Tag / Superconductivity

by David D. Nolte

Frontiers of Physics: The Year in Review (2022)

Physics forged ahead in 2022, making a wide range of advances. From a telescope far out in space to a telescope that spans the size of the Earth, from solid state physics and quantum computing at ultra-low temperatures to particle and nuclear physics at ultra-high energies, the year saw a number of firsts. Here’s a list of eight discoveries of 2022 that define the frontiers of physics.

James Webb Space Telescope

“First Light” has two meanings: the “First Light” that originated at the beginning of the universe, and the “First Light” that is collected by a new telescope. In the beginning of this year, the the James Webb Space Telescope (JWST) saw both types of first light, and with it came first surprises.

an undulating, translucent star-forming region in the Carina Nebula is shown in this Webb image, hued in ambers and blues; foreground stars with diffraction spikes can be seen, as can a speckling of background points of light through the cloudy nebula
NASA image of the Carina Nebula, a nursery for stars.

The JWST has found that galaxies are too well formed too early in the universe relative to current models of galaxy formation. Almost as soon as the JWST began forming images, it acquired evidence of massive galaxies from only a few hundred million years old. Existing theories of galaxy formation did not predict such large galaxies so soon after the Big Bang.

Another surprise came from images of the Southern Ring Nebula. While the Hubble did not find anything unusual about this planetary nebula, the JWST found cold dust surrounding the white dwarf that remained after the explosion of the supernova. This dust was not supposed to be there, but it may be coming from a third member of the intra-nebular environment. In addition, the ring-shaped nebula contained masses of swirling streams and ripples that are challenging astrophysicists who study supernova and nebula formation to refine their current models.

Quantum Machine Learning

Machine learning—the training of computers to identify and manipulate complicated patterns within massive data—has been on a roll in recent years, ever since efficient training algorithms were developed in the early 2000’s for large multilayer neural networks. Classical machine learning can take billions of bits of data and condense it down to understandable information in a matter of minutes. However, there are types of problems that even conventional machine learning might take the age of the universe to calculate, for instance calculating the properties of quantum systems based on a set of quantum measurements of the system.

In June of 2022, researchers at Caltech and Google announced that a quantum computer—Google’s Sycamore quantum computer—could calculate properties of quantum systems using exponentially fewer measurements than would be required to perform the same task using conventional computers. Quantum machine learning uses the resource of quantum entanglement that is not available to conventional machine learning, enabling new types of algorithms that can exponentially speed up calculations of quantum systems. It may come as no surprise that quantum computers are ideally suited to making calculations of quantum systems.

Part of Google's Sycamore quantum computer
Science News. External view of Google’s Sycamore quantum computer.

A Possible Heavy W Boson

High-energy particle physics has been in a crisis ever since 2012 when they reached the pinnacle of a dogged half-century search for the fundamental constituents of the universe. The Higgs boson was the crowning achievement, and was supposed to be the vanguard of a new frontier of physics uncovered by CERN. But little new physics has emerged, even though fundamental physics is in dire need of new results. For instance, dark matter and dark energy remain unsolved mysteries despite making up the vast majority of all there is. Therefore, when physicists at Fermilab announced that the W boson, a particle that carries the nuclear weak interaction, was heavier than predicted by the Standard Model, some physicists heaved sighs of relief. The excess mass could signal higher-energy contributions that might lead to new particles or interactions … if the excess weight holds up under continued scrutiny.

Science magazine. April 8, 2022

Imaging the Black Hole at the Center of the Milky Way

Imagine building a telescope the size of the Earth. What could it see?

If it detected in the optical regime, it could see a baseball on the surface of the Moon. If it detected at microwave frequencies, then it could see the material swirling around distant black holes. This is what the Event Horizon Telescope (EHT) can do. In 2019, it revealed the first image of a black hole: the super-massive black hole at the core of the M87 galaxy 53 million light years away. They did this Herculean feat by combining the signals of microwave telescopes from across the globe, combining their signals interferometrically to create an effective telescope aperture that was the size of the Earth.

