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Journal of Physics Conference Series

Neoclassical light – An assessment of the voyage into Hilbert space

Harry J. Kimble

Published Nov 1, 2009• 3 citations
Publisher

Abstract

I thank Rodger Walser and his colleagues for organizing this conference to celebrate George \nSudarshan’s birthday and landmark achievements in science. It is an honor for me to be here and \nalso a great pleasure to be back in Austin to join the chorus of the FOGS. \nI would like begin with a brief historical introduction and then turn to topics that we \nhaven’t heard so much about thus far in the symposium, namely experiments in Quantum Optics. \nLet me remind you that blackbody radiation has had a profound impact on physics since the time \nof Planck. However, even in more modern times after the development of quantum mechanics \nand quantum electrodynamics, one really did not know how to describe the underlying field \nfluctuations as required for diverse interference phenomena. Emil Wolf laid critical foundations \nfor this enterprise with his theory of classical coherence developed in collaboration with Max \nBorn in their classic book Principles of Optics. \nA great challenge to the physics community was the experiment by R. H. Brown and R. \nQ. Twiss in 1956 [1], which led to a confusing and controversial time for photons and fields. In \n1958 Leonard Mandel helped to resolve the controversy by explaining how light fluctuations are \nconverted to photocurrents in the detection process, albeit in with a classical description of the \nfield [2]. The confusion arose from the effort to understand, on the one hand, interference \nphenomena that are expressed in terms of the complex amplitude of the electromagnetic field, for \nwhich only a classical description was available. On the other hand, quantum electrodynamics \nhad been developed based upon energy eigenstates (i.e., Fock states) with photons as quanta. It \nwas really difficult to understand how the electric and magnetic fields behave in terms of these \nquantum states. For example, the expectation value of any electromagnetic field is zero in a Fock \nstate. The confusion was compounded by the historic invention of the maser and laser and by the \npressing need for quantum theories of the dynamical processes of these and other laboratory \nadvances.

DOI
10.1088/1742-6596/196/1/012015

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This book attempts to bridge the enormous gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light in one step. Hence, while it is suitable as a reference for the specialist in quantum optics, it also targets the nonspecialists from other disciplines who need to understand light and its uses in research. With a unique approach it introduces a single analytic tool, namely the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross‐disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including laser tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency (EIT), squeezed light, and cavity quantum electrodynamics (QED). A systematic approach is used that starts with the simplest systems – stationary two‐level atoms – then introduces atomic motion, adds more energy levels, and moves on to discuss first‐, second‐, and third‐order coherence effects that are the basis for analyzing new optical phenomena in incompletely characterized systems. Unconventional examples and original problems are used to engage even seasoned researchers in exploring a mathematical methodology with which they can tackle virtually any new problem involving light. An extensive bibliography makes connections with mathematical techniques and subject areas which can extend the benefit of each section to guide readers further. The steady progression from “simple” to “elaborate” makes the book accessible not only to students from traditional subject areas that make use of light (physics, chemistry, electrical engineering, and materials science), but also to researchers from the “hyphenated” subjects of modern science and engineering: the biophysicists using mechanical effects of light, photochemists developing coherent control for rare species detection, biomedical engineers imaging through scattering media, electromechanical engineers working on molecular design of materials for electronics and space, electrical and computer engineers developing schemes for quantum computation, cryptography, frequency references, and so on. To try to identify techniques and ideas that are universal enough to be applied across the bewildering landscape of research on intersecting boundaries of emerging modern disciplines is a great challenge of out time. “Lectures on Light” offers selected insights on quantum dynamics and quantum theory of light for exactly this purpose.

