phonons – Close Read

Physicists produce video of time crystal in action 😱

Have you heard of time crystals?

A crystal is any object whose atoms are arranged in a fixed pattern in space, with the pattern repeating itself. So what we typically know to be crystals are really space crystals. We didn’t have to bother with the prefix because space crystals were the only kind of crystals we knew until time crystals came along.

Time crystals are crystalline objects whose atoms exhibit behaviour that repeats itself in time, as periodic events. The atoms of a time crystal spin in a fixed and coordinated pattern, changing direction at fixed intervals.

Physicists sometimes prefer to quantify these spin patterns as quasiparticles to simplify their calculations. Quasiparticles are not particles per se. To understand what they are, consider a popular one called phonons. Say you strike a metal spoon on the table, producing a mild ringing sound. This sound is the result of sound waves propagating through the metal’s grid of atoms, carrying vibrational energy. You could also understand each wave to be a particle instead, carrying the same amount of energy that each sound wave carries. These quasiparticles are called phonons.

In the same way, patterns of spinning charged particles also carry some energy. Each electron in an atom, for example, generates a tiny magnetic field around itself as it spins. The directions in which the electrons in a material spin collectively determine many properties of the material’s macroscopic magnetic field. Sometimes, shifts in some electrons’ magnetic fields could set off a disturbance in the macroscopic field – like waves of magnetic energy rippling out. You could quantify these ‘spin waves’ in the form of quasiparticles called magnons. Note that magnons quantify spin waves; the waves themselves can be from electrons, ions or other charged particles.

As quasiparticles, magnons behave like a class of particles called bosons – which are nature’s force-carriers. Photons are bosons that mediate the electromagnetic force; W and Z bosons mediate the weak nuclear force responsible for radioactivity; gluons mediate the strong nuclear force, which carries the energy you see released by nuclear weapons; scientists have hypothesised the existence of gravitons, for gravity, but haven’t found them yet. Like all bosons, magnons don’t obey Pauli’s exclusion principle and they can be made to form exotic states of matter like superfluids and Bose-Einstein condensates.

Other quasiparticles include excitons and polarons (useful in the study of electronic circuits), plasmons (of plasma) and polaritons (of light-matter interactions).

Physicist Frank Wilczek proposed the existence of time crystals in 2012. One reason time crystals are interesting to physicists is that they break time-translation symmetry in their ground state.

This statement has two important parts. The first concerns time-translation symmetry-breaking. Scientists assume the laws of physics are the same in all directions – yet we still have objects like crystals, whose atoms are arranged in specific patterns that repeat themselves. Say the atoms of a crystal are arranged in a hexagonal pattern. If you kept the position of one atom fixed and rotated the atomic lattice around it or if you moved to the left or right of that atom, in both cases by an arbitrary amount, your view of the lattice will also change. This happens because crystals break spatial symmetry. Similarly, time symmetry is broken if an event repeats itself in time – like, say, a magnetic field whose structure changes between two shapes over and over.

The second part of the statement concerns the (thermodynamic) ground state – the state of any quantum mechanical system when it has its lowest possible energy. (‘Quantum mechanical system’ is a generic term for any system – like a group of electrons – in which quantum mechanical effects have the dominant influence on the system’s state and behaviour. An example of a non-quantum-mechanical system is the Solar System, where gravity dominates.) Wilczek revived interest in time crystals as objects that break time-translation symmetry in their ground states. Put another way, they are quantum mechanical systems whose constituent particles perform a periodic activity without changing the overall energy of the system.

The advent of quantum mechanics and relativity theory in the early 20th century alerted physicists to the existence of various symmetries and, through the work of Emmy Noether, their connection to different conservation laws. For example, a system in which the laws of nature were the same throughout history and will be in future – i.e. preserves time-translation symmetry – will also conserve energy. Does this mean time crystals violate the law of conservation of energy? No. The atoms’ or electrons’ spin is not the result of the electrons’ or atoms’ kinetic energy but is an inherent quantum mechanical property. This energy can’t be used to perform work the same way, say, a motor can pump water. The system’s total energy is still conserved.

Now, physicists from Germany have reported that they have observed a time crystal ‘in action’ – a feat notable on three levels. First, it’s impressive that they have created a time crystal in the first place (even if they are not the first to do so). The researchers passed radio frequency waves through a strip of nickel-iron alloy a few micrometers wide. According to ScienceAlert, this ‘current’ “produced an oscillating magnetic field on the strip, with magnetic waves travelling onto it from both ends”. As a result, they “stimulated the magnons in the strip, and these moving magnons then condensed into a repeating pattern”.

