The 2023 Nobel Prize in Chemistry: Quantum Dots

In this piece, which is written in Norwegian, Sølve Selstø gives a brief explanation of last year’s Nobel Prize in chemistry. It certainly falls within the quantum scope. The piece was published in last year’s last issue of Fra fysikkens verden, which is published by Norsk fysisk selskap.

Nobelprisen i kjemi 2023 er delt likt mellom dei tre forskarane:

  • Moungi Bawendi Massachusetts Institute of Technology (MIT), Cambridge, MA, USA
  • Louis Brus Columbia University, New York, NY, USA
  • Alexei Ekimov Nanocrystals Technology Inc., New York, NY, USA

for «oppdainga og syntetiseringa av kvanteprikkar (engelsk: quantum dots).».

Som mange veit, fekk Marie Skłodowska-Curie nobelprisen i både kjemi og fysikk. Då «vår eigen» Lars Onsager fekk ein hyggeleg telefon med invitasjon til Stockholm, var det ikkje straks opplagt for han om det var for å ta imot fysikk-eller kjemiprisen. Det var kjemiprisen. Også i år er nobelprisen i kjemi ei stadfesting av overlappet mellom dei to fagfelta.

Det heile begynte på tidleg 1980-talet – då både Yekimov og Brus, uavhengig av kvarandre, lukkast i lage nano-krystall med ein eigenskap dei kalla quantum size effect – kvante-eigenskaper som var bestemt av storleiken på krystalla. Når ein sendte lys på dei, oppdaga dei høg absorbering for spesi­fikke bølgelengder – bølgelengder som viste seg å auke med storleiken på nano-krystalla. Eit tiår seinare klarte Bawendi å finne ein svært presis og effektiv metode for å kontrollere storleiken på slike krystall. Det gjorde han mellom anna ved å justere temperaturen på væska dei blei danna i.

Det hadde lenge vore kjent at ulike stoff, atom og molekyl, kan identifiserast ut frå korleis dei respon­derer på ulike bølgelengder når ein sender lys på dei. Dette kallar vi spektroskopi; eit atom, for eksempel, absorberer foton med bølgelengder som samsvarar med energidifferensen mellom to kvante-tilstan­dar. Alternativt, ved å sørge for at mange av atoma i ein gass blir eksitert, at elektron går til ein høgare energi-tilstand, vil ein etterpå kunne observere utsendt lys med heilt spesifikke bølgelengder når atomet spontant går tilbake til grunnstilstanden sin.

Dette er altså ein direkte konsekvens av kvanti­sering – det at dei moglege energiane for eit bunde, mikroskopisk system er avgrensa til eit diskret sett.Eit atom får sitt eige, spesielle «fingeravtrykk» av moglege bølgelengder når det absorberer eller emit­terer lys. Det gjer oss i stand til å identifisere ukjend stoff – ikkje berre i eit laboratorium, men til og med på fjerne stjerner.

Det er mykje det same vi ser med nano-krystalla til Wavendi, Brus og Yekimov. Slike krystall er eksem­pel på det vi kallar kvanteprikkar – halvleiarstrukturar som evnar å fange inn nokre få elektron i eit område så lite at dei følger kvantefysiske lover. Slike kvan­teprikkar har det til felles med atom at energien til elektrona er kvantisert. Dette er hovudgrunnen til at kvanteprikkar ofte blir kalla kunstige atom.

Men mykje er også ulikt om vi samanliknar atom og kvanteprikkar. Sistnemnde er større; mens eit atom er nokre tidels nanometer store, er kvante­prikkar typisk fleire nanometer eller nokre titals nanometer i utstrekning. Men den viktigaste for­skjellen er nok denne: Der energinivåa, strukturen, til atom er prisgitt naturkonstantar som elemen­tærladninga, Planck-konstanten og elektronmassen, kan strukturen til kvanteprikkane justerast. Vi kan langt på veg konstruere dei slik at dei har dei spek­troskopiske eigenskapane vi ønsker!

Nobelprisvinnarane har klart og tydeleg demon­strert korleis dette kan gjerast ved å justere storleiken på kvanteprikkane. For nano-krystall som sender ut lys i den synlege delen av det elek­tromagnetiske spektrumet når dei går over til ein lågare energitilstand, vil ein relativt stor krystall sende raudt lys, mens bølgelengda vil bevege seg mot den lilla delen av spektrumet når kvanteprik­ken blir mindre.

