NCSA NEWS

Add enough antifreeze and the water in your car's cooling system will keep on flowing through the iciest winter. Applying basically the same idea, say NCSA physicists David Ceperley and M. Carmen Gordillo, you can prevent hydrogen from freezing into a solid as it usually does at low temperatures (below 14° Kelvin). Their simulations show, furthermore, that when it gets even chillier (1.2° K) this unfreezable liquid hydrogen shifts to the strange, frictionless state of matter known as superfluidity.

Their work (reported in Physical Review Letters, 20 Oct. 97) opens new avenues for research in condensed-matter physics by adding hydrogen to the exclusive list of substances that become superfluid. At the top of this list is helium, which has been a focal point of research into low-temperature properties of matter since it was first liquefied in 1908.

Since hydrogen is in many fundamental respects similar to helium, physicists speculated for years that hydrogen should be a candidate for superfluidity. Hydrogen molecules, however, attract each other more strongly than do helium atoms and normally combine at low temperatures to form a solid. Ceperley and Gordillo surmised that adding impurities to liquid hydrogen would suppress this molecular urge to get together and solidify. "It's so close to becoming a liquid," says Ceperley, "if we could just make the liquid more stable, then maybe it could become a superfluid."

Simulations on NCSA's HP-Convex Exemplar confirmed this insight. With an exact quantum approach that Ceperley derived from 1950s work by Richard Feynman, the researchers modeled hydrogen molecules on a flat surface salted with potassium atoms. The repulsive effect of the alkali-metal stops the hydrogen molecules from combining to freeze into a solid, explains Ceperley, and the liquid hydrogen undergoes a transition to superfluidity just above absolute zero.

Liquids that flow without friction

Although a number of this century's outstanding physicists have contributed to the understanding of superfluidity, it remains one of the fascinating phenomena of physics. No one knew there was such a thing until early liquefied helium experiments by the Dutch physicist J. Kamerlingh Onnes. In 1910 he found that helium wouldn't freeze even at one degree above absolute zero -- as cold as he could go -- and measurements showed, strangely, that as liquid helium declined in temperature its density peaked at 2.2° K. Later studies by Dutch, Canadian, and Russian physicists, including the noted theorist Lev Landau, identified this density maximum as a transition to a special state, which by the late 1930s was called superfluidity.

Experiments show that superfluid helium has no viscosity and flows through even the tiniest capillary tubes with no resistance. Perhaps the most striking demonstration of superfluid defiance of the ordinary is its behavior in a rotating container. Put a cup of coffee on a turntable and the coffee rotates with the cup. Place liquid helium above superfluid temperature inside a rotating container, explains Ceperley, and it acts like the cup of coffee. As you cool it through the superfluid transition, however, the liquid stops rotating and comes to rest. That's the lower-energy state that superfluids get into. They completely insulate themselves from what's going on around them."

Landau and others recognized these strange behaviors as quantum phenomena occurring at an observable scale. "It's a manifestation at the macroscopic level of the fact that the quantum particles are indistinguishable," says Ceperley. Instead of moving independently, like the atoms of a liquid normally do, atoms of superfluid helium cohere in a collective state. The effect is similar to a laser beam, notes Ceperley, in that in both cases -- photons from the laser and helium atoms or hydrogen molecules -- the quantum particles are bosons, particles with integral spin. "The physical effect is that the more there are in a particular state, the more want to go into that state."

Superfluidity also bears similarities to its better known first cousin, superconductivity, another macroscopic realization of quantum effects. "If you try to put a magnetic field on a superconductor, you can't," says Ceperley. "It pushes out the magnetic field. It's like rotation to a superfluid." Similarly, as it's possible to establish current in a superconducting circuit that will flow forever, superfluid helium can be made to flow in a loop, a "superflow" that continues as long as superfluid conditions are maintained.

Line dancing in imaginary time

In the 1950s, Feynman's ideas were limited by computational technology. Ceperley developed PIMC into a practical numerical algorithm for calculating superfluid properties: "Essentially, Feynman showed that this quantum system is equivalent mathematically to a classical system of exchanging polymers. The thermodynamic properties -- energy, pressure and superfluid properties -- have exact equivalents in the classical domains, and the PIMC simulation translates from one domain to the other. There are many refinements needed to make it effective on computers, and that's what we developed."

The method relies on a simple mathematical transformation -- changing time in Schrödinger's equation, the fundamental equation of quantum mechanics, to imaginary time. "You can only do these calculations -- many-body quantum calculations in imaginary time -- so we have to make a virtue of necessity." The calculations trace the particles as they move in imaginary time and, like a game of musical chairs, they must either return to their starting place or the starting place of another particle.

In this formalism, says Ceperley, it turns out that superfluidity is equivalent to what happens if you progress from one position to the next in a line dance. "It takes a long time to get back to where you started. If the line is 20 couples long, it takes 20 iterations. That's the property we look for -- it's called a permutation of labels -- an exchange that extends across the system. If you look at those paths, you'll see they're all linked together, like one huge molecule, and that's superfluidity, in this imaginary time."

Looking ahead

As part of the effort of the Alliance, they will also work to forge PIMC into a generalized computational tool. "We hope that eventually PIMC can be a 'black box,' " says Ceperley. "A nonexpert could specify temperature, particle masses, spins, interactions, chemical potentials, and boundary conditions of the quantum system, and the computer could return estimates of various observables, complete with error bars. It should be a major goal of computational many-body physics to show how this can be done."

References:
M. C. Gordillo & D. M. Ceperley, "Superfluidity in H2 Films," Physical Review Letters 79, 3010 (1997).

D. M. Ceperley & M. C. Gordillo, "Conditions of Superfluidity in Molecular Hydrogen," Proceedings of the International Workshop on Condensed Matter Theories, v. 12, ed. J. W. Clark, P. V. Plant (Nova Science, New York: 1997).