Second, while quasiparticles are not actual particles per se, they exhibit some properties of particles. One of them is scattering, like two billiard balls might bounce off each other to go off in different directions at different speeds. Similarly, the researchers created more magnons and scattered them off the magnons involved in the repeating pattern. The post-scatter magnons had a shorter wavelength than they did originally, in line with expectations, and the researchers also found that they could control this wavelength by adjusting the frequency of the stimulating radio waves.

An ability to control such values often means the process could have an application. The ability to precisely manipulate systems involving the spin of electrons has evolved into a field called spintronics. Like electronics makes use of the electrical properties of subatomic particles, spintronics is expected to leverage spin-related properties and enable ultra-fast hard-drives and other technologies.

Third, the researchers were able to produce a video showing the magnons moving around. This is remarkable because the thing that makes a time crystal so unique is the result of quantum mechanical processes, which are microscopic in nature. It’s not often that you can observe their effects on the macroscopic scale. The principal reason the researchers were able achieve this is feat is the method they used to create the time crystal.

Previous efforts to create time crystals have used systems like quantum gases and Bose-Einstein condensates, both of which require sophisticated apparatuses to work with, in ultra-cold conditions, and whose behaviour researchers can track only by carefully measuring their physical and other properties. On the other hand, the current experiment works at room temperature and uses a more ‘straightforward’ setup that is also fairly large-scale – enough to be visible under an X-ray microscope.

Working this microscope is no small feat, however. Charged particles emit radiation when they’re accelerated along a circular path. An accelerator called BESSY II in Berlin uses this principle to produce X-rays. Then the microscope, called MAXYMUS, focuses the X-rays onto an extremely small spot – a few nanometers wide – and “scans across the sample”, according to its official webpage. A “variety of X-ray detectors”, including a camera, observe how the X-rays interact with the sample to produce the final images. Here’s the resulting video of the time crystal, captured at 40 billion frames per second:

I asked one of the paper’s coauthors, Joachim Gräfe, a research group leader in the department of modern magnetic systems at the Max Planck Institute for Intelligent Systems, Stuttgart, two follow-up questions. He was kind enough to reply in detail; his answers are reproduced in full below:

A time crystal represents a system that breaks time translation symmetry in its ground state. When you use radio-frequency waves to stimulate the magnons in the nickel-iron alloy, the system is no longer in its ground state – right?

The ground state debate is the interesting part of the discussion for theoreticians. Our paper is more about the experimental observation and an interaction towards a use case. It is argued that a time crystal cannot be a thermodynamic ground state. However, it is in a ground state in a periodically alternating potential, i.e. a dynamic ground state. The intriguing thing about time crystals is that they are in ground states in these periodically alternating potentials, but they do not/will not necessarily have the same periodicity as the alternating potential.
The condensation of the magnonic time crystal is a ground state of the system in the presence of the RF field (the periodically alternating potential), but it will dissipate through damping when the RF field is switched off. However, even in a system without damping, it would not form without the RF field. It really needs the periodically alternating potential. It is really a requirement to have a dynamic system to have a time crystal. I hope I have not confused you more than before my answer. Time crystals are quite mind boggling. 😵🤯

Previous experiments to observe time crystals in action have used sophisticated systems like quantum gases and Bose-Einstein condensates (BECs). Your experiment’s setup is a lot more straightforward, in a manner of speaking. Why do you think previous research teams didn’t just use your setup? Or does your setup have any particular difficulty that you overcame in the course of your study?

Interesting question. With the benefit of hindsight: our time crystal is quite obvious, why didn’t anybody else do it? Magnons only recently have emerged … as a sandbox for bosonic quantum effects (indeed, you can show BEC and superfluidity for magnons as well). So it is quite straightforward to turn towards magnons as bosons for these studies. However, our X-ray microscope (at the synchrotron light source) was probably the only instrument at the time to have the required spatial and temporal resolution with magnetic contrast to shoot a video of the space-time crystal. Most other magnon detection methods (in the lab) are indirect and don’t yield such a nice video.
On the other hand, I believe that the interesting thing about our paper is not that it was incredibly difficult to observe the space time crystal, but that it is rather simple to create one. Apparently, you can easily create a large (magnonic) space time crystal at room temperature and do something with it. Showing that it is easy to create a space time crystal opens this effect up for technological exploitation.