Men storleiken er ikkje det einaste som tel. Fason­gen påverkar også spektrumet. Og det spelar ei rolle kva kvanteprikken er laga av; typisk er det snakk om ein halvleiar-krystall beståande av to grunn­stoff. Kvanteprikkane til nobelprisvinnarane blei konstruerte ved å la små krystallar gro i glas eller i ei væske. Frie enkelt-elektron kan også fangast inn i fastestoff-strukturar sett saman av ulike typar halvleiarar. Her blir fleire ulike geometriar og teknikkar brukte. Ein kan også bruke statiske elek­triske felt til å fange inn elektron i slike samansette halvleiarar-strukturar. Slike kvanteprikkar er spe­sielt fleksible sidan ein, ved å justere den elektriske spenninga, kan endre den romlege avgrensinga. På den måten endrar ein også energi-strukturen til det kvantiserte systemet. I tillegg kan ein manipulere systemet ved å legge på fleire felt, både magnetiske og elektriske, statiske og dynamiske.

Uansett korleis ein gjer det, er det gull verd at vi er i stand til å justere på energinivåa til kvanteprikk­ane – ikkje berre frå eit vitskapleg perspektiv, men også teknologisk. Sidan ein kan finjustere kva farge kvanteprikkane kan sende ut, kan dei for eksem­pel brukast til å gjere LED-lys betre, noko ein alt har tatt i bruk for å lage TV-skjermar. Men dette er ikkje i nærleiken av dei mest spanande bruksom­råda. Kvanteprikkar kan brukast til å gjere fleire faststoff-applikasjonar betre. Dei blir brukt til å lage singel-elektron transistorar. Og ein håpar å kunne bruke dei til å produsere solceller med langt høgare verknadsgrad enn tradisjonelle solceller.

Ved å sørge for at væsker med kvanteprikkar festar seg til spesielt vev, som for eksempel ein svulst, kan kirurgar få svært gode bilde av vevet dei skal operere i – eller fjerne.

Kvanteprikkar er også kandidatar til å lage kvan­te-bits, qubits. Enkelt-elektron i ein kvanteprikk kan styrast mellom ulike kvantetilstandar på ein kon­trollert måte. Ved å sette fleire slike kontrollerbare kvantesystem saman kan ein lage ein kvantedata­maskin. Håpar vi.

Potensialet er stort! Bawendi, Brus og Yekimov har vore med å opne døra til eit spanande rom. Vi har tatt steget over dørstokken, det skal bli span­ande å sjå kva meir vi finn der inne.

Referansar

On Quantum Supremacy (some reflections induced by Maksym Teslyk’s post)

He has attained supremacy in one particular line: he succeeds in inspiring a mysterious thrill (M. R. James)

The concept of High Concept crystallized in Hollywood in the 1980s: A movie whose title answers the question “What that movie is about?” and whose plot can be explained in two sentences. It is a highly visual movie and it has an appeal to all types of viewers, from retired army officers to nurses to young IT nerds. You can start watching  this movie from any point of its narrative and enjoy it and have a good feeling at the end. All this however does not mean that high-concept movies are mental toys made for dummies – these movies  are highly original and orchestrated  in a very thoughtful way. High Concept movies are planned to be box-office bombs (“We have no obligation to make history. We have no obligation to make art. We have no obligation to make a statement. Our obligation is to make money“, Don Simpson). Examples: “Top Gun” and “Jurassic Park”.

Low Concept movies are on the other edge of the spectrum: Complex plots (sometimes opposite – so trivial that you can pitch them in one sentence like “two guys are sitting in a restaurant and talking all the time”) and character (not action) – driven narratives. These movies are targeted to a specific audience, they are more demanding and often full of connotations – to literature, art, and other movies. Prospects for commercial success are slim. Examples: “My Nights Are More Beautiful Than Your Days” and “Faces”.

The High/Low Concepts can  be extended to science: A high-concept paper is a paper presenting exciting new results which is reflected in  the paper’s title and whose idea can be grasped by a lay person. Such a paper usually gets media coverage and journalists are happy to write about it. Example: “Washing Away Postdecisional Dissonance” or “Analytic thinking promotes religious disbelief”. Low-concept papers: Traditional scientific papers which can only be comprehended by experts. Examples: Open a random issue of “Journal of Topology” and pick a random paper.

Quantum supremacy using a programmable superconducting processor” (October, 2019) is a trickster, a low-concept wolf in a high-concept’s skin. The title tells about the message needed to be spread: Supremacy of quantum computers over classical ones has been demonstrated! Media coverage: It was mentioned in 409 News stories, 67 Blog posts, and 2,026 Tweets. It was hyped in newspapers and magazines, it was discussed in podcasts. By now, many lay people have heard of it.

