De Broglie Dissertation Help

Focus: The de Broglie Wavelength of a Packet of Light

Phys. Rev. Focus 3, 21


In his 1924 doctoral dissertation the French physicist Louis de Broglie suggested that a wavelength is associated with any particle, and it was found that on a quantum level particles like electrons do indeed exhibit wavelike phenomena such as interference and diffraction. In the 5 April PRL, physicists present experimental evidence for the existence of a photonic de Broglie wavelength–wave features associated with a packet of photons interfering with itself.

In 1994 Joseph Jacobson and Yoshihisa Yamamoto of Stanford University predicted that a packet of more than one photon–multiple photons bound together–would have a de Broglie wavelength reduced from that of each photon’s individual wavelength, the reduction being inversely proportional to the number of photons. A dramatic reduction of the wavelength would be possible if all of the photons, as a whole, were divided into two paths by a special beam splitter–a 1,000 photon wave packet of green light would have the de Broglie wavelength of an x-ray, for example.

Sebastião de Pádua and his colleagues at Federal University of Minas Gerais in Brazil were able to verify this prediction for the two-photon case (a biphoton) by performing a clever experiment that measures the interference effects of the wave packet after it was sent through a simple double slit. By preparing the two-photon light state in different ways, they were able to measure the de Broglie wavelength of the two-photon packet as a whole or of its constituent quanta. They verified Yamamoto’s prediction for the case of two photons, the first evidence for his prediction of the general case.

The researchers generated the twin photons by a process called “spontaneous parametric down-conversion,” in which a crystal which has nonlinear optical properties can absorb a single photon and emit a pair of photons, each with half the energy of the original. They found that the key to their experiment lay in modification of the Argon laser beam they used to generate the photons. By placing a wire in front of the beam, they were able to change its intensity in directions perpendicular to the beam’s direction, and by focusing this wire onto the double slit they were able to observe the interference pattern of the wave packet interfering with itself. They found the characteristic pattern with wavelength half that of each individual photon.

“What’s interesting in this experiment,” said Pádua, “is that you can see the interference of the two photon packet as a whole with itself, and you can see the interference with each quanta of the two-photon packet with itself. And you can separate the two effects by manipulating the pump laser beam.”

Yamamoto hopes the group’s work will encourage others. “This is the first experimental evidence for the existence of the photonic de Broglie wavelength, even for two photons,” he said. “This experiment hopefully will trigger the effort to observe larger wave packets.” However, that requires a nonlinear beam splitter–one that splits photons not individually, but which splits the packet as a whole. “This is non trivial,” said Yamamoto.

–David Appell

David Appell is a freelance science writer.

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Alternative Titles: Louis-Victor, 7e duc de Broglie, Louis-Victor-Pierre-Raymond, 7e duc de Broglie

Louis de Broglie, in full Louis-Victor-Pierre-Raymond, 7e duc de Broglie, (born August 15, 1892, Dieppe, France—died March 19, 1987, Louveciennes), French physicist best known for his research on quantum theory and for predicting the wave nature of electrons. He was awarded the 1929 Nobel Prize for Physics.

Early life

De Broglie was the second son of a member of the French nobility. From the Broglie family, whose name is taken from a small town in Normandy, have come high-ranking soldiers, politicians, and diplomats since the 17th century. In choosing science as a profession, Louis de Broglie broke with family tradition, as had his brother Maurice (from whom, after his death, Louis inherited the title of duke). Maurice, who was also a physicist and made notable contributions to the experimental study of the atomic nucleus, kept a well-equipped laboratory in the family mansion in Paris. Louis occasionally joined his brother in his work, but it was the purely conceptual side of physics that attracted him. He described himself as “having much more the state of mind of a pure theoretician than that of an experimenter or engineer, loving especially the general and philosophical view.” He was brought into one of his few contacts with the technical aspects of physics during World War I, when he saw army service in a radio station in the Eiffel Tower.

De Broglie’s interest in what he called the “mysteries” of atomic physics—namely, unsolved conceptual problems of the science—was aroused when he learned from his brother about the work of the German physicists Max Planck and Albert Einstein, but the decision to take up the profession of physicist was long in coming. He began at 18 to study theoretical physics at the Sorbonne, but he was also earning his degree in history (1909), thus moving along the family path toward a career in the diplomatic service. After a period of severe conflict, he declined the research project in French history that he had been assigned and chose for his doctoral thesis a subject in physics.

Theory of electron waves

In this thesis (1924) de Broglie developed his revolutionary theory of electron waves, which he had published earlier in scientific journals. (Seede Broglie wave.) The notion that matter on the atomic scale might have the properties of a wave was rooted in a proposal Einstein had made 20 years before. Einstein had suggested that light of short wavelengths might under some conditions be observed to behave as if it were composed of particles, an idea that was confirmed in 1923. The dual nature of light, however, was just beginning to gain scientific acceptance when de Broglie extended the idea of such a duality to matter. (Seewave-particle duality.)

De Broglie’s proposal answered a question that had been raised by calculations of the motion of electrons within the atom. Experiments had indicated that the electron must move around a nucleus and that, for reasons then obscure, there are restrictions on its motion. De Broglie’s idea of an electron with the properties of a wave offered an explanation of the restricted motion. A wave confined within boundaries imposed by the nuclear charge would be restricted in shape and, thus, in motion, because any wave shape that did not fit within the atomic boundaries would interfere with itself and be canceled out. In 1923, when de Broglie put forward this idea, there was no experimental evidence whatsoever that the electron, the corpuscular properties of which were well established by experiment, might under some conditions behave as if it were radiant energy. De Broglie’s suggestion, his one major contribution to physics, thus constituted a triumph of intuition.

The first publications of de Broglie’s idea of “matter waves” had drawn little attention from other physicists, but a copy of his doctoral thesis was sent to Einstein, whose response was enthusiastic. Einstein stressed the importance of de Broglie’s work both explicitly and by building further on it. In this way the Austrian physicist Erwin Schrödinger learned of the hypothetical waves, and on the basis of the idea, he constructed a mathematical system, wave mechanics, that has become an essential tool of physics. Not until 1927, however, did Clinton Davisson and Lester Germer in the United States and George Thomson in Scotland find the first experimental evidence of the electron’s wave nature.

Later career and writings

After receiving his doctorate, de Broglie remained at the Sorbonne, becoming in 1928 professor of theoretical physics at the newly founded Henri Poincaré Institute, where he taught until his retirement in 1962. He also acted, after 1945, as an adviser to the French Atomic Energy Commissariat.

In addition to winning the Nobel Prize for Physics, de Broglie received, in 1952, the Kalinga Prize, awarded by the United NationsEconomic and Social Council, in recognition of his writings on science for the general public. He was a foreign member of the British Royal Society, a member of the French Academy of Sciences, and, like several of his forebears, a member of the Académie Française.

De Broglie’s keen interest in the philosophical implications of modern physics found expression in addresses, articles, and books. The central question for him was whether the statistical considerations that are fundamental to atomic physics reflect an ignorance of underlying causes or whether they express all that there is to be known; the latter would be the case if, as some believe, the act of measuring affects, and is inseparable from, what is measured. For about three decades after his work of 1923, de Broglie held the view that underlying causes could not be delineated in a final sense, but, with the passing of time, he returned to his earlier belief that the statistical theories hide “a completely determined and ascertainable reality behind variables which elude our experimental techniques.”

Barbara Lovett ClineThe Editors of Encyclopaedia Britannica


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