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# Curved space-time in the quantum simulator

New techniques can be used to answer questions that were previously inaccessible experimentally - including questions about the connection between quanta and the theory of relativity.

The theory of relativity works great for explaining cosmic-scale phenomena, such as the gravitational waves produced when black holes collide. Quantum theory works great for explaining phenomena at the particle scale, such as the behavior of individual electrons in the atom. However, it has not yet been possible to combine the two in a completely satisfactory manner. The search for a "quantum theory of gravitation" is considered one of the great unsolved tasks of science.

One of the reasons for this is that the mathematics in this area is extremely complicated and at the same time it is extremely difficult to carry out suitable experiments: You would have to create situations in which both phenomena of the theory of relativity play an important role, for example one curved by heavy masses space-time, and at the same time quantum effects become visible, for example the combined particle and wave nature of light.

At the Vienna University of Technology, a new approach has now been developed: With a so-called "quantum simulator", such questions can be investigated: You do not examine the system you actually want to learn something about (namely quantum particles in a curved space-time), but rather create it instead, a "model system", a simulation that is easier to handle, from which one can then learn something about the system that is actually interesting by analogy. The team has now been able to show that this quantum simulator works extremely well. The results of the international cooperation with the University of Crete, the Nanyang Technological University and the Free University of Berlin have now been published in the specialist journal PNAS.

Learning from one system about anotherThe basic idea behind the quantum simulator is simple: many systems in quantum physics are similar. Even if we are dealing with completely different types of particles, or with physical systems that at first glance have little to do with each other, it is possible that the systems on a deeper level obey the same laws and equations. This means that you can learn about a particular system by examining another system.

"So we take a quantum system that we know we can control and adapt very well in experiments," says Prof. Jörg Schmiedmayer from the Atomic Institute at TU Vienna. "In our case, these are ultra-cold atomic clouds that are held and manipulated by an atomic chip with electromagnetic fields." If these atomic clouds are adapted in a suitable way so that their properties can be translated into another quantum system, one can model system learn something about the other system - similar to how one can learn something about the oscillation of a pendulum on a string from the oscillation of a mass attached to a metal spring: They are two different physical systems, but one can be integrated into translate the other.

The gravitational lensing effect"We have now been able to show that effects can be produced in this way that can be used to simulate the curvature of space-time," says Mohammadamin Tajik from the Vienna Center for Quantum Science and Technology (VCQ) - Atomic Institute of the TU Vienna, first author of the current papers. In the vacuum of space, light propagates in a so-called "light cone": the speed of light is constant, light travels the same distance in equal times in every direction. However, if the light is influenced by heavy masses, such as the sun's gravity, then these light cones are bent. The paths taken by light are no longer perfectly straight in a curved space-time. This is then referred to as a "gravitational lens effect".

The same can now also be shown in the atomic clouds. Instead of the speed of light, the speed of sound is examined there. "Now we have a system in which there is an effect that corresponds to space-time curvature or gravitational lensing, but at the same time it is a quantum system that can be described with quantum field theories," says Mohammadamin Tajik. "So in this way we have a completely new tool to study the connection between relativity and quantum theory."

A model system for quantum phenomena in curved space-timeThe experiments show that the shape of the light cones, lens effects, reflections and other phenomena in these atomic clouds can be demonstrated in exactly the same way as one would expect in relativistic cosmic systems. This is not only interesting for generating new data for theoretical basic research - also in solid state physics and in the search for new materials one encounters questions that have a similar structure and can therefore be answered by such experiments.

"We now want to control these atomic clouds even better so that we can obtain even more far-reaching data. For example, interactions between the particles can still be specifically modified," explains Jörg Schmiedmayer. In this way, the quantum simulator can reproduce physical situations that are so complicated that even supercomputers cannot calculate them.

The quantum simulator thus becomes a new, additional source of information for quantum research - in addition to theoretical calculations, computer simulations and direct experiments. When studying the atomic clouds, the research team hopes to come across new phenomena that may have been completely unknown up to now, which also take place on a cosmic, relativistic scale - but without a look at tiny particles, they might never have been discovered.

https://www.tuwien.at/tu-wien/aktuelles/news/news/gekruemmte-raumzeit-im-quanten-simulator