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In the early hours of 9 February 2001, the physics community lost one of its most distinguished members, Leonard Mandel, after a long illness. Mandel was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester, having become emeritus only a few months before he died, at the age of 73, at his home in Pittsford, New York.Born on 9 May 1927 in Berlin, Germany, where his father had emigrated from Eastern Europe, Mandel received a BSc in mathematics and physics in 1947 and a PhD in nuclear physics in 1951 from Birkbeck College, University of London, in the UK. He became a technical officer at Imperial Chemical Industries Ltd in Welwyn, UK, in 1951. In 1955, he became a lecturer and, later, senior lecturer at Imperial College, University of London. He remained at Imperial College until 1964, when he joined the University of Rochester as a professor of physics. Mandel is widely credited as being one of the founding fathers of the field of quantum optics. Although he made seminal contributions across most of quantum optics, the central theme of his research was the exploration of the nature of light through insightful theoretical analyses and a set of pioneering experiments that have become landmarks in the field. Not since the beginning of quantum mechanics has an individual so intimately investigated and so dramatically advanced our understanding of the quantum aspects of light.Mandel’s early interest in quantum optics was stimulated by the Hanbury Brown–Twiss experiments, in which correlations in the fluctuations of photocurrents from two photodetectors illuminated by light from a distant source reveal information about the spatial coherence properties of the light. Mandel’s entrance into the debate about the appropriate theoretical description of this experiment was a basic paper published in 1958 in the Proceedings of the Physical Society (London) in which the so-called Mandel formula for photoelectric counting made its first appearance.In 1968, Mandel’s research group performed the now famous experiment involving interference at the single photon level: Two beams derived from independent lasers were attenuated to a level such that the average interval between photon emissions was very long compared to the transit time through the apparatus. Interference fringes were nonetheless recorded. As in the Hanbury Brown–Twiss experiment, the detection scheme explored interference of the fourth order in the amplitudes of the fields, as opposed to the more familiar second-order interference (as in a Michelson interferometer, for example), but now with an ingenious extension. Over the next three decades, Mandel continued to refine fourth-order interferometry into a powerful tool for investigating the quantum nature of light. It is now a standard technique used worldwide.Perhaps spurred by the debate about the quantum statistical properties of lasers and other light sources, Mandel and his students were among the first to carry out basic experiments from 1967 to 1968 to elucidate the coherence properties of the laser in the transition from incoherent to coherent emission around threshold. In the ensuing decades, those early studies grew into diverse investigations of more complex laser behavior, including mode correlation and competition in ring lasers, and optical bistability and first-order phase transitions in dye lasers. Mandel played a leading role in the quest to investigate states of the electromagnetic field with manifestly quantum or nonclassical characteristics. In 1977, his group made a historic advance in this endeavor with the first observation of photon anti-bunching in the case of the fluorescent light from a single atom. Subsequently, Mandel and one of his students made the first measurements of another nonclassical effect, namely, sub-Poissonian photon statistics. In the early 1980s, Mandel initiated what would become a landmark set of experiments involving pairs of photons produced by the fission of a pump photon in the process of parametric down conversion. Following earlier work by others on the correlation between photon pairs in atomic cascades, Mandel and his students first demonstrated a key nonclassical aspect of the down conversion process and were able to achieve a localized one-photon state.Pursuing the theme of fourth-order interference with pairs of photons in the late 1980s, Mandel and his students demonstrated quantum spatial beating, violations of local realism, and phase memory due to quantum entanglement with the vacuum. His group showed that P. A. M. Dirac’s well-known statement about single-photon interference must be modified to assert that, in fourth-order interference, a pair of photons interferes only with the pair itself. He and his students also introduced what became known as the Hong-Ou-Mandel interferometer. Beyond what had by then become “the standard model” of manifestly quantum effects, Mandel’s genius for probing the quantum realm led to advances throughout the 1990s that challenged and ultimately redefined our understanding of the quantum character of light and, more generally, of quantum measurement. For example, in 1991, Mandel and his students reported a remarkable experiment involving interference from the superposition of fields from two different but coherent parametric processes. They showed that the mere possibility of making a measurement destroyed an interference pattern, even if this possibility went unrealized. In 1995, Mandel’s group, in an experiment with photon pairs, demonstrated a central tenet of quantum mechanics: that there is no physical reality for elemental quantum processes in the absence of a measurement. Mandel supervised the thesis research of 39 students, many of whom have subsequently become leading figures in science and technology. He earned the lifelong respect of his students for his detailed and conscientious stewardship of their scientific development. He made frequent rounds of his laboratories to interact with each of his students and to provide help ranging from optical alignment and electronic design to theoretical calculations. Not wanting to interrupt a student at work, he would sometimes quietly approach in his soft-soled shoes to view the activity at hand, leading to more than a few startled heart skips. In response to a student’s query, “Can you see a signal yet?” as some component of an apparatus was being aligned, would come his distinctively British reply, “Not a sausage!” Once, when the need arose to regulate the water cooling for an oil diffusion pump, he solved the problem the next morning with a flow switch commandeered from a washing machine at home.In addition to his work at the frontiers of physics, Mandel was an excellent teacher. He had a special interest in neophyte science students and developed the first course at the University of Rochester for non-science majors, which he taught regularly for 20 years. From 1966 to 1995, he was one of the main organizers of a well-known series of international conferences called the Rochester Conferences on Coherence and Quantum Optics. Mandel was the coauthor of Optical Coherence and Quantum Optics (Cambridge U. Press, 1995) and the coeditor of several conference proceedings. In 1980, a paper on coherence properties of optical fields, which he coauthored in 1965, was designated a Citation Classic by the Institute of Scientific Publications. In 1988, that paper was listed as one of the 100 most-cited articles published in the Review of Modern Physics since 1955. Mandel received many top awards, including the Frederic Ives Medal (1993) and the Max Born Medal (1982) from the Optical Society of America. He received the Marconi Medal (1987) from the Italian Research Council and the Thomas Young Award (1989) from the British Institute of Physics. In May 2001, Mandel was elected posthumously to membership in the National Academy of Sciences.Mandel was a scientist with a warm personality, humility, compassion, and a delightful sense of humor. He enjoyed a happy family life with his wife Jeanne, a ballet teacher with whom he shared the love for ballet, and with their two children. He adored his four grandchildren and took lively interest in all their activities. Those of us who were fortunate to have been associated with Mandel as students, colleagues, or friends will remember him with deep affection and utmost respect. He will be greatly missed. Leonard Mandel PPT|High resolution© 2001 American Institute of Physics.