But what is the essence? How precisely has supremacy been demonstrated? What is the idea of the proof-of-concept experiment reported? Even physicists or IT experts or mathematicians  are hardly able to get answers to these questions by simply reading the paper — because it is too cryptic, too demanding (one has to read several others – no less cryptic and demanding!  – papers before), and too technical. It is a Klein bottle, a promise of a joy of learning something really new and exciting which turns out to be a depressing realization that what is presented in the paper is super-specific and  expertise-demanding and therefore – incomprehensible.

So, what is the problem? The QC research is anyway a highly specialized field which demands substantial expertise. Should be Google blamed for this? Of course, not. However, my feeling is that the Google strategy in presenting results is on purpose cryptic and bombastic at the same time. It is OK, it is just a strategy, indeed legitimate as many others. It is my problem: I simply do not like it.

On the origin of quantum advantage, by Maksym Teslyk

Quantum computing seems to be a popular trend all over the word nowadays. Many of us have heard that private companies, e.g., D-Wave Systems, Google quantum AI, IBM with its very latest quantum processor Condor, etc., are working hard on the construction and design of quantum computation facilities. Even more on that, the academic community is also involved in the race – and OsloMet is no exception here.

One may wonder why are we working so hard and investing so much time and resources to build a quantum computer? Maybe all this activity is nothing more but a hype, and the focus on common and well-known classical machines, which we know how to produce, would be a better strategy? What are the benefits of calculations based on quantum algorithms, instead of classical ones?

One may suggest pure math to answer these questions. However, algorithm complexity theory is not of great help. There are plenty of issues which it cannot solve. For example, one may try the NP problem, which is believed to be hard enough to be included in the Millenium Prize Problems listing. And introducing quantum complexity classes just makes the approach even more challenging.

The opposite solution is solely practice. One may design a quantum device able to solve some (abstract) tasks which is unsolvable by any existing (or forthcoming) classical computer. The approach attracts much attention today, but cannot provide any satisfiable answer – see, e.g., the recent efficient simulation of quantum processors.

Ok, but we know that the properties of elementary pieces of information exhibit significant differences. For example, any classical bit can be represented as a switch between two mutually excluding classical states. Quantum bits, or qubits, are encoded with the Bloch sphere – they are two-dimensional, unlike bits. Such a seemingly strange and counter-intuitive representation originates from the quantum superposition principle, allowing for a quantum system to contain both mutually excluding outcomes simultaneously. Combined with linearity of unitary operators performing quantum evolution, this allows to hack the computation. Namely, one may encode all the possible combinations of the onset data into a single input state and obtain all the possible outputs in a single run of a quantum processor. Obviously, such a recipe won’t work for classical switches.

So, have we found the answer? On the one hand, both quantum superposition and linearity of operators allow one to use quantum interference at its full power. This can be easily illustrated with the help of, e.g., quantum Bernstein-Vazirani algorithm which outperforms the classical one. On the other hand, the Gottesmann-Knill theorem challenges this and makes the whole approach a bit unclear.

If the properties of information cannot explain the quantum advantage, maybe we should look for something which cannot be reproduced within any classical device at all? How about entanglement? Indeed, this phenomenon, blamed by A. Einstein as a ‘spooky action at a distance’, exhibits the possibility of correlations at the level which is unattainable in the terms of non-quantum physics. It is also known as quantum non-locality and violates Bell inequalities which any classical system, regardless its properties and working principles, should obey.

Entangled states imply the existence of a quantum communication channel and can be used to transfer data far more efficiently than any existing communication networks. These are not just words: we do have such quantum protocols as quantum teleportation or superdense coding, and both are heavily based on entanglement.

So, we see that quantum non-locality may be treated as a quantum resource allowing more efficient information transfer. Moreover, it was shown that if the entanglement which is produced by some quantum circuit is upper-bounded, then it can be efficiently simulated classically. Therefore, one may conclude that entanglement speeds up quantum computation. However, another study could not detect any significant role of this resource in the Shor’s algorithm. Taking into account that the algorithm is one of the most efficient among the ones known to date, we must admit that the role of entanglement in the speed-up requires further clarification.

