Born at Gorlitz in Germany, Dehmelt left the Berlin Gymnasium in 1940 to join the German army. He was allowed for a time to study physics at Breslau University but, in 1945, he was taken prisoner by the Americans at Bastoigne. After the war he continued his education at Göttingen, gaining his PhD there in 1950. He went to America in 1952 as a postdoctoral student at Duke University, North Carolina, and remained there until 1955. He then moved to the University of Washington, Seattle, where he was appointed professor of physics in 1961, the same year he became a naturalized American citizen.

Dehmelt worked for many years on the seemingly impossible task of imprisoning a single electron for an extended period in a suitable container. In this manner Dehmelt hoped to measure more accurately the magnetic moment (g) of the electron. Earlier experiments by H. R. Crane at Michigan University had involved passing a beam of electrons through a magnetic field. But the evidence gathered in this manner necessarily involves the interactions of other electrons.

In 1955 Dehmelt began work on what later become known as a Penning trap. In 1973 he succeeded in isolating a single electron and went on to show (1975) how accuracy could be further improved by ‘cooling’ the electron (i.e. decreasing its kinetic energy). In this way it proved possible to measure g with an accuracy of 4 parts in a trillion.

The Penning trap operates with a combination of electrical and magnetic fields. An electron in a uniform magnetic field cannot move across the field lines, but is able to escape by moving parallel to the field. To avoid this, an electric field is imposed upon the magnetic field. This field is produced by three electrodes – two negatively charged end traps, and a positively charged encircling nickel ring.

For his work in this area Dehmelt shared the 1989 Nobel Prize for physics with Wolfgang Paul and Norman Ramsey.