Quantum Field Simulator – Relativistic scalar field in curve spacetime*

Ultracold gases offer an experimental platform with pristine control of parameters as well as unique readout capabilities making new observables experimentally accessible. In this talk, I will present how we can simulate the dynamics of a scalar field in time dependent curved spacetime.

As experimental platform we have chosen a two-dimensional ultracold potassium gas, which allows for controlled realizations of density distributions as well as the control of the stiffness of the gas via controlling the microscopic interaction between the atoms via a Feshbach resonance. With that control at hand, we can realize a Friedmann-Lemaitre-Robertson-Walker metric in two dimensions. This is the most general form of a metric satisfying the constraints of homogeneity and isotropy.

We demonstrate the realization of curved space via quantum wave packet dynamics and give results in hyperbolic and spherical spatial geometry. Extending the concept of curvature to time we confirm the expected particle production if the scale factor is changed in time. Building on the unique readout capabilities, we not only access the number of generated particles but also for the first time the phase of the excitation amplitudes. The quantitative agreement with new analytical predictions for time dependent metrics benchmarks the simulator and with that establishes the new class of quantum field simulators implementing relativistic quantum actions. I will also describe how the expansion of a two-dimensional universe is connected to the physics of scattering a quantum particle of an effective one-dimensional potential. With that the quantum field simulator can solve scattering problems and opens the general perspective of computation in physical structures.