We may consider the problem at the very abstract level also. Any process obeys some set of rules, which can be formalized in the terms of underlying logic. The formalism was developed almost a century ago. It clearly demonstrates that any classical system obeys the rules of Boolean logic, which can be inferred from the relations among the subsets of a phase space, and that any quantum system is governed by the relations among the linear subspaces of the Hilbert space (quantum logic). The key difference between these two systems originates from the commutation properties of classical functions and quantum operators, respectively.

The Huygens-Fresnel principle allows to compare both logics with such different algebraic structures. Namely, let us consider a wave propagating from point A to B. In the terms of wave optics we know that the transition should take into account all possible paths through space. However, in case the wavelength is negligible, all these additional paths vanish but the one governed by far more simple ray optics. The same procedure may be applied to quantum circuits in terms of the path integral formalism. Taking the de Broglie wavelength to the zeroth limit determines their transition to classical calculations. Unfortunately, the estimation of information lost under the limit does not reproduce the corresponding increase of computational inefficiency. To sum up, we know that quantum advantage exists. This can be easily illustrated with the help of Grover’s search algorithm, which outperforms any classical analog. On the other hand, the origin of the advantage looks fuzzy. And everyone is highly invited to participate in solving the puzzle.

Where relativity meets the quantum

A while ago, in an episode of the popular Scandinavian talk show Skavlan, the founder of Norwegian Air Shuttle, Bjørn Kjos, met with famous mathematician and Fields medalist Cedric Villani. Kjos was talking about how he had been trying to solve the Schrödinger equation – seemingly impressing Villani quite a bit. “Wow, you are brave!” he exclaimed. However, I suppose he would have been even more impressed if Kjos had taken on the Dirac equation.

You may have learned that when material things start approaching the speed of light, the absolute speed limit of nature, our world starts looking strange. According to Einstein’s theory of relativity, things become shorter and time evolves more slowly.

Perhaps you have also heard that no-one has succeeded in formulating a theory comprising both quantum physics and relativity. Luckily, this is only partly true. More specifically, it is true when it comes to Einstein’s theory of general relativity, which deals with gravitation and is essential to our understanding of how the universe came about and evolves.

General theory’s predecessor, special relativity, however, is happily united by quantum physics. This union is entitled the Dirac equation, which the Brit Paul Dirac introduced in 1928 – only a couple of years after Erwin Schrödinger published his famous equation. Dirac and Schrödinger shared a Nobel price for that only a few years later.

Paul Dirac in 1933 – the year when he shared a Nobel price in physics with Erwin Schrödinger.

The Dirac equation includes the Schrödinger equation as a special case – except that it also encompasses the strange notion of electron spin. This is, however, not the strangest thing that emerges from Dirac’s equation.

The equation is plagued with several issues which makes it hard to solve – also numerically. One of these issues is that it features solutions of negative energy – in addition to the expected ones. The meaning of these odd solutions remained a mystery for a while – even to Paul Dirac himself. In an interesting interview conducted by Friedrich Hund in 1982 – well worth seeing – he talks about how he spent a year or so pondering on how to deal with them. His solution, eventually, was to postulate a sea of occupied states – a sea from which particles could be promoted leaving behind a hole. Somewhat exotic, you may think.

These notions are, as it turns out, related to the existence of anti-matter. For every particle there is an odd twin with much of the same properties – except that most of them have opposite sign. Not a very intuitive conclusion; you cannot blame anyone – including Dirac – for being puzzled by this notion. I guess this is one of the many concepts emerging from quantum physics which merits the exclamation “who ordered that?!”. (The quote originates from Isodor Rabi, the father of the MR technique, when he heard about the discovery of the muon particle, one of the electron’s heavier siblings.)

Nonetheless, anti-matter exists; we have seen it. Moreover, we have seen that pairs of particle and anti-particle may be created – they may emerge out of nothing, so to speak. Needless to say, this complicates life for anyone who may want to describe quantum physics close to the speed of light theoretically or computationally. We cannot even say for sure how many particles we are dealing with!

Luckily for us, there is a window between the point where classical, classical in the meaning non-relativistic, breaks down and the point at which pair creation needs to be considered. For instance, with the strongest of lasers, electrons may be accelerated to a certain fraction of the speed of light – thus necessitating a relativistic treatment. Even in cases where these laser fields are not strong enough to start producing particle anti-particle pairs, the numerical description is still hard enough. Thus, we were thrilled to see that relativistic effects could, to a large extent, be treated by introducing the concept of relativistic mass into the Schrödinger equation. In effect, the electron becomes a bit heavier as it becomes faster. This, in turn, contributes to enhance the effect of atomic stabilization – the notion that an atom becomes less likely to be torn apart by a laser field as you increase the strength of the laser. In other words: Yet another non-intuitive feature of quantum physics – perhaps a topic for a future blog post.

