One of the Many Quirks of Quantum

John Urwin
By John Urwin May 10, 2012 17:02

One of the Many Quirks of Quantum

The world of quantum mechanics is, to the average person, a world of science fiction. This quirky corner of physics tends to be far removed from our everyday lives. However, the phenomena that emerge from the equations of quantum mechanics are very real. One of the most intriguing facets of quantum mechanics — to scientists and science fiction fans alike — is that of persistent current: a natural electric current that flows perpetually without a power source.

Though the theoretical physics behind this phenomenon is relatively well-established, only recently have these currents been measured flowing through large resistive metal wires. On the vanguard of this research are Yale Professors of Physics and Applied Physics Jack Harris and Leonid Glazman, whose recent work measuring quantum currents in metal wires has reinvigorated the field. At first seeming to defy conventional notions of energy conservation, these perpetual currents are quite possibly as intriguing as they are revolutionary.

Quantum in a Nutshell (The ABCs of E=hv)

The core tenet of quantum mechanics is the postulate that all particles exhibit both wave and particle properties. Strange, yes, but true according to theory and experiment. While we may not be able to completely understand exactly what this means, we can appreciate the apparently paradoxical conclusions that emerge from the equations of quantum theory. For instance, we cannot precisely know both the position and speed of a particle at one moment in time. Furthermore, we know that energy is quantized, meaning that particles can only absorb and emit energy in definite amounts.

Quantization emerges naturally from the fundamental wave character of matter. Just as waves on a string can only possess certain energy levels, so too do three-dimensional standing waves. Because particles behave as both particles and waves in quantum mechanics, particles are treated as standing waves and thus have wave properties, including quantized energy levels.

Standing waves on a string come in discrete energy levels (n = 1,2,3,4…) in the same way that standing waves in three dimensions are only allowed certain energy levels. The top string has energy n=1 and contains one node at each end. The next allowed energy level is n = 2, with an additional node in the center. As can be seen, quantization emerges naturally from the boundary conditions of standing waves. Courtesy of UCLA.

Larger masses can be accurately described by classical mechanics since the effects of quantization are not noticeable because they are so small—think pixels on an HD-TV. At small masses, however, the wave properties become crucial for accurately modeling particle behavior. For instance, instead of treating electrons as point particles with a set mass of 9.31 × 10-31 kg, they are treated as three-dimensional standing waves that occupy “clouds.” The exact shapes of these “clouds” are dictated by wave equations, mathematical formulas whose solutions are known as atomic orbitals. Described by four quantum numbers, atomic orbitals are the basis for modern atomic theory.

Upon further analysis, another interesting phenomenon emerges: zero-point energy. Unlike waves on a string, whose lowest energy state is motionless, the lowest energy state for a quantum wave is both fluctuating and dispersed. In other words, no quantum equivalent exists for a flat string. Rather, the lowest energy state for a quantum wave involves motion, meaning that every electron around every nucleus is constantly moving. Theoretically, if one were able to orient the electrons in a metal ring, a current could be produced that would never dissipate!

From e and I: Orienting zero-point motion

Just as a ball falls down when released in the air, electrons too fall down their potential energy gradient to the lowest possible energy level. However, unlike a ball, whose lowest energy level is the ground, an electron’s lowest state is an orbital. As discussed above, these orbitals contain energy, even at their lowest level. For a single electron orbiting a single atom, this ground state is the 1s orbital, a sphere without any nodes. Unlike the ball, however, electrons cannot be “lifted” by any arbitrary amount. Because of energy quantization, electrons can only occupy discrete orbitals with unique energy levels. The next level up from the 1s orbital is the 2s orbital, which is also spherical but more dispersed. One more level up, and the electron enters the 2p orbital, which resembles a dumbbell.

Shapes and energies of s, p, and d atomic orbitals. Courtesy of Chemical Computing Group.

With benzene, a hexagonal ring of six carbons, the first electron added would occupy a hybrid orbital that permeates the entire ring. The second does the same. And the third. All the way until all 42 electrons have been added. Again, applying a magnetic field perpendicular to the face of this molecule will orient the charge and cause an internal rotation. However, because benzene is a ring, the electrons will circulate around the entire ring, not just around a molecule, causing a current to be produced. Moreover, when the field is held at a constant value, the oriented electrons will continue to circulate and form a small current around the ring.

A diagram of a benzene ring, consisting of six carbons arranged in a hexagonal conformation. Courtesy of ChemBase.

Going one step further: take a metal wire a few micrometers in diameter, comprising millions upon millions of electrons and protons. Just as with benzene, applying a magnetic field will induce a tiny current around the wire and, again, after the induced current fades away, a persistent current should remain. In this way, a magnetic field theoretically should be able to induce a persistent current in small metal rings, one that should never dissipate.

Putting Theory to Rest

While scientists theorized and debated these small currents throughout the 1980s, it wasn’t until this decade that researchers were able to devise sensitive enough instrumentation to accurately measure them. Currents can be measured both directly and indirectly. The direct method, utilized in everyday multimeters, opens the circuit and redirects the current through a device that measures it directly. Even though the persistent currents are small, they are well within the detectable range of household multimeters commercially available. However, this method breaks the circuit, which destroys the persistent current.

In contrast, the indirect approach infers the current by measuring the magnetic fields the circulating charge produces. While straightforward, the old 1980s magnetometers were neither sensitive nor reliable enough to give accurate data. Moreover, they often gave contradictory data, which only fueled the debates over the nature of these persistent currents.

Harris and Glazman recently devised a simple yet elegant solution. By placing aluminum rings on micromechanical cantilevers in a magnetic field, Harris and his students could accurately measure the current produced by measuring the angle displaced by the cantilever supporting the rings. Placing an electrical current in a magnetic field creates a force that ultimately causes the displacement observed in the cantilever. Remarkably, this technique yielded data with sensitivity orders of magnitude greater than what was previously achievable.

Diagram of the cantilever instrument used to measure the magnitude of the persistent currents. Courtesy of Professor Harris.

Harris and Glazman also tested a wide range of variables theorized to affect the strength and character of the currents produced, including temperature, ring size, and orientation of the applied magnetic field. Most remarkable is how consistent their data was with all the theoretical predictions. For instance, as expected, as the temperature increases, the amperage of the current dwindles, resulting in a minuscule current at normal temperatures.

While we will not be using persistent currents to power our cell phones any time soon, the ramifications of this research are wide-reaching. Besides putting to rest a decades-old debate, these elegant experiments once again confirm the accuracy of quantum mechanics and reveal the strange and quirky beauty of our universe.

About the Author
John Urwin is a sophomore Molecular Biophysics and Biochemistry major in Jonathan Edwards College. He has previously worked in Professor Colón-Ramos’ lab studying nervous system development in C. elegans.

Acknowledgements
The author would like to thank Professor Jack Harris for his time and expertise.

Further Reading
L.P. Levy et al, “Magnetization of mesoscopic copper rings: Evidence for persistent currents,” Physical Review Letters 17 (April 1990).
Will Shanks, “Persistent Current in Normal Metal Rings,” Ph.D. thesis, Yale University, 2011.

John Urwin
By John Urwin May 10, 2012 17:02