The next obvious candidate was the black hole at the center of our own galaxy, the Milky Way. Even though our own black hole is much smaller than the one in M87, ours is much closer, and both subtend about the same solid angle. The challenge was observing it through the swirling stars and dust at the core of our galaxy. In May of this year, the EHT unveiled the first image of our own black hole, showing the radiation emitted by the in-falling material.

BBC image of the black hole at the core of our Milky Way galaxy.

Tetraneutrons

Nuclear physics is a venerable part of modern physics that harkens back to the days of Bohr and Rutherford and the beginning of quantum physics, but in recent years it has yielded few new surprises (except at the RHIC collider which smashes heavy nuclei against each other to create quark-gluon plasma). That changed in June of 2022, when researchers in Germany announced the successful measurement of a tetraneutron–a cluster of four neutrons bound transiently together by the strong nuclear force.

Neutrons are the super-glue that holds together the nucleons in standard nuclei. The force is immense, strong enough to counteract the Coulomb repulsion of protons in a nucleus. For instance, Uranium 238 has 92 protons crammed within a volume of about 10 femtometer radius. It takes 146 neutrons to bind these together without flying apart. But neutrons don’t tend to bind to themselves, except in “resonance” states that decay rapidly. In 2012, a dineutron (two neutrons bound in a transient resonance state) was observed, but four neutrons were expected to produce an even more transient resonance (a three-neutron state is not allowed). When the German group created the tetraneutron, it had a lifetime of only about 1×10-21 seconds, so it is extremely ephemeral. Nonetheless, studying the properties of the tetraneutron may give insights into both the strong and weak nuclear forces.

Hi-Tc superconductivity

When Bednorz and Müller discovered Hi-Tc superconductivity in 1986, it set off both a boom and a crisis. The boom was the opportunity to raise the critical temperature of superconductivity from 23 K that had been the world record held by Nb3Ge for 13 years since it was set in 1973. The crisis was that the new Hi-Tc materials violated the established theory of superconductivity explained by Bardeen-Cooper-Schrieffer (BCS). There was almost nothing in the theory of solid state physics that could explain how such high critical temperatures could be attained. At the March Meeting of the APS the following year in 1987, the session on the new Hi-Tc materials and possible new theories became known as the Woodstock of Physics, where physicists camped out in the hallway straining their ears to hear the latest ideas on the subject.

One of the ideas put forward at the session was the idea of superexchange by Phil Anderson. The superexchange of two electrons is related to their ability to hop from one lattice site to another. If the hops are coordinated, then there can be an overall reduction in their energy, creating a ground state of long-range coordinated electron hopping that could support superconductivity. Anderson was perhaps the physicist best situated to suggest this theory because of his close familiarity with what was, even then, known as the Anderson Hamiltonian that explicitly describes the role of hopping in solid-state many-body phenomena.

Ever since, the idea of superexchange has been floating around the field of Hi-Tc superconductivity, but no one had been able to pin it down conclusively, until now. In a paper published in the PNAS in September of 2022, an experimental group at Oxford presented direct observations of the spatial density of Cooper pairs in relation to the spatial hopping rates—where hopping was easiest then the Cooper pair density was highest, and vice versa. This experiment provides almost indisputable evidence in favor of Anderson’s superexchange mechanism for Cooper pair formation in the Hi-Tc materials, laying to rest the crisis launched 36 years ago.

Holographic Wormhole

The holographic principle of cosmology proposes that our three-dimensional physical reality—stars, galaxies, expanding universe—is like the projection of information encoded on a two-dimensional boundary—just as a two-dimensional optical hologram can be illuminated to recreate a three-dimensional visual representation. This 2D to 3D projection was first proposed by Gerald t’Hooft, inspired by the black hole information paradox in which the entropy of a black hole scales as surface area of the black hole instead of its volume. The holographic principle was expanded by Leonard Susskind in 1995 based on string theory and is one path to reconciling quantum physics with the physics of gravitation in a theory of quantum gravity—one of the Holy Grails of physics.

