30.03.2023 change 30.03.2023

How waves propagate in quantum droplets

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In quantum droplets - a new state of matter, known only for a few years (a 'liquefied' Bose-Einstein condensate) - it is possible to observe unusual quantum waves called solitons with very interesting properties, according to the analyses of Polish physicists. A theoretical paper on this topic was published in the prestigious Physical Review Letters.


Solitons are self-reinforcing waves caused by non-linear effects in the medium. They can be imagined as a shifting increase (or decrease) in the density of matter. Such waves can propagate in very different media and are known to be stable. Once excited, a soliton travels, over long (in theory - infinitely long) distances without changing shape. Even if it encounters an obstacle, it overcomes it, and the wave looks the same as before.

Solitons are relatively easy to excite, observe and describe in narrow and long spaces - channels, tubes, optical fibres.

'The simplest experimental set-up in which solitons were observed was a coastal water canal. The first experiments more than 100 years ago involved horses walking along the bank of the canal and dragging a weight across the water. Under certain conditions, a single wave can be created in this way, a build-up of water. It not only moves steadily in the canal, it can also be observed when it travels flows out of the canal far into the sea', says Professor Krzysztof Pawłowski from Center for Theoretical Physics PAS (see examples HERE and HERE).

'Solitons may seem very esoteric, but it is an important issue in many branches of physics and mathematics', describes Professor Krzysztof Pawłowski. He adds that solitons can be used in telecommunications. Stable waves that do not change shape can be useful in transmitting information, e.g. in optic fibres.


Solitons can be obtained in different objects. And now Polish theoreticians have shown for the first time that they can also be obtained in quantum droplets - a state of matter known only for a few years.

Professor Krzysztof Pawłowski reminds that quantum droplets were first observed by chance in the 2016 Bose-Einstein condensate experiment (in the Tilman Pfau group in Stuttgart).


What is a Bose-Einstein condensate? 'Every particle is a wave and a particle at the same time. Atoms also have a wave nature, but their wavelengths are ultra-short - on the order of the size of atoms. However, it turns out that if the temperature is very low, the wave nature of atoms becomes more pronounced - the atom becomes more 'fuzzy'. If there are a lot of particles and they are bosons, their waves add up, creating one macroscopic wave of matter. One wave function is therefore shared by all particles. In a standard material, we know where each atom is. In a condensate, atoms are 'spilt' - they fill the entire volume of the gas cloud', says the physicist, co-author of the publication.

This state of matter has been observed so far in ultracold, very rarefied gases, where particles are separated from the environment by electromagnetic traps.

'Condensate is a state that has been studied for several decades and it was not expected that it would surprise us with anything else', the scientist says. It turned out, however, that under certain conditions condensate can be divided into elongated, levitating droplets. They have the shape of tubes with a diameter of the order of one hundred micrometers. 'They look more or less like drops of water on a table: they have surface tension and a flat top', the scientist describes. So one can imagine that quantum droplets are a liquefied Bose-Einstein condensate.

So far, little is known about the properties of quantum droplets. Theorists investigate what interesting things can be observed in connection with them.


Now a team from Poland has shown for the first time that solitons can be observed in quantum droplets. It turns out that solitons in quantum droplets can be arbitrarily wide. This is an interesting conclusion because the solitons in the Bose-Einstein condensate are difficult to observe live, because they are very narrow.

'If ultracold gases of atoms have magnetic properties, we assume that their atoms are properly arranged - the magnetic field forms a thin tube, in which particles are located. Solitons can move in such a tube. We deal with dark solitons that are visible as rarefaction of matter inside the tube', the scientist describes.

Until now, the solitons in the condensate had a width of a fraction of a micrometer, which is below the resolution of optical microscopes. It would not be possible to take a picture or record a video of them. This may change if quantum droplets are taken into account.

'In our research, we show that the width of solitons can be controlled in quantum droplets. They can be arbitrarily wide', says the researcher. The limitation is, of course, the size of the quantum droplet.

The first author of the paper, Jakub Kopyciński, who pursues a PhD at the Center for Theoretical Physics PAS, recalls how he felt after several months of trying to solve the equation describing the behaviour of ultracold atoms (this equation was only one line). 'I then said in conversation, 'I don't think this result is particularly interesting, but I'd like to be surprised'. And then, when I finally made a graph showing the width of the soliton, my eyes widened in amazement. I nervously rushed to check the calculations, but each attempt ended with the same conclusion - the width of these solitons could be changed in an unlimited range approach', says Jakub Kopyciński.

'This is a theoretical result, awaiting experimental confirmation. However, I hope that there will soon be groups that will create solitons in quantum droplets and measure them', says Professor Krzysztof Pawłowski.

When asked if such an unusual wave propagates inside a droplet or jumps to other nearby droplets, the professor says that when a soliton passes through a droplet, it does not change its shape and it should be possible to observe it in subsequent droplets along the path of this wave.

Jakub Kopyciński comments that researching this area of knowledge is quite a challenge, but it is also very motivating. 'This is a very fast-growing branch of our field, and each new piece of knowledge improves our understanding of the world and can be an interesting starting point for further discoveries. Discoveries that - I hope - will one day find everyday applications', concludes the doctoral candidate.

PAP - Science in Poland, Ludwika Tomala

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