A Short History of the Photon

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 [1], 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 [2].  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 [3] 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 [4].  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 [5].  Partly based on Milliken’s confirmation of Einstein’s theory of the photon, Einstein was awarded the Nobel Prize in Physics in 1921.

Einstein at a blackboard.

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 [6].  The photon was given its modern name by Gilbert Lewis in 1926 [7].

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.

G. I. Taylor

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 [8].  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 [4], 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 [9]

Paul Dirac in his early days.

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?” [10].

Bohr and Einstein at Paul Ehrenfest’s house in 1925.

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 [11], 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.

Entangled versus separable states. When the states are separable, no measurement on photon A has any relation to measurements on photon B. However, in the entangled case, all measurements on A are related to measurements on B (and vice versa) regardless of what decision is made to make what measurement on either photon, or whether the photons are separated by great distance. The entangled wave-function is “nonlocal” in the sense that it encompasses both particles at the same time, no matter how far apart they are.

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.

R. Hanbury Brown

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 [12].

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 [13]. 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.

Theodore Maiman

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 [14]. 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.

Roy Glauber

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 [15]. 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 [16], 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 [17]. 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 [18]. 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.

TimeLine:

  • 1900 – Planck (1901). “Law of energy distribution in normal spectra.” Annalen Der Physik 4(3): 553-563.
  • 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
  • 1915 – Millikan, R. A. (1916). “A direct photoelectric determination of planck’s “h.”.” Physical Review 7(3): 0355-0388. Photoelectric effect.
  • 1916 – Einstein, A. (1916). “Strahlungs-Emission un -Absorption nach der Quantentheorie.” Verh. Deutsch. Phys. Ges. 18: 318.. Einstein predicts stimulated emission
  • 1923 –Compton, Arthur H. (May 1923). “A Quantum Theory of the Scattering of X-Rays by Light Elements”. Physical Review. 21 (5): 483–502.
  • 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.
  • 1932 – E. P. Wigner: Phys. Rev. 40, 749 (1932)
  • 1935 – A. Einstein, B. Podolsky, N. Rosen: Phys. Rev. 47 , 777 (1935). EPR paradox.
  • 1935 – N. Bohr: Phys. Rev. 48 , 696 (1935). Bohr’s response to the EPR paradox.
  • 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
  • 1964 – P. L. Kelley, W.H. Kleiner: Phys. Rev. 136 , 316 (1964)
  • 1966 – F. T. Arecchi, E. Gatti, A. Sona: Phys. Rev. Lett. 20 , 27 (1966); F.T. Arecchi, Phys. Lett. 16 , 32 (1966)
  • 1966 – J. S. Bell: Physics 1 , 105 (1964); Rev. Mod. Phys. 38 , 447 (1966) Bell inequalities
  • 1967 – R. F. Pfleegor, L. Mandel: Phys. Rev. 159 , 1084 (1967) Interference at single photon level
  • 1967 – M. O. Scully, W.E. Lamb: Phys. Rev. 159 , 208 (1967).  Quantum theory of laser
  • 1967 – B. R. Mollow, R. J. Glauber: Phys. Rev. 160, 1097 (1967); 162, 1256 (1967) Parametric converter
  • 1969 – M. O. Scully, W.E. Lamb: Phys. Rev. 179 , 368 (1969).  Quantum theory of laser
  • 1969 – M. Lax, W.H. Louisell: Phys. Rev. 185 , 568 (1969).  Quantum theory of laser
  • 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

References

• 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.

[1] Planck (1901). “Law of energy distribution in normal spectra.” Annalen Der Physik 4(3): 553-563.

[2] A. Einstein (1905). “Generation and conversion of light with regard to a heuristic point of view.” Annalen Der Physik 17(6): 132-148

[3] A. Einstein (1909). “On the current state of radiation problems.” Physikalische Zeitschrift 10: 185-193.

[4] Einstein, A. (1916). “Strahlungs-Emission un -Absorption nach der Quantentheorie.” Verh. Deutsch. Phys. Ges. 18: 318; Einstein, A. (1917). “Quantum theory of radiation.” Physikalische Zeitschrift 18: 121-128.

[5] Millikan, R. A. (1916). “A direct photoelectric determination of planck‘s “h.”.” Physical Review 7(3): 0355-0388.