While it is an elegant cosmic idea, the holographic principle could not be viewed as anything down to Earth, until now. In November 2022 a research group at Caltech published a paper in Nature describing how they used Google’s Sycamore quantum computer (housed at UC Santa Barbara) to manipulate a set of qubits into creating a laboratory-based analog of a Einstein-Rosen bridge, also known as a “wormhole”, through spacetime. The ability to use quantum information states to simulate a highly-warped spacetime analog provides the first experimental evidence for the validity of the cosmological holographic principle. Although the simulation did not produce a physical wormhole in our spacetime, it showed how quantum information and differential geometry (the mathematics of general relativity) can be connected.

One of the most important consequences of this work is the proposal that ER = EPR (Einstein-Rosen = Einstein-Podolsky-Rosen). The EPR paradox of quantum entanglement has long been viewed as a fundamental paradox of physics that requires instantaneous non-local correlations among quantum particles that can be arbitrarily far apart. Although EPR violates local realism, it is a valuable real-world resource for quantum teleportation. By demonstrating the holographic wormhole, the recent Caltech results show how quantum teleportation and gravitational wormholes may arise from the same physics.

Net-Positive-Energy from Nuclear Fusion

Ever since nuclear fission was harnessed to generate energy, the idea of tapping the even greater potential of nuclear fusion to power the world has been a dream of nuclear physicists. Nuclear fusion energy would be clean and green and could help us avoid the long-run disaster of global warming. However, achieving that dream has been surprisingly frustrating. While nuclear fission was harnessed for energy (and weapons) within only a few years of discovery, and a fusion “boost” was added to nuclear destructive power in the so-called hydrogen bomb, sustained energy production from fusion has remained elusive.

In December of 2022, the National Ignition Facility (NIF) focussed the power of 192 pulsed lasers onto a deuterium-tritium pellet, causing it to implode, and the nuclei to fuse, releasing about 50% more energy that it absorbed. This was the first time that controlled fusion released net positive energy—about 3 million Joules out from 2 million Joules in—enough energy to boil about 3 liters of water. This accomplishment represents a major milestone in the history of physics and could one day provide useful energy. The annual budget of the NIF is about 300 million dollars, so there is a long road ahead (probably several more decades) before this energy source can be scaled down to an economical level.

Laser fusion experiment yields record energy at LLNL's National Ignition Facility | Lawrence Livermore National Laboratory
NIF image.

By David D. Nolte Jan. 16, 2023

by David D. Nolte

A Short History of Quantum Tunneling

Quantum physics is often called “weird” because it does things that are not allowed in classical physics and hence is viewed as non-intuitive or strange.  Perhaps the two “weirdest” aspects of quantum physics are quantum entanglement and quantum tunneling.  Entanglement allows a particle state to extend across wide expanses of space, while tunneling allows a particle to have negative kinetic energy.  Neither of these effects has a classical analog.

Quantum entanglement arose out of the Bohr-Einstein debates at the Solvay Conferences in the 1920’s and 30’s, and it was the subject of a recent Nobel Prize in Physics (2022).  The quantum tunneling story is just as old, but it was recognized much earlier by the Nobel Prize in 1972 when it was awarded to Brian Josephson, Ivar Giaever and Leo Esaki—each of whom was a graduate student when they discovered their respective effects and two of whom got their big idea while attending a lecture class. 

Always go to class, you never know what you might miss, and the payoff is sometimes BIG

Ivar Giaever

Of the two effects, tunneling is the more common and the more useful in modern electronic devices (although entanglement is coming up fast with the advent of quantum information science). Here is a short history of quantum tunneling, told through a series of publications that advanced theory and experiments.

Double-Well Potential: Friedrich Hund (1927)

The first analysis of quantum tunneling was performed by Friedrich Hund (1896 – 1997), a German physicist who studied early in his career with Born in Göttingen and Bohr in Copenhagen.  He published a series of papers in 1927 in Zeitschrift für Physik [1] that solved the newly-proposed Schrödinger equation for the case of the double well potential.  He was particularly interested in the formation of symmetric and anti-symmetric states of the double well that contributed to the binding energy of atoms in molecules.  He derived the first tunneling-frequency expression for a quantum superposition of the symmetric and anti-symmetric states

where f is the coherent oscillation frequency, V is the height of the potential and hν is the quantum energy of the isolated states when the atoms are far apart.  The exponential dependence on the potential height V made the tunnel effect extremely sensitive to the details of the tunnel barrier.

