
Emulating curved space with heptagons
Looking for new bathroom tiles? Why don't you try regular 7gons this time! Only requirement: You'd need to live in hyperbolic space of constant negative curvature. To see how this would be like, such heptagonal tilings have been realized in recent breakthrough experiments in circuit quantum electrodynamics, where photons are tricked into believing that space is hyperbolic. In the present theoretical work, we took on the question how well hyperbolic space is emulated with such lattice implementations. We provide a dictionary between discrete and continuous hyperbolic space that applies even to moderately sized systems and can be used for calculations using Feynman diagrams. This sets the stage for the quantum simulation of curved space in tabletop experiments to address challenges at the interface of quantum manybody systems, quantum gravity, and quantum information.



New particles and forces in solids
The fundamental building blocks of our Universe are subatomic particles, such as electrons, and the mutual forces between them, such as magnetism. We do not quite know why, but among the electron and all its cousins, none of these fundamental particles has a particlespecific number called "spin" of 3/2: Instead, they all have spin 0, 1/2, 1, or 2. Even more unexpectedly perhaps, last year, the missing particle with spin 3/2 has been found wandering through certain solid materials like the Palladiumcompound with chemical formula PdBiSe. It is not a fundamental particle though, but rather an electron modified by the surrounding crystal. Still, this enables us to study the so far unknown properties and forces among particles with spin 3/2 through solid state experiments. In this theoretical work, we investigated for the first time the potential forces in such materials and identified three major ways how one spin3/2particle will interact with another spin3/2particle. The findings will guide future experiments to search for these forces and thereby build a bridge between particle physics and solid state physics.



Ordering against confinement
The development of order in a manyparticle system is the prime example when, in the words of Aristotle, "the whole is greater than the sum of its parts". Consider for instance a block of iron. Below its melting temperature at around 1500°C, the atoms occupy welldefined positions on a crystalline lattice, similar to the audience on their seats in a soldout concert hall. By knowing the position of a few atoms one can predict the position of the others due to the periodic structure: The atoms are ordered over a long distance. On heating above the melting temperature, however, this longranged order is lost and the crystalline structure gives away to a less structured liquid state through a phase transition. The detection and characterization of ordered states and the corresponding phase transitions is a key focus of current manybody physics research  in a variety of system, often much more complicated than simple iron  with huge technological applications. In our work we theoretically studied the ordered superfluid state of an ensemble of atoms confined to a twodimensional geometry at very low temperatures. The analysis was inspired by recent experiments in collaboration with the present authors covered in Murthy et al., Phys. Rev. Lett. 115, 010401 (2015), where the associated ordering had been measured for the first time. A tricky element in these experiments is the presence of an additional trapping potential, which makes the atoms want to sit in the center of the trap. Think of a football game with free choice of seats: The central regions close to the game will be seated first, whereas the crowd will thin out towards the outer regions. In the present article we could show theoretically that the presence of the trap still allows for superfluid order, although with a very characteristic power law decay of correlation towards the outer regions, which arises from the interplay between ordering and confinement. Such correlations have indeed been observed in the mentioned experiments. We thereby also confirm that the superfluid ordered state was reached in the experiments and give a guidance to the conception of future cold atom experiments.


Thermodynamics close to the absolute zero of temperature
One of the few formulas probably everybody remembers from their
physics or chemistry classes in school is the equation of state of an
ideal gas given by PV=NkT. It relates the volume V and pressure P of a
gas of N atoms or molecules to its temperature T; the conversion
factor k is Boltzmann's constant. The formula finds application in a
vast range of fields from engineering and life sciences to meteorology
and ecology. Despite this remarkable success, its validity is
restricted to situations where quantum mechanical and interaction
effects between the particles can be neglected  which is typically
guaranteed at high enough temperatures. However, for electrons in many
novel and technologically promising solid state materials, such as
hightemperature superconductors or graphene, both conditions are not
satisfied. This is because in these materials the electrons (which are
fermions) interact strongly with each other and, in addition, are
constrained to move in a twodimensional plane. How does the formula
PV=NkT change when quantum, interaction, and reduced dimension effects
become important? To answer this question, we have confined a gas of
fermionic atoms in a twodimensional plane and cooled it to
temperatures only a few billionths of a Kelvin above absolute zero.
With this setup we have measured for the first time the equation of
state of the gas as a function of temperature and atomic interaction
strength. The obtained formula can be applied for phenomenological
treatments of not only cold atom systems but also other quantum
systems with similar conditions. Our results may form the basis for
further theoretical and experimental studies of novel quantum
materials with possibly groundbreaking technological applications.
 "Equation of State of Ultracold Fermions in the 2D BECBCS Crossover Region"
Boettcher, Bayha, Kedar, Murthy, Neidig, Ries, Wenz, Zürn, Jochim, Enss Phys. Rev. Lett. 116, 045303 (2016), [arXiv:1509.03610] Editors' Suggestion Viewpoint in Physics, Press release Heidelberg University