[6] Compton, A. H. (1923). “A quantum theory of the scattering of x-rays by light elements.” Physical Review 21(5): 0483-0502.

[7] Lewis, G. N. (1926). “The conservation of photons.” Nature 118: 874-875.

[8] Taylor, G. I. (1910). “Interference fringes with feeble light.” Proceedings of the Cambridge Philosophical Society 15: 114-115.

[9] 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.

[10] Einstein, A., B. Podolsky and N. Rosen (1935). “Can quantum-mechanical description of physical reality be considered complete?” Physical Review 47(10): 0777-0780.

[11] Bohr, N. (1935). “Can quantum-mechanical description of physical reality be considered complete?” Physical Review 48(8): 696-702.

[12] Brown, R. H. and R. Q. Twiss (1956). “Correlation Between Photons in 2 Coherent Beams of Light.” Nature 177(4497): 27-29; [1] R. H. Brown and R. Q. Twiss, “Test of a new type of stellar interferometer on Sirius,” Nature, vol. 178, no. 4541, pp. 1046-1048, (1956).

[13] Purcell, E. M. (1956). “Question of Correlation Between Photons in Coherent Light Rays.” Nature 178(4548): 1448-1450.

[14] Maimen, T. H. (1960). “Stimulated optical radiation in ruby.” Nature 187: 493.

[15] Glauber, R. J. (1963). “Photon Correlations.” Physical Review Letters 10(3): 84.

[16] Sudarshan, E. C. G. (1963). “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams.” Physical Review Letters 10(7): 277-&.; Mehta, C. L. and E. C. Sudarshan (1965). “Relation between quantum and semiclassical description of optical coherence.” Physical Review 138(1B): B274.

[17] Carmichael, H. J. and D. F. Walls (1975). “Quantum treatment of spontaneous emission from a strongly driven 2-level atom.” Journal of Physics B-Atomic Molecular and Optical Physics 8(6): L77-L81.

[18] Kimble, H. J., M. Dagenais and L. Mandel (1977). “Photon anti bunching in resonance fluorescence.” Physical Review Letters 39(11): 691-695.

Quantum Seeing without Looking? The Strange Physics of Quantum Sensing

Quantum sensors have amazing powers.  They can detect the presence of an obstacle without ever interacting with it.  For instance, consider a bomb that is coated with a light sensitive layer that sets off the bomb if it absorbs just a single photon.  Then put this bomb inside a quantum sensor system and shoot photons at it.  Remarkably, using the weirdness of quantum mechanics, it is possible to design the system in such a way that you can detect the presence of the bomb using photons without ever setting it off.  How can photons see the bomb without illuminating it?  The answer is a bizarre side effect of quantum physics in which quantum wavefunctions are recognized as the root of reality as opposed to the pesky wavefunction collapse at the moment of measurement.

The ability for a quantum system to see an object with light, without exposing it, is uniquely a quantum phenomenon that has no classical analog.

All Paths Lead to Feynman

When Richard Feynman was working on his PhD under John Archibald Wheeler at Princeton in the early 1940’s he came across an obscure paper written by Paul Dirac in 1933 that connected quantum physics with classical Lagrangian physics.  Dirac had recognized that the phase of a quantum wavefunction was analogous to the classical quantity called the “Action” that arises from Lagrangian physics.  Building on this concept, Feynman constructed a new interpretation of quantum physics, known as the “many histories” interpretation, that occupies the middle ground between Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics.  One of the striking consequences of the many histories approach is the emergence of the principle of least action—a classical concept—into interpretations of quantum phenomena.  In this approach, Feynman considered ALL possible histories for the propagation of a quantum particle from one point to another, he tabulated the quantum action in the phase factor, and he then summed all of these histories.

One of the simplest consequences of the sum over histories is a quantum interpretation of Snell’s law of refraction in optics.  When summing over all possible trajectories of a photon from a point above to a point below an interface, there are a subset of paths for which the action integral varies very little from one path in the subset to another.  The consequence of this is that the phases of all these paths add constructively, producing a large amplitude to the quantum wavefunction along the centroid of these trajectories.  Conversely, for paths far away from this subset, the action integral takes on many values and the phases tend to interfere destructively, canceling the wavefunction along these other paths.  Therefore, the most likely path of the photon between the two points is the path of maximum constructive interference and hence the path of stationary action.  It is simple so show that this path is none other than the classical path determined by Snell’s Law and equivalently by Fermat’s principle of least time.  With the many histories approach, we can add the principle of least (or stationary) action to the list of explanations of Snell’s Law.  This argument holds as well for an electron (with mass and a de Broglie wavelength) as it does for a photon, so this not just a coincidence specific to optics but is a fundamental part of quantum physics.

