Physicists at the University of Bonn have demonstrated experimentally that an important theory in statistical physics applies to so-called “Bose-Einstein condensates”. Their results now make it possible to measure some properties of quantum “superparticles” and to infer properties of the system that would otherwise be difficult to observe. The study is now published in Physical review letters.
Suppose that in front of you is a vessel filled with an unknown liquid. Your goal is to find out how much the particles in it (atoms or molecules) move back and forth randomly due to their thermal energy. However, you don’t have a microscope with which you can visualize these positional fluctuations known as “Brownian motion”.
It turns out that you don’t need that at all: you can also tie an object to a string and drag it through the liquid. The more force you have to apply, the more viscous the fluid will be. The more viscous it is, the less the particles in the fluid change position in the medium. So the viscosity at a given temperature can be used to predict the extent of the fluctuations.
The physical law that describes this basic relationship is fluctuation and dispersion theory. In simple words, it states: the more force you need to apply to confuse the system from the outside, the less random (that is, statistical) it will fluctuate on its own if you leave it alone. “We have now confirmed the validity of the theory for the first time for a special group of quantum systems: Bose-Einstein condensates,” explains Dr. Julian Schmidt from the Institute of Applied Physics at the University of Bonn.
Superphotons are made up of thousands of light particles
Bose-Einstein condensates are strange forms of matter that can arise due to a quantum mechanical effect: Under certain conditions, particles, whether they are atoms, molecules, or even photons (particles that make up light), become indistinguishable. Several hundred or thousands of them merge into a single “superparticle” – the Bose-Einstein condensate (BEC).
In a liquid at a finite temperature, molecules move back and forth at random. The warmer the liquid, the more pronounced these temperature fluctuations are. Bose-Einstein condensates can also fluctuate: the number of condensed particles varies. This variability also increases with temperature. “If the theory of oscillation and scattering applies to BECs, the greater the fluctuation in the number of particles, the greater the sensitivity of the response to external perturbation,” Schmidt asserts. “Unfortunately, the number of fluctuations in BECs normally studied in very cold atomic gases is too small to test this relationship.”
However, the research group of Professor Dr. Martin Weitz, within which Schmidt is the leader of a small research group, is working with Bose-Einstein condensates made of photons. For this system, the limitation does not apply. “We make photons in BECs interact with dye molecules,” explains the physicist, who recently won a prestigious award for young scientists from the European Union, known as the ERC Start Grant. When photons interact with dye molecules, it frequently happens that the molecule “swallows” a photon. Thus the dye becomes strongly excited. He can later release this excitation energy by “spitting” a photon.
Low-energy photons are often swallowed up
“Due to the contact with the dye molecules, the number of photons in our BECs shows large statistical fluctuations,” says the physicist. In addition, the researchers can precisely control the strength of this difference: In the experiment, photons are trapped between two mirrors, where they bounce back and forth in the manner of a game of table tennis. The distance between the mirrors can vary. The larger it is, the lower the energy of the photons. Since low-energy photons are less likely to excite the dye molecule (so they are more often swallowed), the number of intense light particles now fluctuates much less.
The Bonn physicists have now investigated how the extent of the oscillation relates to the “response” of the BEC. If the fluctuation and dissipation theory holds, then this sensitivity should decrease as the volatility decreases. “In fact, we were able to confirm this effect in our experiments,” confirms Schmitt, who is also a member of the interdisciplinary research area (TRA) “Material” at the University of Bonn and the excellence group “ML4Q – Matter and Light for Quantum Computing”. As with liquids, it is now possible to infer the microscopic properties of a Bose-Einstein condensate from microscopic response parameters that can be measured more easily. “This opens the way for new applications, such as the precise determination of temperature in complex photovoltaic systems,” says Schmidt.
The project was funded by the German Research Foundation (DFG), as part of the European Union’s “Photons for Quantum Simulation” project, and the German Federal Ministry for Economic Affairs and Climate Action (BMWK).