Mapping helium atoms' quantum states.

Imagine, as Plato once did, prisoners chained in a cave so they can see only the shadows of things outside their prison, not the things themselves. Physicists face a similar situation in the quantum realm when they try to observe atoms and electrons in motion. They cannot see such physical objects as they are; they can only detect aspects of those objects, which appear particlelike or wavelike, depending on the type of observation.

To build up a picture of a hidden object from the different shadows it casts, one can use a method called tomography For example, one can generate an image of a person's internal organs from measurements of the intensities of X rays that have passed through in different directions.

A special sort of tomography can be used to measure the quantum state of atoms or photons. With this technique, Jurgen Mlynek and his colleagues at the University of Konstanz in Germany determined the quantum state of moving helium atoms and have shown experimentally, for the first time, that the atoms' motion has wavelike characteristics.

The researchers report their findings in the March 13 Nature.

According to quantum theory, an atom can behave like a wave. Thus, atoms traversing a pair of slits should produce an interference pattern. Atoms reach a detector only at positions where the waves reinforce each other, producing a pattern of evenly spaced bars.

Mlynek and his colleagues set up an experiment in which a beam of helium atoms passes through a pair of slits in a screen. If an atom moved like a tiny pellet, it would either pass through a slit or strike the barrier. All the information about an atom's state of motion at any moment would be given by its position and its momentum, the product of its mass and velocity.

The Heisenberg uncertainty principle, however, asserts that the position and momentum of a quantum particle can't be determined simultaneously to a high precision. If one quantity is known very precisely, the other has a corresponding uncertainty.

"You can never determine the complete quantum state in one measurement," says Christopher Monroe of the National Institute of Standards and Technology in Boulder, Colo. "The idea [of quantum tomography] is to take many measurements to piece together the state, just like a CAT scan."

The relationship between a quantum particle's position and its momentum forms a mathematical entity called the Wigner function. By applying quantum tomography to helium atoms passing through a pair of slits, Mlynek and his team obtained data to calculate the Wigner function and, in effect, map the quantum state of the moving helium atoms.

Researchers have already measured the states of various quantum systems, including arrays of photons, a vibrating molecule, and a single ion trapped in a magnetic field (SN: 5/25/96, p. 325). The work of Mlynek and his team represents an important extension of these efforts, says Monroe.

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