A more subtle consequence of the sum over histories view of quantum phenomena is Young’s double slit experiment for electrons, shown at the top of Fig 1.  The experiment consists of a source that emits only a single electron at a time that passes through a double-slit mask to impinge on an electron detection screen.  The wavefunction for a single electron extends continuously throughout the full spatial extent of the apparatus, passing through both slits.  When the two paths intersect at the screen, the difference in the quantum phases of the two paths causes the combined wavefunction to have regions of total constructive interference and other regions of total destructive interference.  The probability of detecting an electron is proportional to the squared amplitude of the wavefunction, producing a pattern of bright stripes separated by darkness.  At positions of destructive interference, no electrons are detected when both slits are open.  However, if an opaque plate blocks the upper slit, then the interference pattern disappears, and electrons can be detected at those previously dark locations.  Therefore, the presence of the object can be deduced by the detection of electrons at locations that should be dark.

Fig. 1  Demonstration of the sum over histories in a double-slit experiment for electrons. In the upper frame, the electron interference pattern on the phosphorescent screen produces bright and dark stripes.  No electrons hit the screen in a dark stripe.  When the upper slit is blocked (bottom frame), the interference pattern disappears, and an electron can arrive at the location that had previously been dark.

Consider now when the opaque plate is an electron-sensitive detector.  In this case, a single electron emitted by the source can be detected at the screen or at the plate.  If it is detected at the screen, it can appear at the location of a dark fringe, heralding the presence of the opaque plate.  Yet the quantum conundrum is that when the electron arrives at a dark fringe, it must be detected there as a whole, it cannot be detected at the electron-sensitive plate too.  So how does the electron sense the presence of the detector without exposing it, without setting it off? 

In Feynman’s view, the electron does set off the detector as one possible history.  And that history interferes with the other possible history when the electron arrives at the screen.  While that interpretation may seem weird, mathematically it is a simple statement that the plate blocks the wavefunction from passing through the upper slit, so the wavefunction in front of the screen, resulting from all possible paths, has no interference fringes (other than possible diffraction from the lower slit).  From this point of view, the wavefunction samples all of space, including the opaque plate, and the eventual absorption of a photon one place or another has no effect on the wavefunction.  In this sense, it is the wavefunction, prior to any detection event, that samples reality.  If the single electron happens to show up at a dark fringe at the screen, the plate, through its effects on the total wavefunction, has been detected without interacting with the photon. 

This phenomenon is known as an interaction-free measurement, but there are definitely some semantics issues here.  Just because the plate doesn’t absorb a photon, it doesn’t mean that the plate plays no role.  The plate certainly blocks the wavefunction from passing through the upper slit.  This might be called an “interaction”, but that phrase it better reserved for when the photon is actually absorbed, while the role of the plate in shaping the wavefunction is better described as one of the possible histories.

Quantum Seeing in the Dark

Although Feynman was thinking hard (and clearly) about these issues as he presented his famous lectures in physics at Cal Tech during 1961 to 1963, the specific possibility of interaction-free measurement dates more recently to 1993 when Avshalom C. Elitzur and Lev Vaidman at Tel Aviv University suggested a simple Michelson interferometer configuration that could detect an object half of the time without interacting with it [1].  They are the ones who first pressed this point home by thinking of a light-sensitive bomb.  There is no mistaking when a bomb goes off, so it tends to give an exaggerated demonstration of the interaction-free measurement. 

The Michelson interferometer for interaction-free measurement is shown in Fig. 2.  This configuration uses a half-silvered beamsplitter to split the possible photon paths.  When photons hit the beamsplitter, they either continue traveling to the right, or are deflected upwards.  After reflecting off the mirrors, the photons again encounter the beamsplitter, where, in each case, they continue undeflected or are reflected.  The result is that two paths combine at the beamsplitter to travel to the detector, while two other paths combine to travel back along the direction of the incident beam. 

