English translation of the original Chinese article. Publication dates and the extent of recovered text are preserved. Figures retain their original labels. Read the Chinese original.
Institute for Quantum Computing, University of Waterloo
Keywords: liquid helium, boson, fermion, superfluid
Helium-3: a quieter sibling with another trickWhile research on helium-4 was in full swing, its sibling helium-3 remained obscure and largely overlooked, chiefly because it was extremely scarce. In the early years, helium-3 could only be separated from already rare helium deposits, where helium occurs as a by-product of natural gas. Its exceptionally low relative abundance made helium-3 expensive to obtain and severely limited research. From the 1950s onward, enough helium-3 became available through the beta decay of tritium for its investigation to spread throughout the scientific community.
Figure 1: Pressure–temperature phase diagrams for helium-3 (top) and helium-4 (bottom). Helium-3’s transition temperatures are extremely low, so a logarithmic temperature scale is used to show its features. Note the enormous difference between the temperature ranges. Image source: http://ltl.tkk.fi/research/theory/helium.html
The phase diagram in Figure 1 shows that helium-3 also becomes superfluid at sufficiently low temperatures. If superfluidity is a special state of collective motion by bosons following the “hall rule,” how can helium-3 atoms, which are fermions, break the “tower rule” and all condense into the lowest-energy state? Another remarkable research field, superconductivity, had already suggested an answer. A superconductor is a conductor whose resistance abruptly becomes zero, and which is perfectly diamagnetic, below a critical temperature. Onnes’s team discovered this unusual behaviour by accident in 1911, shortly after helium had been liquefied, by immersing mercury in liquid helium. Conductors without electrical resistance have enabled many technological innovations, including superconducting magnets, magnetic levitation and circuits without dissipation. Room-temperature superconductors remain a long-sought dream.
The charge carriers in metals are electrons. As fermions, they too obey the “tower rule.” Theory shows, however, that below the critical temperature—the superconducting transition temperature—two electrons meeting certain conditions can overcome their electromagnetic repulsion through the mediating action of the surrounding lattice and form a bound state called a Cooper pair. Unlike atoms tightly bound together in an ordinary molecule, paired electrons roam separately through space. Only the lattice knows how they sense traces of one another while wandering, maintaining a pairing relationship at a distance. A Cooper pair consists of an even number of fermions and is therefore a boson. At sufficiently low temperatures, pairs undergo a process resembling Bose–Einstein condensation (BEC), producing superconductivity. Their collective motion does not readily dissipate energy; macroscopically, this dissipation-free motion of electron pairs appears as zero electrical resistance. Bardeen, Cooper and Schrieffer of the United States received the 1972 Nobel Prize in Physics for the BCS theory of superconductivity. Later, researchers discovered that Cooper pairs can even pass through a thin insulating layer between two superconductors by tunnelling. Josephson of Britain received the 1973 Nobel Prize in Physics for his theoretical work on this effect. Josephson junctions are now core components of qubits in superconducting quantum-computing circuits.
Similarly to the formation of superconductivity, helium-3 atoms can form Cooper pairs through nuclear-spin interactions at sufficiently low temperatures. These bosonic pairs then condense into the lowest-energy state, turning liquid helium-3 into a superfluid. Their collective motion again does not readily dissipate energy, and dissipation-free atomic motion appears macroscopically as liquid flow without viscosity. Helium atoms are three orders of magnitude heavier than electrons, so their Fermi temperature—the temperature at which fermions begin to show the effects of the “tower rule”—is also three orders of magnitude lower. Quantum effects in liquid helium-3 therefore emerge only far below the critical temperatures of ordinary superconductors. Unlike superconductivity and helium-4 superfluidity, both found soon after liquid helium became available, the predicted helium-3 superfluid long failed to appear in the laboratory. Limits on cooling techniques and discouraging estimates of its transition temperature gradually weakened confidence in its discovery. In 1971, Lee, Osheroff and Richardson in the United States finally achieved helium-3 superfluidity using Pomeranchuk compression cooling at about 2 mK, just two thousandths of a degree above absolute zero. Their original aim was actually to investigate the magnetic properties of solid helium-3 in a mixture of liquid and solid, and they initially misattributed the new phenomena to the solid. Soon, however, they realised they came from the long-awaited helium-3 superfluid. They received the 1996 Nobel Prize in Physics for the discovery. Abrikosov and Ginzburg of Russia and Leggett of Britain received the 2003 Nobel Prize in Physics for theoretical contributions to superconductivity and superfluidity.
