Confirmed the validity of a central theorem of physics for Bose-Einstein condensates

Confirmed the validity of a central theorem of physics for Bose-Einstein condensates

Physicists at the University of Bonn have experimentally shown that an important theorem of statistical physics applies to so-called “Bose-Einstein condensates”. Their results now make it possible to measure certain properties of quantum “superparticles” and to deduce features of the system that would otherwise be difficult to observe. The study has now been published in Physical review letters.

Suppose that in front of you is a container filled with an unknown liquid. Your goal is to find out how far the particles (atoms or molecules) move from one place to another at random due to their thermal energy. However, you do not have a microscope with which you can visualize these position fluctuations known as “Brownian motion.”

Turns out you don’t need that at all – you can also just tie an object to a string and pull it through the liquid. The more force you have to apply, the more viscous your liquid will be. And the more viscous it is, the less the particles in the liquid change position on average. Therefore, the viscosity at a given temperature can be used to predict the extent of fluctuations.

The physical law that describes this fundamental relationship is the fluctuation-dissipation theorem. In simple words, it states: the more force you need to apply to disturb a system from the outside, the less it will fluctuate randomly (i.e. statistically) by itself if you leave it alone. “We have now confirmed for the first time the validity of the theorem for a special group of quantum systems: Bose-Einstein condensates,” explains Dr. Julian Schmitt from the Institute for Applied Physics at the University of Bonn.

“Super photons” made of thousands of light particles

Bose-Einstein condensates are exotic forms of matter that can arise due to a quantum mechanical effect: under certain conditions, particles, be they atoms, molecules, or even photons (particles that make up light), become indistinguishable. Many hundreds or thousands of them merge into a single “superparticle” – the Bose-Einstein condensate (BEC).

In a liquid at finite temperature, the molecules move back and forth at random. The hotter the liquid, the more pronounced are these thermal fluctuations. Bose-Einstein condensates can also fluctuate: the number of condensed particles varies. And this fluctuation also increases with increasing temperature. “If the fluctuation-dissipation theorem is applied to BECs, the greater the fluctuation in their number of particles, the more sensitive they should respond to an external disturbance,” Schmitt stresses. “Unfortunately, the number of fluctuations in BECs generally studied in ultracold atomic gases is too small to test this relationship.”

However, the research group of Prof. Dr. Martin Weitz, within which Schmitt is a junior research group leader, works with Bose-Einstein condensates made of photons. And for this system, the limitation does not apply. “We make the photons from our BECs interact with dye molecules,” explains the physicist, who recently won a highly endowed prize for young scientists from the European Union, known as the ERC Starting Grant. When photons interact with dye molecules, it often happens that one molecule “swallows” a photon. Thus, the dye is energetically excited. It can later release this exciting energy by “spitting out” a photon.

Low energy photons are swallowed less frequently.

“Due to contact with the dye molecules, the number of photons in our BECs shows large statistical fluctuations,” says the physicist. Furthermore, the researchers can precisely control the strength of this variation: In the experiment, photons are trapped between two mirrors, where they are reflected back and forth like a game of ping-pong. The distance between the mirrors can be varied. The bigger it gets, the lower the energy of the photons. Since low-energy photons are less likely to excite a dye molecule (so they are swallowed less often), the number of condensed light particles now fluctuates much less.

The Bonn physicists now investigated how the extent of the fluctuation is related to the “response” of the BEC. If the jitter-dissipation theorem holds, this sensitivity should decrease as the jitter decreases. “In fact, we were able to confirm this effect in our experiments,” emphasizes Schmitt, who is also a member of the Transdisciplinary Research Area (TRA) “Matter” at the University of Bonn and the Cluster of Excellence “ML4Q — Matter”. and light for quantum computing.” As with liquids, it is now possible to infer the microscopic properties of Bose-Einstein condensates from more easily measured macroscopic response parameters. “This opens the way to new applications, such as the precise determination of temperature in complex photonic systems,” says Schmitt.


The project was funded by the German Research Foundation (DFG), as part of the EU project “Photons for Quantum Simulation”, and the German Federal Ministry for Economic Affairs and Climate Action (BMWK).

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