Fig. 2 A quantum-seeing in the dark (QSD) detector with a photo-sensitive bomb. A single photon is sent into the interferometer at a time. If the bomb is NOT present, destructive interference at the detector guarantees that the photon is not detected. However, if the bomb IS present, it destroys the destructive interference and the photon can arrive at the detector. That photon heralds the presence of the bomb without setting it off. (Reprinted from Mind @ Light Speed)

The paths of the light beams can be adjusted so that the beams that combine to travel to the detector experience perfect destructive interference.  In this situation, the detector never detects light, and all the light returns back along the direction of the incident beam.  Quantum mechanically, when only a single photon is present in the interferometer at a time, we would say that the quantum wavefunction of the photon interferes destructively along the path to the detector, and constructively along the path opposite to the incident beam, and the detector would detect no photons.  It is clear that the unobstructed path of both beams results in the detector making no detections.

Now place the light sensitive bomb in the upper path.  Because this path is no longer available to the photon wavefunction, the destructive interference of the wavefunction along the detector path is removed.  Now when a single photon is sent into the interferometer, three possible things can happen.  One, the photon is reflected by the beamsplitter and detonates the bomb.  Two, the photon is transmitted by the beamsplitter, reflects off the right mirror, and is transmitted again by the beamsplitter to travel back down the incident path without being detected by the detector.  Three, the photon is transmitted by the beamsplitter, reflects off the right mirror, and is reflected off the beamsplitter to be detected by the detector. 

In this third case, the photon is detected AND the bomb does NOT go off, which succeeds at quantum seeing in the dark.  The odds are much better than for Young’s experiment.  If the bomb is present, it will detonate a maximum of 50% of the time.  The other 50%, you will either detect a photon (signifying the presence of the bomb), or else you will not detect a photon (giving an ambiguous answer and requiring you to perform the experiment again).  When you perform the experiment again, you again have a 50% chance of detonating the bomb, and a 25% chance of detecting it without it detonating, but again a 25% chance of not detecting it, and so forth.  All in all, every time you send in a photon, you have one chance in four of seeing the bomb without detonating it.  These are much better odds than for the Young’s apparatus where only exact detection of the photon at a forbidden location would signify the presence of the bomb.

It is possible to increase your odds above one chance in four by decreasing the reflectivity of the beamsplitter.  In practice, this is easy to do simply by depositing less and less aluminum on the surface of the glass plate.  When the reflectivity gets very low, let us say at the level of 1%, then most of the time the photon just travels back along the direction it came and you have an ambiguous result.  On the other hand, when the photon does not return, there is an equal probability of detonation as detection.  This means that, though you may send in many photons, your odds for eventually seeing the bomb without detonating it are nearly 50%, which is a factor of two better odds than for the half-silvered beamsplitter.  A version of this experiment was performed by Paul Kwiat in 1995 as a postdoc at Innsbruck with Anton Zeilinger.  It was Kwiat who coined the phrase “quantum seeing in the dark” as a catchier version of “interaction-free measurement” [2].

A 50% chance of detecting the bomb without setting it off sounds amazing, until you think that there is a 50% chance that it will go off and kill you.  Then those odds don’t look so good.  But optical phenomena never fail to surprise, and they never let you down.  A crucial set of missing elements in the simple Michelson experiment was polarization-control using polarizing beamsplitters and polarization rotators.  These are common elements in many optical systems, and when they are added to the Michelson quantum sensor, they can give almost a 100% chance of detecting the bomb without setting it off using the quantum Zeno effect.

The Quantum Zeno Effect

Photons carry polarization as their prime quantum number, with two possible orientations.  These can be defined in different ways, but the two possible polarizations are orthogonal to each other.  For instance, these polarization pairs can be vertical (V)  and horizontal (H), or they can be right circular  and left circular.  One of the principles of quantum state evolution is that a quantum wavefunction can be maintained in a specific state, even if it has a tendency naturally to drift out of that state, by repeatedly making a quantum measurement that seeks to measure deviations from that state.  In practice, the polarization of a photon can be maintained by repeatedly passing it through a polarizing beamsplitter with the polarization direction parallel to the original polarization of the photon.  If there is a deviation in the photon polarization direction by a small angle, then a detector on the side port of the polarizing beamsplitter will fire with a probability equal to the square of the sine of the deviation.  If the deviation angle is very small, say Δθ, then the probability of measuring the deviation is proportional to (Δθ)2, which is an even smaller number.  Furthermore, the probability that the photon will transmit through the polarizing beamsplitter is equal to 1-(Δθ)2 , which is nearly 100%.

