Expanding universe in the lab

By analyzing the large-scale structure of the Universe, cosmologists have deduced that space expanded rapidly in the moments after the big bang. During this expansion, the Universe was empty except for the quantum fields present in the vacuum. How these fields evolved in the curved spacetime of an expanding Universe remains an open question whose solution could help scientists understand how the particles came into being. Researchers at the University of Heidelberg, Germany, have now produced an analog system to study these areas [1]. In a Bose-Einstein Condensate (BEC) of ultracold atoms, they demonstrate properties that correspond to curved space and time, providing a new tool for simulating quantum field evolution in an expanding universe.

Reproducing a curved spacetime is not an easy task, as it requires contorting both the spatial aspect and the temporal aspect of the system. Spatial curvature concerns the geometry of the system: whether it is flat, spherical or hyperbolic. The curvature of time involves the evolution of the system: whether it is expanding, contracting or static. In 1980, William Unruh of the University of British Columbia, Canada pointed out that sound waves propagating in a moving fluid offer an analogy to light waves propagating in curved spacetime. Since then, other types of simulators have been developed, all using fluid flow to reproduce curvature effects.

Building on these concepts, Markus Oberthaler and his colleagues at the University of Heidelberg devised an analog of curved spacetime in a still BEC fluid. Their trick was to control the speed of sound in the BEC. For example, by slowing down the speed of sound, they could increase the effective distance between two points, since sound will take longer to travel from point to point. This speed control can be used to create efficient “curvature” of spacetime.

The researchers realized their system by confining ultracold potassium-39 ions in an optical trap. The trap altered the BEC density distribution, allowing spatial control of the speed of sound. The researchers showed, for example, that a particular trap configuration generated a density profile with a smooth peak in the center, resulting in high sound velocity in the center and low around the periphery. Sound waves passing through this gas should move away from the center in the expected pattern for a 2D projection of a hyperbolic universe.

To verify that their BEC approximated a curved geometry in space, the researchers focused a laser beam near the center of the BEC and observed density vibrations that correspond to quantized sound waves called phonons. They measured the position of these phonons as they propagated outward from the focal point and found that the trajectories matched predictions for spatially curved geometry. They repeated these experiments for hyperbolic and spherical geometries.

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For temporal control of the speed of sound, the team applied a uniform magnetic field to the gas, which altered the microscopic interaction forces between the potassium atoms. By weakening these interactions over time, the BEC behaved as if it were expanding. “This is an important step because we can implement the expansion without actively expanding the system or changing the density distribution,” says Oberthaler.

To study the effects of the expansion, the researchers observed how the density distribution of the BEC changed after the interaction strength decreased, corresponding to a universe that roughly tripled in size. They found that increased density fluctuations appeared on a large scale after the ramp, as expected in expanding space. These increased density fluctuations corresponded to “particle production” in the phonon field, consistent with quantum field theory predictions for an expanding universe.

By modifying the behavior of the ramp, the researchers observed how density fluctuations changed over time in scenarios of acceleration, deceleration and uniform expansion. In most cases, density contrast correlations increased after the ramp, as expected for a growing sound cone. The time course of density fluctuations also corresponded to the so-called Sakharov oscillations, which are predicted in models of the expanding universe.

Chen-Lung Hung, a physicist who works with ultracold quantum gases at Purdue University in Indiana, says the demonstration brings together decades of theory and experimental concepts. “The tools were there, but this is the first time that everything has come together well to show that it is possible to design curved spacetime and key experimental signatures.” It may be possible to simulate acoustic black holes and visualize the evolution of quantum fields in these new geometries in a tabletop experiment, Hung adds.

According to Stefano Liberati, who studies quantum and classical gravity at the International Institute for Advanced Studies in Italy, the most exciting thing about the BEC simulator is that it is very versatile. “They can separately control curvature and time dependence, which gives the possibility not only of standard model simulations, but also of simulating exotic physics,” he says.

–Rachel Berkowitz

Rachel Berkowitz is the corresponding editor for physics journal based in Vancouver, Canada.

References

1. C.Viermann et al.“Quantum Field Simulator for Dynamics in Curved Spacetime,” Nature 611260 (2022).

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