Fairbank was born at Minneapolis in Minnesota and educated at Whitman College, Walla Walla, Washington, and at the University of Washington. He gained his PhD at Yale in 1948. He spent the war years at the Radiation Laboratory of the Massachusetts Institute of Technology. After working at Amherst, Maryland (1947–52) and Duke University, North Carolina (1952–59), Fairbank was appointed professor of physics at Stanford, a post he held until his death from a heart attack in 1989.

In 1977, Fairbank, in collaboration with George Larue, claimed to have experimental evidence for the existence of a quark. The concept of quarks, with an electric charge –1/3 or +2/3 the electron charge, had been proposed by Murray Gell-Mann in 1963 to explain the behavior of hadrons. It was known that it would be unlikely that quarks could be produced at the energies available in particle accelerators. However, it was possible that some might be created in the atmosphere as a result of high-energy cosmic rays. A number of physicists set up ingenious sensitive experiments to “hunt the quark.”

Fairbank's technique was a much more sensitive and sophisticated version of Robert Millikan's oil-drop experiment for measuring the charge of the electron. A small sphere (0.25 millimeter diameter) of niobium was suspended between metal plates at a temperature close to absolute zero. The charge on the sphere could be measured by the electric field between the plates.

When Fairbank examined his results he found that in the case of one ball there was “a nonzero residual change of magnitude –0.37 ± 0.03.” At first, Fairbank warned, the results did not necessarily imply the presence of a quark as there could well be spurious charge forces present. Consequently, Fairbank spent a good deal of time eliminating these and numerous other possible distortions from his experimental setup.

Theorists were suspicious of Fairbank's work because free quarks are thought to be impossible to produce – the doctrine of “quark confinement.” Despite this, Fairbank announced in 1979 that, using modified apparatus, he had detected a second particle with a fractional charge.

While no-one has managed to reproduce Fairbank's experiments, he was sufficiently respected as a careful and skillful experimentalist for his work to be taken seriously. Consequently, for some particle physicists at least, the issue of quark confinement remains an open question.