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I thank Rodger Walser and his colleagues for organizing this conference to celebrate George \nSudarshan’s birthday and landmark achievements in science. It is an honor for me to be here and \nalso a great pleasure to be back in Austin to join the chorus of the FOGS. \nI would like begin with a brief historical introduction and then turn to topics that we \nhaven’t heard so much about thus far in the symposium, namely experiments in Quantum Optics. \nLet me remind you that blackbody radiation has had a profound impact on physics since the time \nof Planck. However, even in more modern times after the development of quantum mechanics \nand quantum electrodynamics, one really did not know how to describe the underlying field \nfluctuations as required for diverse interference phenomena. Emil Wolf laid critical foundations \nfor this enterprise with his theory of classical coherence developed in collaboration with Max \nBorn in their classic book Principles of Optics. \nA great challenge to the physics community was the experiment by R. H. Brown and R. \nQ. Twiss in 1956 [1], which led to a confusing and controversial time for photons and fields. In \n1958 Leonard Mandel helped to resolve the controversy by explaining how light fluctuations are \nconverted to photocurrents in the detection process, albeit in with a classical description of the \nfield [2]. The confusion arose from the effort to understand, on the one hand, interference \nphenomena that are expressed in terms of the complex amplitude of the electromagnetic field, for \nwhich only a classical description was available. On the other hand, quantum electrodynamics \nhad been developed based upon energy eigenstates (i.e., Fock states) with photons as quanta. It \nwas really difficult to understand how the electric and magnetic fields behave in terms of these \nquantum states. For example, the expectation value of any electromagnetic field is zero in a Fock \nstate. The confusion was compounded by the historic invention of the maser and laser and by the \npressing need for quantum theories of the dynamical processes of these and other laboratory \nadvances.
This book attempts to bridge the enormous gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light in one step. Hence, while it is suitable as a reference for the specialist in quantum optics, it also targets the nonspecialists from other disciplines who need to understand light and its uses in research. With a unique approach it introduces a single analytic tool, namely the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross‐disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including laser tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency (EIT), squeezed light, and cavity quantum electrodynamics (QED). A systematic approach is used that starts with the simplest systems – stationary two‐level atoms – then introduces atomic motion, adds more energy levels, and moves on to discuss first‐, second‐, and third‐order coherence effects that are the basis for analyzing new optical phenomena in incompletely characterized systems. Unconventional examples and original problems are used to engage even seasoned researchers in exploring a mathematical methodology with which they can tackle virtually any new problem involving light. An extensive bibliography makes connections with mathematical techniques and subject areas which can extend the benefit of each section to guide readers further. The steady progression from “simple” to “elaborate” makes the book accessible not only to students from traditional subject areas that make use of light (physics, chemistry, electrical engineering, and materials science), but also to researchers from the “hyphenated” subjects of modern science and engineering: the biophysicists using mechanical effects of light, photochemists developing coherent control for rare species detection, biomedical engineers imaging through scattering media, electromechanical engineers working on molecular design of materials for electronics and space, electrical and computer engineers developing schemes for quantum computation, cryptography, frequency references, and so on. To try to identify techniques and ideas that are universal enough to be applied across the bewildering landscape of research on intersecting boundaries of emerging modern disciplines is a great challenge of out time. “Lectures on Light” offers selected insights on quantum dynamics and quantum theory of light for exactly this purpose.
In the early hours of 9 February 2001, the physics community lost one of its most distinguished members, Leonard Mandel, after a long illness. Mandel was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester, having become emeritus only a few months before he died, at the age of 73, at his home in Pittsford, New York.Born on 9 May 1927 in Berlin, Germany, where his father had emigrated from Eastern Europe, Mandel received a BSc in mathematics and physics in 1947 and a PhD in nuclear physics in 1951 from Birkbeck College, University of London, in the UK. He became a technical officer at Imperial Chemical Industries Ltd in Welwyn, UK, in 1951. In 1955, he became a lecturer and, later, senior lecturer at Imperial College, University of London. He remained at Imperial College until 1964, when he joined the University of Rochester as a professor of physics. Mandel is widely credited as being one of the founding fathers of the field of quantum optics. Although he made seminal contributions across most of quantum optics, the central theme of his research was the exploration of the nature of light through insightful theoretical analyses