Schrödinger’s Tardigrade, by Sergiy Denysov

So far there is only one animal was involved into quantum physics, that is the famous Schrödinger’s cat. Now some researchers claim that there is one more.

In February 2019, I came across the piece “Quantum theory: the weird world of teleportation, tardigrades and entanglement” [1]: Gröblacher is also interested in experiments involving living creatures … He is currently working on putting a sheet of nitride into a superposition of states … “A superposition state of these membranes would allow us to demonstrate that objects that are visible to the naked eye still behave quantum, and we can really test decoherence – the transition between classical and quantum mechanics,” he says. He hopes to extend the experiment by placing tiny living organisms called tardigrades onto the membrane of silicon nitride, putting them into superposition too.

Targidrates are known for being tough [2]. These micro-animals (their official title) can enter a ‘hibernation state’ of near complete dehydration and metabolism rate decreased by factor 1/1000, and, being in this state, survive an exposure to outer space (almost perfect vacuum), high-intensity radiation of all kinds (including gamma rays), and pressure up to 1200 atmosphere. Therefore, they might hopefully withstand the cryogenic environment required to achieve ground state cooling of the membrane. If there an animal able to survive superposition this must be a tardigrade.

After reading the piece, my immediate thought was: But would the tardy feel the difference between just the groundstate and superposition of the groundstate and the first excited state of the membrane? And in what measurable terms? Or is this difference is simply negligible on the background of the mere exposure to the cryogenic environment?

Another thought back then: The typical size of silicon nitride membranes Gröblacher is dealing with is 0.5 mm. This is also the typical size of tardigrades. I do not know the masses of the membranes and tardigrades but expect them to be comparable. It is not possible to maintain the extra-high quality factor of such membranes after placing on them a tardigrade – unless the membranes are on-purpose designed and curved, with ‘nests’ for tardys (a-la seats of Space Jockeys [3]).

Three years have passed and in 2022 a work with a sensational title, “Entanglement in a qubit-qubit-tardigrade system”, was published in New journal of Physics [4].

Sketch of the experiment reported in the paper [4].

The authors claimed that hey set a tardigrade into entanglement with two qubits — and the former has survived it (“The animal is then observed to return to its active form after 420 hours at sub 10 mK temperatures and pressure of 6 × 10−6 mbar, setting a new record for the conditions that a complex form of life can survive“). But had the animal really been quantum entangled?

To prove it, one has to measure the quantum properties of the tardigrade, which the experiment does not do. Instead, a model was used (“The tomographic data shows entanglement in the qubit-qubit-tardigrade system, with the tardigrade modelled as an ensemble of harmonic oscillators or collection of electric dipoles“). Well, the quantum community is sceptical about such a ’proof’.

Also, there is a strong scepticism about that entanglement can be obtained by simply placing a tardy on top of a qubit. After that the qubit is no longer a resonator with well-tuned characteristics so one should not talk about ‘groundstate’ and ‘excited state’. From the point of view of quantum physics, a tardy is a system with macroscopically many degrees of freedom so it decoheres the qubit by working as an external environment. But doesn’t the environment become entangled with the object it is acting on? But is it measurable?

The problem is that the animal is not a quantum object in a sense that its state cannot be described as a superposition of a few basis states. So where is the entanglement? In such situation, the entanglement cannot be located and thus cannot be measured. We could also say that we are entangled with an electron in a oxygen atom of 02 floating somewhere inside out right lung – but it is not measurable and therefore does not exist (at least for quantum physics).

Anyway, the ‘entanglement’ claimed in the paper was not assessed in experiment and therefore the clam is much stronger than the experimental data can support. Schrödinger’s tardigrade is not yet here and Schrödinger’s cat has to wait for a companion.

[1] https://www.sciencefocus.com/science/quantum-theory-the-weird-world-of-teleportation-tardigrades-and-entanglement

[2] https://en.wikipedia.org/wiki/Tardigrade

[3] https://cdna.artstation.com/p/assets/images/images/004/247/248/large/mickael-goyec-orthographic-plansj.jpg?1481702424

[4] K. S. Lee at al., Entanglement in a qubit-qubit-tardigrade system, New Journal of Physics 24, 123024 (2022); https://iopscience.iop.org/article/10.1088/1367-2630/aca81f#:~:text=In%20particular%2C%20for%20any%20finite,electric%20field%2C%20see%20Appendix%20F%20.