Journal of Physics B-Atomic Molecular and Optical Physics 8(6): L77-L81. Photon anti-bunching predicted in resonance fluorescence
- 1977 – H. J. Kimble, M. Dagenais and L. Mandel (1977) Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691-5: Kimble, Dagenais and Mandel demonstrate the effect of antibunching
• Parts of this blog are excerpted from Mind at Light Speed, D. Nolte (Free Press, 2001) that tells the story of light’s central role in telecommunications and in the future of optical and quantum computers.
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