This is what happens in Fig. 3 when the photo-sensitive bomb IS present. A single H-polarized photon is injected through a switchable mirror into the interferometer on the right. In the path of the photon is a polarization rotator that rotates the polarization by a small angle Δθ. There is nearly a 100% chance that the photon will transmit through the polarizing beamsplitter with perfect H-polarization reflect from the mirror and return through the polarizing beamsplitter, again with perfect H-polarization to pass through the polarization rotator to the switchable mirror where it reflects, gains another increment to its polarization angle, which is still small, and transmits through the beamsplitter, etc. At each pass, the photon polarization is repeatedly “measured” to be horizontal. After a number of passes N = π/Δθ/2, the photon is switched out of the interferometer and is transmitted through the external polarizing beamsplitter where it is detected at the H-photon detector.

Now consider what happens when the bomb IS NOT present. This time, even though there is a high amplitude for the transmitted photon, there is that Δθ amplitude for reflection out the V port. This small V-amplitude, when it reflects from the mirror, recombines with the H-amplitude at the polarizing beamsplitter to produce a polarization that has the same tilted polarizaton that it started with, sending it back in the direction from which it came. (In this situation, the detector on the “dark” port of the internal beamsplitter never sees the photon because of destructive interference along this path.) The photon is then rotated once more by the polarization rotator, and the photon polarization is rotated again, etc.. Now, after a number of passes N = π/Δθ/2, the photon has acquired a V polarization and is switched out of the interferometer. At the external polarizing beamsplitter it is reflected out of the V-port where it is detected at the V-photon detector.

Fig. 3  Quantum Zeno effect for interaction-free measurement.  If the bomb is present, the H-photon detector detects the output photon without setting it off.  The switchable mirror ejects the photon after it makes π/Δθ/2 round trips in the polarizing interferometer.

The two end results of this thought experiment are absolutely distinct, giving a clear answer to the question whether the bomb is present or not. If the bomb IS present, the H-detector fires. If the bomb IS NOT present, then the V-detector fires. Through all of this, the chance to set off the bomb is almost zero. Therefore, this quantum Zeno interaction-free measurement detects the bomb with nearly 100% efficiency with almost no chance of setting it off. This is the amazing consequence of quantum physics. The wavefunction is affected by the presence of the bomb, altering the interference effects that allow the polarization to rotate. But the likelihood of a photon being detected by the bomb is very low.

On a side note: Although ultrafast switchable mirrors do exist, the experiment was much easier to perform by creating a helix in the optical path through the system so that there is only a finite number of bounces of the photon inside the cavity. See Ref. [2] for details.

In conclusion, the ability for a quantum system to see an object with light, without exposing it, is uniquely a quantum phenomenon that has no classical analog.  No E&M wave description can explain this effect.


Further Reading

I first wrote about quantum seeing the dark in my 2001 book on the future of optical physics and technology: Nolte, D. D. (2001). Mind at Light Speed : A new kind of intelligence. (New York, Free Press)

More on the story of Feynman and Wheeler and what they were trying to accomplish is told in Chapter 8 of Galileo Unbound on the physics and history of dynamics: Nolte, D. D. (2018). Galileo Unbound: A Path Across Life, the Universe and Everything (Oxford University Press).

Paul Kwiat introduced to the world to interaction-free measurements in 1995 in this illuminating Scientific American article: Kwiat, P., H. Weinfurter and A. Zeilinger (1996). “Quantum seeing in the dark – Quantum optics demonstrates the existence of interaction-free measurements: the detection of objects without light-or anything else-ever hitting them.” Scientific American 275(5): 72-78.


References

[1] Elitzur, A. C. and L. Vaidman (1993). “QUANTUM-MECHANICAL INTERACTION-FREE MEASUREMENTS.” Foundations of Physics 23(7): 987-997.

[2] Kwiat, P., H. Weinfurter, T. Herzog, A. Zeilinger and M. A. Kasevich (1995). “INTERACTION-FREE MEASUREMENT.” Physical Review Letters 74(24): 4763-4766.