and a set of pioneering experiments that have become landmarks in the field. Not since the beginning of quantum mechanics has an individual so intimately investigated and so dramatically advanced our understanding of the quantum aspects of light.Mandel’s early interest in quantum optics was stimulated by the Hanbury Brown–Twiss experiments, in which correlations in the fluctuations of photocurrents from two photodetectors illuminated by light from a distant source reveal information about the spatial coherence properties of the light. Mandel’s entrance into the debate about the appropriate theoretical description of this experiment was a basic paper published in 1958 in the Proceedings of the Physical Society (London) in which the so-called Mandel formula for photoelectric counting made its first appearance.In 1968, Mandel’s research group performed the now famous experiment involving interference at the single photon level: Two beams derived from independent lasers were attenuated to a level such that the average interval between photon emissions was very long compared to the transit time through the apparatus. Interference fringes were nonetheless recorded. As in the Hanbury Brown–Twiss experiment, the detection scheme explored interference of the fourth order in the amplitudes of the fields, as opposed to the more familiar second-order interference (as in a Michelson interferometer, for example), but now with an ingenious extension. Over the next three decades, Mandel continued to refine fourth-order interferometry into a powerful tool for investigating the quantum nature of light. It is now a standard technique used worldwide.Perhaps spurred by the debate about the quantum statistical properties of lasers and other light sources, Mandel and his students were among the first to carry out basic experiments from 1967 to 1968 to elucidate the coherence properties of the laser in the transition from incoherent to coherent emission around threshold. In the ensuing decades, those early studies grew into diverse investigations of more complex laser behavior, including mode correlation and competition in ring lasers, and optical bistability and first-order phase transitions in dye lasers. Mandel played a leading role in the quest to investigate states of the electromagnetic field with manifestly quantum or nonclassical characteristics. In 1977, his group made a historic advance in this endeavor with the first observation of photon anti-bunching in the case of the fluorescent light from a single atom. Subsequently, Mandel and one of his students made the first measurements of another nonclassical effect, namely, sub-Poissonian photon statistics. In the early 1980s, Mandel initiated what would become a landmark set of experiments involving pairs of photons produced by the fission of a pump photon in the process of parametric down conversion. Following earlier work by others on the correlation between photon pairs in atomic cascades, Mandel and his students first demonstrated a key nonclassical aspect of the down conversion process and were able to achieve a localized one-photon state.Pursuing the theme of fourth-order interference with pairs of photons in the late 1980s, Mandel and his students demonstrated quantum spatial beating, violations of local realism, and phase memory due to quantum entanglement with the vacuum. His group showed that P. A. M. Dirac’s well-known statement about single-photon interference must be modified to assert that, in fourth-order interference, a pair of photons interferes only with the pair itself. He and his students also introduced what became known as the Hong-Ou-Mandel interferometer. Beyond what had by then become “the standard model” of manifestly quantum effects, Mandel’s genius for probing the quantum realm led to advances throughout the 1990s that challenged and ultimately redefined our understanding of the quantum character of light and, more generally, of quantum measurement. For example, in 1991, Mandel and his students reported a remarkable experiment involving interference from the superposition of fields from two different but coherent parametric processes. They showed that the mere possibility of making a measurement destroyed an interference pattern, even if this possibility went unrealized. In 1995, Mandel’s group, in an experiment with photon pairs, demonstrated a central tenet of quantum mechanics: that there is no physical reality for elemental quantum processes in the absence of a measurement. Mandel supervised the thesis research of 39 students, many of whom have subsequently become leading figures in science and technology. He earned the lifelong respect of his students for his detailed and conscientious stewardship of their scientific development. He made frequent rounds of his laboratories to interact with each of his students and to provide help ranging from optical alignment and electronic design to theoretical calculations. Not wanting to interrupt a student at work, he would sometimes quietly approach in his soft-soled shoes to view the activity at hand, leading to more than a few startled heart skips. In response to a student’s query, “Can you see a signal yet?” as some component of an apparatus was being aligned, would come his distinctively British reply, “Not a sausage!” Once, when the need arose to regulate the water cooling for an oil diffusion pump, he solved the problem the next morning with a flow switch commandeered from a washing machine at home.In addition to his work at the frontiers of physics, Mandel was an excellent teacher. He had a special interest in neophyte science students and developed the first course at the University of Rochester for