The mechanism in which fermions first pair into bosons and then undergo BEC to become superfluid is not limited to superconductors and laboratory superfluids. Scientists believe that pulsars—the neutron stars often called interstellar lighthouses—in the distant Universe may also contain superfluids. Their extremely high density gives them a Fermi temperature of approximately 1012 K. The estimated transition temperature at which two neutrons form a Cooper pair through the strong interaction is about 109 K. Meanwhile, a neutron star’s actual temperature is about 108 K. Its neutrons may therefore pair into Cooper pairs because the temperature is “low enough,” placing them in a superfluid state.
At low temperatures, liquid helium-3 automatically excludes impurities, including helium-4, making it exceptionally pure. Low-temperature conditions and measurement limitations make experiments very difficult, but the purity of the samples lends considerable confidence to hard-won findings. By the time of this article, researchers had developed a fairly comprehensive understanding of pure helium-3 superfluids. Pairing between helium-3 atoms is also more complex than electron pairing in superconductors. Its superfluid properties are therefore richer than those of conventional superconductors and helium-4, which does not need to form Cooper pairs. Pure superfluid helium-3 has consequently become an ideal testing ground for quantum theoretical models.
In 1986, Bednorz of West Germany and Müller of Switzerland discovered a new high-temperature superconductor with a critical temperature of about 30 K, far above the below-10 K critical temperatures of conventional superconductors. This sparked another wave of research seeking room-temperature superconductivity, and unusually, the two received the Nobel Prize in Physics the very next year. At the time of writing, the highest critical temperature found was about 140 K, allowing superconductivity using inexpensive liquid nitrogen, which boils at 77 K. Researchers later found that Cooper-pair formation in these newer superconductors differs from the conventional mechanism and instead resembles pairing in superfluid helium-3. By adding impurities to pure superfluid helium-3 in a controlled way, researchers can systematically investigate their effects on unconventional pairing. Moving from simple systems to more complex ones provides guidance and evidence for high-temperature-superconductivity research.
Superfluid helium-3 is also a topological superfluid. Topological insulators synthesised in laboratories in recent years are a new class of materials that conduct on their surfaces but insulate internally. The topology of their energy levels makes surface conductivity highly stable, creating substantial prospects for applications. Like these unusual insulators, helium-3 superfluids have special surface energy states. Their properties are determined entirely by the topology of the internal energy states, making them resistant to impurities and outside disturbances and allowing them to remain stable. In 2016, Thouless, Haldane and Kosterlitz, working in Britain and the United States, received that year’s Nobel Prize in Physics for pioneering work on topological phase transitions. Superfluid helium-3 will once again serve as an ideal testing ground, offering illuminating clues for theoretical and experimental studies of such transitions.
Research on superfluid helium-3 is, of course, extremely challenging. Liquid helium is electrically insulating, so the electrical measurement techniques already well established for conductors and superconductors cannot be used. How can its surface and bulk properties be detected sensitively and effectively? How can impurities be introduced in a controlled way? These are among the leading questions in helium-3 superfluidity research at the time described here.
ConclusionFrom helium’s discovery through its liquefaction to the discovery and investigation of superfluids, helium research runs through 150 years of modern scientific development. Its theoretical breakthroughs and technical advances have opened many new fields and earned many Nobel Prizes in Physics. Frontier research on helium still carries the task of extending human understanding. We have good reason to believe that researchers will continue to discover and explain remarkable properties of this extraordinary quantum liquid, gaining deeper insight into the Universe from this small window onto it.
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Sources for this correction: U.S. Department of Energy · Tritium beta decay.
Editorial note: On October 10, 2026, the process by which tritium produces helium-3 was corrected to beta decay using DOE information. The original author, publication record and historical research narrative are retained.
