Felix Bloch

A draftsman among algebraists

Felix Bloch was born in Zürich on October 23, 1905, the second child of a Jewish grain merchant who had emigrated from Moravia a decade earlier. He read voraciously, played the piano seriously, and was good enough at mathematics that the Eidgenössische Technische Hochschule, the same ETH where Einstein had studied, admitted him in 1924 to study engineering. He switched within his first year to physics, persuaded that engineering was chasing answers while physics was still asking questions.

The Zürich faculty at the time was extraordinary. Erwin Schrödinger lectured on the wave mechanics he had invented only months earlier, and a twenty-something Wolfgang Pauli was beginning to systematize the new spin formalism. Bloch absorbed both. For his doctorate he chose to follow Werner Heisenberg, who in 1927 had taken a chair at Leipzig, and so he went north. Heisenberg, only four years older than Bloch, was already a Nobel laureate in everything but name, and treated his students as collaborators rather than apprentices.

Bloch waves: electrons made periodic

Bloch’s 1928 doctoral thesis answered a question that had stumped the field for years. Classical electron theory, due to Drude and Lorentz, treated the electrons in a metal as a gas of free particles. The picture worked tolerably for conductivity and failed almost everywhere else. Why were some materials insulators while others conducted? Why did the heat capacity of metals refuse to add up the way the gas picture demanded?

Bloch took the new wave mechanics seriously and asked what an electron’s wavefunction looks like in the periodic potential of a crystal lattice. He proved that the solutions are plane waves modulated by a function with the same period as the lattice. Every undergraduate textbook now states the result as Bloch’s theorem, and the modulated plane waves are called Bloch waves. From them follow band structure, the distinction between metals and insulators, and ultimately the silicon transistor. Bloch was twenty-three when he finished it.

In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.

The sketch on a Zürich napkin

While in Europe he sketched, on a scrap of paper now lost, the geometric picture of a single spin-1/2 state as a point on a sphere. The idea was a teaching aid more than a discovery. Pauli’s spinor algebra was elegant but opaque to students, and Bloch had a draftsman’s instinct: he wanted to draw the thing. Two angles parameterize a sphere, two angles parameterize a pure qubit, and the correspondence is exact. The sphere has carried his name ever since.

Flight from Leipzig

The 1930s pushed him out of Europe. After Hitler came to power in January 1933, Bloch was dismissed from his position at the University of Leipzig under the new racial laws. He spent a year in Copenhagen with Niels Bohr, another with Enrico Fermi in Rome, and in 1934 accepted an offer from Stanford, where he would remain for the rest of his career. He became an American citizen in 1939 and, when war came, joined the radar program at Harvard and briefly worked on isotope separation for the Manhattan Project at Los Alamos. Both experiences taught him to think of physics in terms of coils, oscillators, and radio-frequency pulses rather than abstract Hamiltonians, and that habit would shape the work that won him the Nobel.

Nuclear magnetic resonance

In late 1945, back at Stanford, Bloch wondered whether the radio-frequency techniques he had used in radar could detect the magnetic moments of atomic nuclei directly. Edward Purcell at Harvard had the same idea at almost the same moment. Bloch’s group placed a sample of water in a strong magnetic field, drove the proton spins with a tuned coil, and watched the signal precess. The detection of nuclear magnetic resonance in early 1946 was, in effect, the Bloch-sphere picture made experimental: a population of spins tipped by an oscillating field, precessing around the static field at the Larmor frequency, and radiating a coherent signal back into a pickup coil. He shared the 1952 Nobel Prize in Physics with Purcell. The technique he co-invented underlies every modern MRI machine and the whole of chemical NMR spectroscopy.

CERN, and home to Zürich

In 1954 Bloch was elected the first Director General of the brand-new CERN laboratory outside Geneva. He served only one year. He was a theorist at heart, and the politics of an international laboratory in its founding chaos exhausted him quickly. He returned to Stanford and to the teaching he loved, where his lecture notes on quantum mechanics circulated among graduate students for decades before they were finally published. He died in Zürich on September 10, 1983, having lived long enough to see his teaching-aid sphere become the standard language of a field, quantum information, that did not yet have a name when he drew it.

Felix Bloch is the rare physicist whose name attaches to two distinct pieces of modern science: the band-structure framework that gave us semiconductors, and the spin-resonance technique that gave us medical imaging. The sphere is the third, and may yet outlive both.