Superconductivity: From Feshbach to Fermi

(This post is continued from this one.)

After a bit of searching on Wikipedia, I found that the fundamental philosophical underpinnings of superconductivity were to be found in a statistical concept called the Feshbach resonance. If I had to teach superconductivity to those who only knew of the phenomenon superfluously, that’s where I’d begin. So.

Imagine a group of students who have gathered in a room to study together for a paper the next day. Usually, there is that one guy among them who will be hell-bent on gossiping more than studying, affecting the performance of the rest of the group. In fact, given sufficient time, the entire group’s interest will gradually shift in the direction of the gossip and away from its syllabus. The way to get the entire group back on track is to introduce a Feshbach resonance: cut the bond between the group’s interest and the entity causing the disruption. If done properly, the group will turn coherent in its interest and to focusing on studying for the paper.

In multi-body systems, such as a conductor harboring electrons, the presence of a Feshbach resonance renders an internal degree of freedom independent of those coordinates “along” which dissociation is most like to occur. And in a superconductor, a Feshbach resonance results in each electron pairing up with another (i.e., electron-vibrations are quelled by eliminating thermal excitation) owing to both being influenced by an attractive potential that arises out of the electron’s interaction with the vibrating lattice.

Feshbach resonance & BCS theory

For particulate considerations, the lattice-vibrations are quantized in the form of hypothetical particles called phonons. As for why the Feshbach resonance must occur the way it does in a superconductor: that is the conclusion, rather implication, of the BCS theory formulated in 1957 by John Bardeen, Leon Neil Cooper, and John Robert Schrieffer.

The BCS theory essentially treats electrons like rebellious, teenage kids (I must be getting old). As negatively charged electrons pass through the crystal lattice, they draw the positively charged nuclei toward themselves, creating an increase in the positive charge density in their vicinity that attracts more electrons in turn. The resulting electrostatic pull is stronger near nuclei and very weak at larger distances. The BCS theory states that two electrons that would otherwise repel each other will pair up in the face of such a unifying electrostatic potential, howsoever weak it is.

This is something like rebellious teens who, in the face of a common enemy, will unite with each other no matter what the differences between them earlier were.

Since electrons are fermions, they bow down to Pauli’s exclusion principle, which states that no two fermions may occupy the same quantum state. As each quantum state is defined by some specific combination of state variables called quantum numbers, at least one quantum number must differ between the two co-paired electrons.

prof_wolfgang_pauli — Prof. Wolfgang Pauli (1900-1958)

In the case of superconductors, this is particle spin: the electrons in the member-pair will have opposite spins. Further, once such unions have been achieved between different pairs of electrons, each pair becomes indistinguishable from the other, even in principle. Imagine: they are all electron-pairs with two opposing spins but with the same values for all other quantum numbers. Each pair, called a Cooper pair, is just the same as the next!

Bose-Einstein condensates

This unification results in the sea of electrons displaying many properties normally associated with Bose-Einstein condensates (BECs). In a BEC, the particles that attain the state of indistinguishability are bosons (particles with integer spin), not fermions (particles with half-integer spin). The phenomenon occurs at temperatures close to absolute zero and in the presence of an external confining potential, such as an electric field.

Since bosons don’t follow Pauli’s exclusion principle, a major fraction of the indistinguishable entities in the condensate may and do occupy the same quantum state. This causes quantum mechanical effects to become apparent on a macroscopic scale.

By extension, the formulation and conclusions of the BCS theory, alongside its success in supporting associated phenomena, imply that superconductivity may be a quantum phenomenon manifesting in a macroscopic scale.

Note: If even one Cooper pair is “broken”, the superconducting state will be lost as the passage of electric current will be disrupted, and the condensate will dissolve into individual electrons, which means the energy required to break one Cooper pair is the same as the energy required to break the composition of the condensate. So thermal vibrations of the crystal lattice, usually weak, become insufficient to interrupt the flow of Cooper pairs, which is the flow of electrons.

The Meissner effect

In this context, the Meissner effect is simply an extrapolation of Lenz’s law but with zero electrical resistance.

Lenz’s law states that the electromotive force (EMF) because of a current in a conductor acts in a direction that always resists a change in the magnetic flux that causes the EMF. In the absence of resistance, the magnetic fields due to electric currents at the surface of a superconductor cancel all magnetic fields inside the bulk of the material, effectively pushing magnetic field lines of an external magnetic potential outward. However, the Meissner effect manifests only when the externally applied field is weaker than a certain critical threshold: if it is stronger, then the superconductor returns to its conducting state.

