In 1935, Erwin Schrödinger, one of the inventors of quantum mechanics, illustrated his discomfort with the theory by pointing out that its extension to the macroscopic world could lead to bizarre situations such as a cat being simultaneously alive and dead, a so-called superposition state. Today, we can create analogous situations on a small scale, such as putting an atom in a “bowl” and placing it on the left and right sides of the bowl simultaneously.

Superpositions can be used as clocks. For example, the wave function that describes the superposition of two different energy levels in an atom oscillates at a frequency given by the energy level difference divided by Planck’s constant. The duration required to count a prescribed number of these oscillations can be used to define a unit of time such as the second. Today, atomic clocks run at rates that are uncertain at a level of only 1 part in 1017.

Superpositions might also be useful for computation. For example, two energy levels in an atom, labeled "0" and "1," can be used to store information like the bits in our laptops. However, as in the atom/bowl experiment, we can arrange the quantum bit to be in a superposition, thereby storing both states of the bit simultaneously. This property leads to a memory and processing capacity that increases exponentially with the number of bits. This and a related property called “entanglement” would enable a quantum computer to efficiently solve certain classes of problems that are intractable on conventional computers. So far, scientists have constructed quantum computers composed of only a few bits, but with advances in technology, a useful processor may someday become a reality. A macroscopic quantum processor would realize a close analog to Schrödinger’s cat. These topics will be briefly discussed in the context of trapped atomic ions.

Additional reading:

Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, UK, 2000)

“Entangled states of trapped atomic ions,” R. Blatt and D. Wineland, Nature 453, 1008-1015 (2008).