non-science majors, which he taught regularly for 20 years. From 1966 to 1995, he was one of the main organizers of a well-known series of international conferences called the Rochester Conferences on Coherence and Quantum Optics. Mandel was the coauthor of Optical Coherence and Quantum Optics (Cambridge U. Press, 1995) and the coeditor of several conference proceedings. In 1980, a paper on coherence properties of optical fields, which he coauthored in 1965, was designated a Citation Classic by the Institute of Scientific Publications. In 1988, that paper was listed as one of the 100 most-cited articles published in the Review of Modern Physics since 1955. Mandel received many top awards, including the Frederic Ives Medal (1993) and the Max Born Medal (1982) from the Optical Society of America. He received the Marconi Medal (1987) from the Italian Research Council and the Thomas Young Award (1989) from the British Institute of Physics. In May 2001, Mandel was elected posthumously to membership in the National Academy of Sciences.Mandel was a scientist with a warm personality, humility, compassion, and a delightful sense of humor. He enjoyed a happy family life with his wife Jeanne, a ballet teacher with whom he shared the love for ballet, and with their two children. He adored his four grandchildren and took lively interest in all their activities. Those of us who were fortunate to have been associated with Mandel as students, colleagues, or friends will remember him with deep affection and utmost respect. He will be greatly missed. Leonard Mandel PPT|High resolution© 2001 American Institute of Physics.
The field of quantum optics has progressed rapidly in the last twenty five years with the advent of the laser. Over much of this period the phenomena studied could be described adequately by semiclassical treatments. Quite recently however, there has been a revival of interest in genuinely quantum mechanical effects. The Malvern Symposium of December 1985 brought together world experts for a meeting which concentrated largely on these quantum effects. The presentations in this unique meeting combine review material with the very latest results and so will be of value to students of quantum optics and measurement theory at all levels. The first articles cover the exciting topic of the generation of squeezed states of light in the laboratory, and their possible uses. Experimental success has been long sought and very recently attained. The reader will find presented the state of the art in this field. Next to lasing itself, optical bistability has been the most widely studied phenomenon in quantum optics, largely for its technological promise. However, it also provides a fundamental system to study quuantum effects. Recent theoretical studies of optical bistability with small numbers of atoms are surveyed. In such situations quantum features such as antibunching become significant, and the articles in this volume should be a guide to those venturing into this challenging area. In other articles discussions of fluctuations from other noise sources and instabilities in optical bistabilty are presented in a clear and interesting way. Perhaps the least classical state on quantum optics is that describing a single photon. Recent experiments which produce such states are reviewed. A theoretical review of the photon together with some new material is given which delves deeply into relativistic quantum field theory in order to describe the concept of weakly localised photon states. The material here is very rarely presented in the context of quantum optics. The history of the theory of the quantum fluctuations in a laser is then reviewed. An off-shoot of this theory is the study of quantum chaos in dissipative systems and recent results in this new area are given in a succeeding article. There are further stimulating articles on Rydberg atom systems and quantum electrodynamics. The volume ends with an entertaining and incisive study of quantum measurement problems, such as the Schrodinger cat papadox, using concepts and measuring devices found in quantum optics.other_titles
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
Quantum optics was born in the first years of the 20th century. The first papers leading to further ideas of quanta of light were presented by Max Planck and Albert Einstein. Their pioneering papers laid the foundations for the theory of quantum optics. However, one should remember that for the birth of the formal theory of quantisation of light, the development of quantum mechanics was necessary. Interestingly, the word ’photon’ appeared for the first time in a paper by a Gilbert Lewis, a chemist, in 1926 and was later used by P.A.M. Dirac, a physicist, the next year. The modern sense of the term quantum optics was established in 1956 when Hanbury Brown and Twiss built the intensity interferometr and performed their famous experiment in which correlations between two light beams were measured. Although the results of their experiment could be explained on the basis of the classical theory of light, with some quantumcomponent to the process of photodetection, their result is commonly accepted as the beginning of the modern quantum optics era. The next milestone in the development of quantum optics was the invention of laser in 1960. The physical properties of the light generated by lasers were considerably different from those characterising the light generated by classical thermal sources. This fact was a great impulse leading to further development of quantum optics’ ideas. The first of them were presented in the fundamental papers written by Glauber, describing new states of light quantum coherent states.