Feedback enables researchers to control an atom's wave function
by Graham P. Collins
The development of quantum mechanics, the underlying laws that govern matter and energy on the scale of atoms and electrons, has not only revolutionized our understanding of the universe but also has given us such technologies as the transistor, the laser and magnetic resonance imaging. Now Philip H. Bucksbaum and his co-workers at the University of Michigan have combined several recently developed techniques with a feedback system to control the very essence of quantum particles: their wave functions. The Bucksbaum experiment "is true quantum engineering," says physicist Michael G. Raymer of the University of Oregon. "It should open up many new possibilities, most of which we cannot even imagine now."
A wave function defines the physical state of a quantum object. Wave functions are slippery characters, tied to probabilities, not certainties. They obey the famous Heisenberg uncertainty principle: if one characteristic is well defined, a related feature must be highly uncertain. For instance, an electron with a very precise position must have a wide range of possible velocities. Nevertheless, during the past decade a number of research groups have assembled techniques for manipulating and analyzing complete wave functions in detail.
Bucksbaum and his graduate students Thomas C. Weinacht and Jaewook Ahn apply their technique to a type of quantum state known as a Rydberg state, which occurs when an electron in an atom is excited to such a high energy level that it barely remains bound to the atom. "Rydberg states are a great laboratory to test new ideas," Bucksbaum explains. An electron with such high energy can occupy a very large number of quantum states. Combining those states in different proportions (that is, placing them in superposition) sculpts the shape of the electron's wave function. In one combination, for example, the electron is smeared out in a ring around the atom; in another, it is localized and orbits the atom much like a planet orbiting the sun.
The basic tool for such wave function sculpting is a strong, ultrashort laser pulse, which excites the electron from a lower energy level. Through a design developed by Warren S. Warren of acousto-optic modulator--a crystal whose optical properties are governed by precisely shaped sound waves. How the laser's intensity and phase vary over the 150-femtosecond pulse determines how the available excited states combine to produce the electron's sculpted wave function.
But what shape of laser pulse is needed to generate a specific sculpted electron wave function? In principle, this shape can be predicted by computations, but in practice one must contend with nonideal equipment and incomplete understanding of the physical system being controlled.
Bucksbaum's new trick, described in the January 21 issue of Nature, is to use feedback to modify the shaping pulse. His group works with a gas of cesium atoms in batches of about a million atoms. An approximate pulse excites the atoms, and the researchers map the shape of the resulting wave function with quantum holography, a technique they demonstrated a year ago. In optical holography, the three-dimensional shape of an object is reconstructed from its hologram, a special two-dimensional interference pattern. In quantum holography, measurements produce data loosely analogous to a hologram from which the complete wave function of the object can be reconstructed. In accordance with the uncertainty principle, however, each measurement disturbs the quantum "object," so the "hologram" must be built up one pixel at a time over many experimental runs, with thousands of identically prepared atoms measured on each run.
Once the physicists have mapped the resulting wave function, they look at the difference between that one and the desired one. This information is then used to adjust the detailed shape of the laser pulse used on subsequent batches of atoms. Bucksbaum found that after only two or three iterations this feedback zeroed in on the desired wave function.
Quantum control has applications in the burgeoning field of quantum computing, in which the encoding of data onto individual quantum states may allow the development of computers that function on quantum principles. Another application is control of chemical reactions. Shaped optical pulses that induce just the right excitations at specific bonds in a molecule can enhance or suppress alternate reaction pathways. Some groups have independently used feedback for this type of control, but the feedback has not been based on detailed mapping of a wave function.
Quantum physicist Carlos R. Stroud of the University of Rochester cautions that further research is needed to see if Bucksbaum's method is applicable to a wider range of quantum systems. Still, he says, "they have expanded the quantum mechanics toolbox."
GRAHAM P. COLLINS, based in College Park, Md., has written articles for New Zealand Science Monthly and Physics Today.
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