Fig. 1 Friedrich Hund

Electron Emission: Lothar Nordheim and Ralph Fowler (1927 – 1928)

The first to consider quantum tunneling from a bound state to a continuum state was Lothar Nordheim (1899 – 1985), a German physicist who studied under David Hilbert and Max Born at Göttingen and worked with John von Neumann and Eugene Wigner and later with Hans Bethe. In 1927 he solved the problem of a particle in a well that is separated from continuum states by a thin finite barrier [2]. Using the new Schrödinger theory, he found transmission coefficients that were finite valued, caused by quantum tunneling of the particle through the barrier. Nordheim’s use of square potential wells and barriers are now, literally, textbook examples that every student of quantum mechanics solves. (For a quantum simulation of wavefunction tunneling through a square barrier see the companion Quantum Tunneling YouTube video.) Nordheim later escaped the growing nationalism and anti-semitism in Germany in the mid 1930’s to become a visiting professor of physics at Purdue University in the United States, moving to a permanent position at Duke University.

Fig. 2 Nordheim square tunnel barrier and Fowler-Nordheim triangular tunnel barrier for electron tunneling from bound states into the continuum.

One of the giants of mathematical physics in the UK from the 1920s through the 1930’s was Ralph Fowler (1889 – 1944). Three of his doctoral students went on to win Nobel Prizes (Chandrasekhar, Dirac and Mott) and others came close (Bhabha, Hartree, Lennard-Jones). In 1928 Fowler worked with Nordheim on a more realistic version of Nordheim’s surface electron tunneling that could explain thermionic emission of electrons from metals under strong electric fields. The electric field modified Nordheim’s square potential barrier into a triangular barrier (which they treated using WKB theory) to obtain the tunneling rate [3]. This type of tunnel effect is now known as Fowler-Nordheim tunneling.

Nuclear Alpha Decay: George Gamow (1928)

George Gamov (1904 – 1968) is one of the icons of mid-twentieth-century physics. He was a substantial physicist who also had a solid sense of humor that allowed him to achieve a level of cultural popularity shared by a few of the larger-than-life physicists of his time, like Richard Feynman and Stephen Hawking. His popular books included One Two Three … Infinity as well as a favorite series of books under the rubric of Mr. Tompkins (Mr. Tompkins in Wonderland and Mr. Tompkins Explores the Atom, among others). He also wrote a history of the early years of quantum theory (Thirty Years that Shook Physics).

In 1928 Gamow was in Göttingen (the Mecca of early quantum theory) with Max Born when he realized that the radioactive decay of Uranium by alpha decay might be explained by quantum tunneling. It was known that nucleons were bound together by some unknown force in what would be an effective binding potential, but that charged alpha particles would also feel a strong electrostatic repulsive potential from a nucleus. Gamow combined these two potentials to create a potential landscape that was qualitatively similar to Nordheim’s original system of 1927, but with a potential barrier that was neither square nor triangular (like the Fowler-Nordheim situation).

Fig. 3 George Gamow

Gamow was able to make an accurate approximation that allowed him to express the decay rate in terms of an exponential term

where Zα is the atomic charge of the alpha particle, Z is the nuclear charge of the Uranium decay product and v is the speed of the alpha particle detected in external measurements [4].

The very next day after Gamow submitted his paper, Ronald Gurney and Edward Condon of Princeton University submitted a paper [5] that solved the same problem using virtually the same approach … except missing Gamow’s surprisingly concise analytic expression for the decay rate.

Molecular Tunneling: George Uhlenbeck (1932)

Because tunneling rates depend inversely on the mass of the particle tunneling through the barrier, electrons are more likely to tunnel through potential barriers than atoms. However, hydrogen is a particularly small atom and is therefore the most amenable to experiencing tunneling.

