Curved spacetime in the lab

According to Einstein's Theory of Relativity, space and time are inextricably connected. In our Universe, whose curvature is barely measurable, the structure of this spacetime is fixed. In a laboratory experiment, researchers from Heidelberg University have succeeded in realising an effective spacetime that can be manipulated. In their research on ultracold quantum gases, they were able to simulate an entire family of curved universes to investigate different cosmological scenarios and compare them with the predictions of a quantum field theoretical model. The research results were published in Nature.

The emergence of space and time on cosmic time scales from the Big Bang to the present is the subject of current research that can only be based on the observation of our single Universe. The expansion and curvature of space are essential to cosmological models. In a flat space like our current Universe, the shortest distance between two points is always a straight line. "It is conceivable, however, that our Universe was curved in its early phase. Studying the consequences of a curved spacetime is therefore a pressing question in research," states Prof. Dr Markus Oberthaler, a researcher at the Kirchhoff Institute for Physics at Heidelberg University. With his "Synthetic Quantum Systems" research group, he developed a quantum field simulator for this purpose.

The quantum field simulator created in the lab consists of a cloud of potassium atoms cooled to just a few nanokelvins above absolute zero. This produces a Bose-Einstein condensate -- a special quantum mechanical state of the atomic gas that is reached at very cold temperatures. Prof. Oberthaler explains that the Bose-Einstein condensate is a perfect background against which the smallest excitations, i.e. changes in the energy state of the atoms, become visible. The form of the atomic cloud determines the dimensionality and the properties of spacetime on which these excitations ride like waves. In our Universe, there are three dimensions of space as well as a fourth: time.

In the experiment conducted by the Heidelberg physicists, the atoms are trapped in a thin layer. The excitations can therefore only propagate in two spatial directions -- the space is two-dimensional. At the same time, the atomic cloud in the remaining two dimensions can be shaped in almost any way, whereby it is also possible to realise curved spacetimes. The interaction between the atoms can be precisely adjusted by a magnetic field, changing the propagation speed of the wavelike excitations on the Bose-Einstein condensate.

"For the waves on the condensate, the propagation speed depends on the density and the interaction of the atoms. This gives us the opportunity to create conditions like those in an expanding universe," explains Prof. Dr Stefan Flörchinger. The researcher, who previously worked at Heidelberg University and joined the University of Jena at the beginning of this year, developed the quantum field theoretical model used to quantitatively compare the experimental results.

Using the quantum field simulator, cosmic phenomena, such as the production of particles based on the expansion of space, and even the spacetime curvature can be made measurable. "Cosmological problems normally take place on unimaginably large scales. To be able to specifically study them in the lab opens up entirely new possibilities in research by enabling us to experimentally test new theoretical models," states Celia Viermann, the primary author of the "Nature" article. "Studying the interplay of curved spacetime and quantum mechanical states in the lab will occupy us for some time to come," says Markus Oberthaler, whose research group is also part of the STRUCTURES Cluster of Excellence at Ruperto Carola.

The work was conducted as part of Collaborative Research Centre 1225, "Isolated Quantum Systems and Universality in Extreme Conditions" (ISOQUANT), of Heidelberg University.