Now, there are a class of materials called Type II superconductors – as opposed to the Type I class described earlier – that only push some of the magnetic field outward, the rest remaining conserved inside the material in filaments while being surrounded by supercurrents. This state is called the vortex state, and its occurrence means the material can withstand much stronger magnetic fields and continue to remain superconducting while also exhibiting the hybrid Meissner effect.

Temperature & superconductivity

There are also a host of other effects that only superconductors can exhibit, including Cooper-pair tunneling, flux quantization, and the isotope effect, and it was by studying them that a strong relationship was observed between temperature and superconductivity in various forms.

Bardeen_Cooper_Schrieffer — (L to R) John Bardeen, Leon Cooper, and John Schrieffer

In fact, Bardeen, Cooper, and Schrieffer hit upon their eponymous theory after observing a band gap in the electronic spectra of superconductors. The electrons in any conductor can exist at specific energies, each well-defined. Electrons above a certain energy, usually in the valence band, become free to pass through the entire material instead of staying in motion around the nuclei, and are responsible for conduction.

The trio observed that upon cooling the material to closer and closer to absolute zero, there was a curious gap in the energies at which electrons could be found in the material at a particular temperature. This meant that, at that temperature, the electrons were jumping from existing at one energy to existing at some other lower energy. The observation indicated that some form of condensation was occurring. However, a BEC was ruled out because of Pauli’s exclusion principle. At the same time, a BEC-like state had to have been achieved by the electrons.

This temperature is called the transition temperature, and is the temperature below which a conductor transitions into its superconducting state, and Cooper pairs form, leading to the drop in the energy of each electron. Also, the differences in various properties of the material on either side of this threshold are also attributed to this temperature, including an important notion called the Fermi energy: it is the potential energy that any system possesses when all its thermal energy has been removed from it. This is a significant idea because it defines both the kind and amount of energy that a superconductor has to offer for an externally applied electric current.

enrico_fermi — Enrico Fermi, along with Paul Dirac, defined the Fermi-Dirac statistics that governs the behavior all identical particles that obey Pauli’s exclusion principle (i.e., fermions). Fermi level and Fermi energy are concepts named for him; however, as long as we’re discussing eponymy, Fermilab overshadows them all.

In simple terms, the density of various energy states of the electrons at the Fermi energy of a given material dictates the “breadth” of the band gap if the electron-phonon interaction energy were to be held fixed at some value: a direct proportionality. Thus, the value of the energy gap at absolute zero should be a fixed multiple of the value of the energy gap at the superconducting transition temperature (the multiplication factor was found to be 3.5 universally, irrespective of the material).

Similarly, because of the suppression of thermal excitation (because of the low temperature), the heat capacity of the material reduces drastically at low temperatures, and vanishes below the transition temperature. However, just before hitting zero at the threshold, the heat capacity balloons up to beyond its original value, and then pops. It was found that the ballooned value was always 2.5 times the material’s normal heat capacity value… again, universally, irrespective of the material!

The temperature-dependence of superconductors gains further importance with respect to applications and industrial deployment in the context of its possible occurring at higher temperatures. The low temperatures currently necessary eliminate thermal excitations, in the form of vibrations, of nuclei and almost entirely counter the possibility of electrons, or Cooper pairs, colliding into them.The low temperatures also assist in the flow of Cooper pairs as a superfluid apart from allowing for the energy of the superfluid being higher than the phononic energy of the lattice.

However, to achieve all these states in order to turn a conductor into a superconductor at a higher temperature, a more definitive theory of superconductivity is required. One that allows for the conception of superconductivity that requires only certain internal conditions to prevail while the ambient temperature soars. The 1986-discovery of high-temperature superconductors in ceramics by Bednorz and Muller was the turning point. It started to displace the BCS theory which, physicists realized, doesn’t contain the necessary mechanisms for superconductivity to manifest itself in ceramics – insulators at room temperature – at temperatures as high as 125 K.

A firmer description of superconductivity, therefore, still remains elusive. Its construction should not only pave the for one of the few phenomena that hardly appears in nature and natural processes to be fully understood, but also for its substitution against standard conductors that are responsible for lossy transmission and other such undesirable effects. After all, superconductors are the creation of humankind, and only by its hand while they ever be fully worked.

Stages of superconductivity: Researchers’ insight on ‘pseudogap’ an important advance (phys.org)

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