The first example of atom tunneling is associated with hydrogen in the ammonia molecule NH3. The molecule has a pyramidal structure with the Nitrogen hovering above the plane defined by the three hydrogens. However, an equivalent configuration has the Nitrogen hanging below the hydrogen plane. The energies of these two configurations are the same, but the Nitrogen must tunnel from one side of the hydrogen plane to the other through a barrier. The presence of light-weight hydrogen that can “move out of the way” for the nitrogen makes this barrier very small (infrared energies). When the ammonia is excited into its first vibrational excited state, the molecular wavefunction tunnels through the barrier, splitting the excited level by an energy associated with a wavelength of 1.2 cm which is in the microwave. This tunnel splitting was the first microwave transition observed in spectroscopy and is used in ammonia masers.

Fig. 4 Nitrogen inversion in the ammonia molecule is achieved by excitation to a vibrational excited state followed by tunneling through the barrier, proposed by George Uhlenbeck in 1932.

One of the earliest papers [6] written on the tunneling of nitrogen in ammonia was published by George Uhlenbeck in 1932. George Uhlenbeck (1900 – 1988) was a Dutch-American theoretical physicist. He played a critical role, with Samuel Goudsmit, in establishing the spin of the electron in 1925. Both Uhlenbeck and Goudsmit were close associates of Paul Ehrenfest at Leiden in the Netherlands. Uhlenbeck is also famous for the Ornstein-Uhlenbeck process which is a generalization of Einstein’s theory of Brownian motion that can treat active transport such as intracellular transport in living cells.

Solid-State Electron Tunneling: Leo Esaki (1957)

Although the tunneling of electrons in molecular bonds and in the field emission from metals had been established early in the century, direct use of electron tunneling in solid state devices had remained elusive until Leo Esaki (1925 – ) observed electron tunneling in heavily doped Germanium and Silicon semiconductors. Esaki joined an early precursor of Sony electronics in 1956 and was supported to obtain a PhD from the University of Tokyo. In 1957 he was working with heavily-doped p-n junction diodes and discovered a phenomenon known as negative differential resistance where the current through an electronic device actually decreases as the voltage increases.

Because the junction thickness was only about 100 atoms, or about 10 nanometers, he suspected and then proved that the electronic current was tunneling quantum mechanically through the junction. The negative differential resistance was caused by a decrease in available states to the tunneling current as the voltage increased.

Fig. 5 Esaki tunnel diode with heavily doped p- and n-type semiconductors. At small voltages, electrons and holes tunnel through the semiconductor bandgap across a junction that is only about 10 nm wide. Ht higher voltage, the electrons and hole have no accessible states to tunnel into, producing negative differential resistance where the current decreases with increasing voltage.

Esaki tunnel diodes were the fastest semiconductor devices of the time, and the negative differential resistance of the diode in an external circuit produced high-frequency oscillations. They were used in high-frequency communication systems. They were also radiation hard and hence ideal for the early communications satellites. Esaki was awarded the 1973 Nobel Prize in Physics jointly with Ivar Giaever and Brian Josephson.

Superconducting Tunneling: Ivar Giaever (1960)

Ivar Giaever (1929 – ) is a Norwegian-American physicist who had just joined the GE research lab in Schenectady New York in 1958 when he read about Esaki’s tunneling experiments. He was enrolled at that time as a graduate student in physics at Rensselaer Polytechnic Institute (RPI) where he was taking a course in solid state physics and learning about superconductivity. Superconductivity is carried by pairs of electrons known as Cooper pairs that spontaneously bind together with a binding energy that produced an “energy gap” in the electron energies of the metal, but no one had ever found a way to directly measure it. The Esaki experiment made him immediately think of the equivalent experiment in which Cooper pairs might tunnel between two superconductors (through a thin oxide layer) and yield a measurement of the energy gap. The idea actually came to him during the class lecture.

The experiments used a junction between aluminum and lead (Al—Al2O3—Pb). At first, the temperature of the system was adjusted so that Al remained a normal metal and Pb was superconducting, and Giaever observed a tunnel current with a threshold related to the gap in Pb. Then the temperature was lowered so that both Al and Pb were superconducting, and a peak in the tunnel current appeared at the voltage associated with the difference in the energy gaps (predicted by Harrison and Bardeen).

