PICTURE: Artistic impression of the experiment in which Häusler and colleagues first heat one of two quantum gas clouds and then connect them with a two-dimensional channel so that they can balance each other out …. view More
Photo credits: D. Husmann & S. Häusler, ETH Zurich
When a piece of conductive material is heated at one of its ends, a voltage difference can build up across the sample, which in turn can be converted into a current. This is the so-called Seebeck effect, the cornerstone of thermoelectric effects. In particular, the effect offers a way of creating works from a temperature difference. Such thermoelectric motors have no moving part, making them convenient sources of power in various applications, including propelling NASA’s Mars rover Perseverance. The Seebeck effect is also of interest for basic physics, since the magnitude and sign of the induced thermoelectric current are characteristic of the material and indicate how entropy and charge currents are coupled. The group of Prof. Tilman Esslinger from the Department of Physics at ETH Zurich now writes in Physical Review X about the controlled reversal of such a current by changing the strength of the interaction between the components of a quantum simulator, laser fields formed from extremely cold atoms. The ability to induce such a reversal means that the system can be converted from a thermoelectric motor to a cooler.
Which way please?
The experiment, carried out by PhD student Samuel Häusler and colleagues from the Esslinger group, begins with a cloud of fermionic lithium atoms that have cooled to temperatures so low that quantum effects determine the behavior of the ensemble. The cloud is then separated into two independent halves of equal atomic number. One of them is heated before the two reservoirs are connected by a two-dimensional channel. The state of equilibrium that develops in this way is as expected: after a sufficiently long time, the two halves contain the same atomic numbers at the same temperatures. The temporary behavior is more interesting. During the equilibration process, the number of atoms in each reservoir changes, with the atoms flowing between them. In which direction and with which amplitude this happens depends on the thermoelectric properties of the system.
Thanks to the exquisite control over the system, the researchers were able to measure the transient behavior for different interaction strengths and atomic densities within the channel and compare them with a simple model. In contrast to solid-state systems, in which most of the thermoelectric properties can be measured in simple, precisely defined experiments, the parameters in these small atomic clouds are derived from basic quantities such as the atomic density. A key point of the work was to find a method that correctly extracts the thermoelectric quantities over a wide range of parameters.
The team found that the current direction resulted from a competition between two effects (see figure). On the one hand (left) the thermodynamic properties of the reservoirs favor an increase in the number of atoms in the hot reservoir in order to equalize the chemical potentials of the two halves. On the other hand (right) the properties of the channel typically facilitate the transport of hot, energetic particles – since they have a large number of possible paths (or modes) available – which leads to an increase in the atomic number in the cold reservoir.
A super fluid traffic regulator
With a non-interacting gas, it is possible to calculate the dominant trend between the two competing effects once the exact shape of the atomic cloud is known and taken into account. In the system of Häusler et al. This can be done very precisely. Both in the calculation and in the measurements, the initial atomic current flows from the hot to the cold reservoir and is stronger at low atomic densities in the channel. If the interactions are coordinated with the so-called uniform regime, the behavior of the system becomes considerably more difficult to predict. Due to the strong correlations that build up in the gas, the calculation becomes unsolvable without far-reaching approximations.
In this regime, the quantum simulation device developed by the ETH researchers showed that if the mean temperature is sufficiently high and the atomic density in the channel is low, the current also flows from the hot to the cold reservoir. However, it can be reversed if the channel density is increased using an attractive gate potential. Above a certain density threshold, the atoms in the channel go through a phase transition in which they form pairs that show superfluid behavior. This superfluid area in the channel limits the transport of unpaired energetic particles and promotes the transport from the cold to the hot reservoir and thus the reversal of the thermoelectric current.
On the way to better thermoelectric materials thanks to interactions
Understanding the properties of matter through thermoelectric measurement improves the basic understanding of interacting quantum systems. Equally important is finding new ways to develop high-performance thermoelectric materials that can efficiently convert small heat differences into work or, in reverse mode, act as a cooling device (called a Peltier cooler).
The efficiency of a thermoelectric material is characterized by the thermoelectric figure of merit. Häusler et al. have measured a large increase in value of this number when the interactions are started. While this improvement cannot be directly transferred to materials science, this excellent cooling ability could already be used to achieve lower temperatures for atomic gases, which in turn could enable a wide range of novel fundamental experiments in quantum science.
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