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538 NATURE | VOL 410 | 29 MARCH 2001 | www.nature.com

Leonard Mandel, one of the foundingfathers of quantum optics, died at hishome on 9 February at the age of 73. Ourgeneration of optical scientists grew uplearning from Mandel’s work: quiteliterally, he showed us the light by openingup many new avenues of research. He wasan elegant experimentalist and acelebrated theorist. Echoes of hisunmistakable slow but clear voice willcontinue to remind us of the contributionsof this remarkable man.

Mandel was born in Berlin, but movedto Britain when he was a boy. He waseducated at the University of London,studying cosmic rays for his PhD, whichwas awarded in 1951. After a short spell inindustry, Mandel took up an academic postat Imperial College, London. It was theinvestigation of cosmic rays that eventuallyled him to discover what is today known asMandel’s photon-counting formula, which relates the statistical properties of arbitrary optical fields to those ofphotoelectrons detected experimentally.Mandel worked throughout his career toperfect the photon-counting technique for studying a variety of optical fields,from the thermal light of a candle tosophisticated quantum sources. In the1960s, this work enabled physicists tounderstand the statistical properties oflasers operating under different pumpingconditions. Such studies gave support tothe quantum theory of the laser.

Mandel performed his first majorexperiment at Imperial, its simplicity indesign becoming one of his trademarks.The result, typically, was counterintuitive.The experiment showed how interferencebetween independent photon beams canbe observed and that such a possibility ispermitted by quantum physics. Hisdemonstration of two-photon interferencefollowed. This was an experiment that laidthe foundation for later work on quantumentanglement, a concept of statesuperposition first introduced by ErwinSchrödinger.

In 1964 Mandel settled permanently in Rochester, New York, having beenpersuaded to move there by Emil Wolf.Wolf and Mandel wrote several notablepapers together, and also organized theRochester Conferences on QuantumOptics, which laid the foundations of thefield and continue to this day. It was at oneof the early conferences that debate reallybegan to heat up on the need for aquantum theory of light, and Mandelstarted to devote much of his research

to searching for the subtle differencesbetween the classical and quantumdescriptions of light.

Applying a mixture of theory andexperiment, Mandel and colleaguesrevealed several uniquely quantum-mechanical properties of light. In 1977, forinstance, his group observed the ‘photonanti-bunching’ effect, in which photonsfrom a single two-level atom illuminatedby a resonant laser can never be emitted inpairs or more, providing confirmation of a‘quantum jump’. This was followed by thedemonstration of sub-poissonian photonstatistics, which mean that fluctuations in the photon number of an optical fieldare smaller than would be expected forrandom events, such as the fall ofraindrops. These were the first reportedobservations of ‘non-classicality’ requiringa full quantum description of light, andthey changed our perspective on light.

Photon interference was the hallmarkof Mandel's work. In the 1980s his groupcarried out a series of ground-breaking yet ingeniously simple experiments todemonstrate the quantum entanglementof photons and, subsequently, the non-locality of quantum mechanics throughviolations of Bell’s inequalities in theEinstein–Podolsky–Rosen paradox. Thesestudies set the ball rolling for a largenumber of experiments world widedealing with the foundations of quantummechanics, and for newer developmentssuch as quantum teleportation, quantumencryption, and cryptography forquantum-information processing.

As he entered his seventh decade,Mandel was still as productive as ever inaddressing some of the fundamentals of

physics. One of the problems thatbothered Paul Dirac, the founder ofquantum electrodynamics, was how todefine the phase of a quantizedelectromagnetic field: phase is crucial inunderstanding all interferencephenomena. The answer remained elusiveuntil the early 1990s, when Mandelintroduced the concept of measurablephase, and actually measured the phasecharacteristics of a quantized field.

In this same period he demonstratedthe non-existence of a pilot wave, which is at the heart of de Broglie’s waveinterpretation of quantum mechanics.And in another conceptuallystraightforward but mind-bogglingexperiment, Mandel and his studentsdemonstrated the complementarity oflight — that is, its behaviour as either a wave or a particle in differentcircumstances. It was, of course, knownthat placing a detector in its path couldchange the behaviour of light. But Mandelfound that an experimental set up thatmerely has the possibility of making ameasurement, even if only in principle,could bring that change about: no actualmeasurement is required.

Mandel was a private but generousperson. Discussions with him wereinvariably inspiring, often leading to freshideas, as we ourselves can attest. Althoughhis voice was weakened by illness,Mandel’s mind remained as sharp as ever.Only a few months before his death, heand his colleagues published a paper onsqueezing the quantum noise in atomicspin, an approach which may lead toentangled states of atoms.

As well as being a world-classresearcher, Mandel was a great teacher.Many of his 39 PhD students becameleaders in their fields: Jeff Kimble, forinstance, with whom Mandel discoveredthe photon anti-bunching effect, is workingat the forefront of the new field of quantuminformation science, which is based on theconcept of quantum entanglement. Thefield that Mandel opened up, and to which he made so many contributions, has begun to have an impact on theinformation age in which we now live. Hislegacy is to have provided the inspirationfor the next generation of researcherspursuing a deeper understanding of thefundamental laws of nature and theirapplications. G. S. Agarwal and Z. Y. Ou

G. S. Agarwal is in the Physical ResearchLaboratory, Ahmedabad 380 009, India.e-mail: gsa@prl.ernet.inZ. Y. Ou is in the Department of Physics, IndianaUniversity–Purdue University, 402 North BlackfordStreet, Indianapolis, Indiana 46202, USA.e-mail: zou@iupui.edu

Obituary

Leonard Mandel (1927–2001)

Pioneer in quantumapproaches to light

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