Statistical physics theorem also valid in the quantum world, study shows

Statistical physics theorem also valid in the quantum world, study shows

Experimental scheme for measuring the number fluctuations and response function of a Bose-Einstein photon condensate coupled to a reservoir inside a dye microcavity. Part of the cavity emission recorded with a photomultiplier tube (PMT) gives the average condensate population ⟨n⟩; the other part is dispersed on a grating, and the evolution of the spectrally filtered condensate is recorded with a streak camera, giving g(2)(τ) and detuning Δ from the dye cavity. Credit: Physical Review Letters (2023). DOI: 10.1103/PhysRevLett.130.033602

Physicists from the University of Bonn have experimentally demonstrated 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 infer 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 there is a container filled with an unknown liquid. Your goal is to find out how much the particles in it (atoms or molecules) move randomly back and forth due to their thermal energy. However, you do not have a microscope with which you can visualize these fluctuations in position 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 the liquid. And the more viscous it is, the less the particles in the liquid change their position on average. Viscosity at a given temperature can therefore 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 greater the force you have to apply to perturb a system from the outside, the less it will also fluctuate randomly (ie, statistically) on its own if you leave it in peace.

“We have now for the first time confirmed the validity of the theorem for a special group of quantum systems: Bose-Einstein condensates,” explains Dr. Julian Schmitt from the Institute of Applied Physics at the University of Bonn.

“Super photons” made up of thousands of particles of light

Bose-Einstein condensates are exotic forms of matter that can appear 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 randomly. The warmer the liquid, the more pronounced 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 applies to BECs, the larger the fluctuation of their particle number, the more sensitive they should respond to an external perturbation,” says Schmitt. “Unfortunately, the number [of] the fluctuations of BECs typically studied in ultracold atomic gases are too small to test this relationship.”

However, the research group of Prof. Dr. Martin Weitz, in 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 in our BECs interact with the dye molecules,” explains the physicist. When photons interact with dye molecules, it is common for a molecule to “swallow” a photon. The paint thus becomes energetically excited. It can later release this excitation energy by “spitting out” a photon.

Low energy photons are swallowed less often

“Due to the contact with the dye molecules, the number of photons in our BECs shows large statistical fluctuations,” says the physicist. What’s more, the researchers can precisely control the strength of this variation: In the experiment, photons are trapped between two mirrors, where they are bounced back and forth in a game of ping-pong.

The distance between the mirrors can be varied. The higher it becomes, the lower the energy of the photons. Because 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.

Physicists in Bonn have now investigated how the magnitude of the fluctuation is related to the “response” of the BEC. If the fluctuation-dissipation theorem holds, this sensitivity should decrease as the fluctuation decreases.

“We were actually 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 macroscopic response parameters that can be more easily measured. “This opens a path to new applications, such as precise temperature determination in complex photonic systems,” says Schmitt.

More information:
Fahri Emre Öztürk et al., Fluctuation-dissipation relation for a Bose-Einstein photon condensate, Physical Review Letters (2023). DOI: 10.1103/PhysRevLett.130.033602

Provided by Rheinische Friedrich-Wilhelms-Universität Bonn

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