Session C02: Quantum Matter in Synthetic Curved Spacetimes

Hyperbolic quantum matter

Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tiling of two-dimensional hyperbolic space, a non-Euclidean space of negative curvature. Hyperbolic tilings were studied by the geometer H.S.M. Coxeter and popularized through art by M.C. Escher. Recent experiments in circuit quantum electrodynamics and electric circuit networks have demonstrated the coherent propagation of wave-like excitations on hyperbolic lattices. While the familiar band theory of solids adequately describes wave propagation through periodic media in Euclidean space, it is not clear how concepts like crystal momentum and Bloch waves can be extended to hyperbolic space. In this talk, I will discuss a generalization of Bloch band theory for hyperbolic lattices.   

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.   

Tailoring synthetic curved spacetimes

Recent experimental progress has allowed physicists to explore quantum matter in curved spacetimes. I will discuss some new approaches to engineer synthetic curved spacetimes [1-3]. One is to exploit a duality between non-Hermiticity and curved spaces, which equates two distinct languages to unfold deep connections between two active research areas. While providing solutions to long-lasting questions in non-Hermitian quantum mechanics, this duality also enables an unprecedented recipe to design synthetic curved spaces. The other approach is mapping quantum dynamics to certain geometries that are governed by the same symmetries. This geometrization not only delivers new protocols to control quantum dynamics but also leads to a unique perspective of studying spacetimes emergent from quantum dynamics.