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Take a Walk on the Quantum Side


Compounding one challenging concept with another, a team of atomic physicists has put a new twist on the classic “random walk”–an idealized wandering that is key for explaining the diffusion of one liquid in another and myriad other real-world phenomena. This time, researchers have set a single atom ambling according to the rules of quantum mechanics and found that it covers more distance than it would without them. The advance, reported today in Science, could have uses in budding quantum information technologies, the researchers say. But the real accomplishment seems to be the marrying of two classic physics concepts.

In less politically correct times, physics professors explained the random walk as follows. Suppose a drunk stands under a lamppost, staggering to the right or left with equal probability. After some number of steps, N, he is likely to have taken a few more steps to the left than to the right, or vice versa. In fact, after N steps, on average the drunk will have moved a distance proportional to the square root of N from the post. That may seem like a pointless thing to know, but such a random walk neatly describes the motion of a molecule in a sample of liquid or electrons rattling around in a metal.

Now, Michal Karski, Artur Widera, and colleagues at the University of Bonn in Germany have thrown the weirdness of quantum mechanics into the mix. A drunk or any other “classical” object must move either to the left or to the right. But according to quantum mechanics, a tiny particle such as an atom can actually move in opposite directions at the same time and end up in a so-called superposition state in which it’s in two places at once. There is a catch, though: Whenever somebody measures the particle’s position, the delicate quantum state will collapse so that the particle is found in one place or the other.

Taking advantage of all this, the researchers have made a single cesium atom take a “quantum walk” along a chain of spots of laser light formed by two opposing laser beams. Starting with the atom in one spot, they tickle it with radio waves to make it spin in opposite directions–up and down–at once. They then fiddle with the polarizations of the laser beams in a way that pulls the “up” part of the quantum state to the right and the “down” part to the left. That puts the atom in a hard-to-imagine state in which it sits in one spot spinning up while at the same time it sits in the next spot spinning down.

The researchers then repeat the process again and again so that the atom ends up in a quantum state in which it occupies many light spots at once. When the researchers measure the atom’s position, the state collapses to just one spot. But by performing the experiment many times, they can sketch out that state. And they find that, after N steps in the process, an average atom has moved a distance proportional to N from its original spot–farther than it would get classically.

“It is difficult to imagine a cleaner, more textbooklike demonstration of the idea of a quantum walk,” says Poul Jessen, an experimental physicist at the University of Arizona in Tucson. The advance could be more than academic, adds Reinhard Werner, a theorist at the University of Hannover in Germany. In principle, he says, by putting several atoms into the chain of light spots and letting them interact, it might be possible to construct a kind of quantum computer that could crack problems that a conventional computer cannot. A full-blown computer is a long way off, Werner says, but “this is a first step toward more complicated things.”