Fig. 6 Diagram from Giaever “The Discovery of Superconducting Tunneling” at https://conferences.illinois.edu/bcs50/pdf/giaever.pdf

The Josephson Effect: Brian Josephson (1962)

In Giaever’s experiments, the external circuits had been designed to pick up “ordinary” tunnel currents in which individual electrons tunneled through the oxide rather than the Cooper pairs themselves. However, in 1962, Brian Josephson (1940 – ), a physics graduate student at Cambridge, was sitting in a lecture (just like Giaever) on solid state physics given by Phil Anderson (who was on sabbatical there from Bell Labs). During lecture he had the idea to calculate whether it was possible for the Cooper pairs themselves to tunnel through the oxide barrier. Building on theoretical work by Leo Falicov who was at the University of Chicago and later at Berkeley (years later I was lucky to have Leo as my PhD thesis advisor at Berkeley), Josephson found a surprising result that even when the voltage was zero, there would be a supercurrent that tunneled through the junction (now known as the DC Josephson Effect). Furthermore, once a voltage was applied, the supercurrent would oscillate (now known as the AC Josephson Effect). These were strange and non-intuitive results, so he showed Anderson his calculations to see what he thought. By this time Anderson had already been extremely impressed by Josephson (who would often come to the board after one of Anderson’s lectures to show where he had made a mistake). Anderson checked over the theory and agreed with Josephson’s conclusions. Bolstered by this reception, Josephson submitted the theoretical prediction for publication [9].

As soon as Anderson returned to Bell Labs after his sabbatical, he connected with John Rowell who was making tunnel junction experiments, and they revised the external circuit configuration to be most sensitive to the tunneling supercurrent, which they observed in short time and submitted a paper for publication. Since then, the Josephson Effect has become a standard element of ultra-sensitive magnetometers, measurement standards for charge and voltage, far-infrared detectors, and have been used to construct rudimentary qubits and quantum computers.

By David D. Nolte: Nov. 6, 2022

YouTube Video

YouTube Video of Quantum Tunneling Systems

References:

[1] F. Hund, Z. Phys. 40, 742 (1927). F. Hund, Z. Phys. 43, 805 (1927).

[2] L. Nordheim, Z. Phys. 46, 833 (1928).

[3] R. H. Fowler, L. Nordheim, Proc. R. Soc. London, Ser. A 119, 173 (1928).

[4] G. Gamow, Z. Phys. 51, 204 (1928).

[5] R. W. Gurney, E. U. Condon, Nature 122, 439 (1928). R. W. Gurney, E. U. Condon, Phys. Rev. 33, 127 (1929).

[6] Dennison, D. M. and G. E. Uhlenbeck. “The two-minima problem and the ammonia molecule.” Physical Review 41(3): 313-321. (1932)

[7] L. Esaki, New Phenomenon in Narrow Germanium Para-Normal-Junctions, Phys. Rev., 109, 603-604 (1958); L. Esaki, (1974). Long journey into tunneling, disintegration, Proc. of the Nature 123, IEEE, 62, 825.

[8] I. Giaever, Energy Gap in Superconductors Measured by Electron Tunneling, Phys. Rev. Letters, 5, 147-148 (1960); I. Giaever, Electron tunneling and superconductivity, Science, 183, 1253 (1974)

[9] B. D. Josephson, Phys. Lett. 1, 251 (1962); B.D. Josephson, The discovery of tunneling supercurrent, Science, 184, 527 (1974).

[10] P. W. Anderson, J. M. Rowell, Phys. Rev. Lett. 10, 230 (1963); Philip W. Anderson, How Josephson discovered his effect, Physics Today 23, 11, 23 (1970)

[11] Eugen Merzbacher, The Early History of Quantum Tunneling, Physics Today 55, 8, 44 (2002)

[12] Razavy, Mohsen. Quantum Theory Of Tunneling, World Scientific Publishing Company, 2003.