We consider a massive complex scalar field with contact interactions with a source and show that, upon Bose-Einstein condensation, there is an emergent long-range interaction between sources. This interaction becomes long-range in the limit of vanishing self-interaction between Bose-Einstein constituents. More generally, the range is given by ${\ensuremath{\ell}}^{\ensuremath{-}1}\ensuremath{\propto}\sqrt{\ensuremath{\lambda}n/m}$, with $\ensuremath{\lambda}$ being the 2-body self-interaction coupling constant, $n$ the particle number density in the condensate, and $m$ the mass of the condensed particles. Naively this may sound surprising since in $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit gapless excitations of the condensate have dispersion relation ${\ensuremath{\omega}}_{k}={k}^{2}/2m$, yet for the mediated force we have $F\ensuremath{\propto}1/{r}^{2}$. The reason behind this seemingly counterintuitive result lies in the fact that the force is being mediated by the phonon, which happens to acquire a nontrivial derivative interaction with the source. We discuss the potential ramifications of this observation for dark matter models. In particular, we show that this force can compete with gravity on galactic scales for a wide range of dark matter mass, provided that the interaction with baryons allows the presence of an extended dark matter condensate core. The effect could be of particular interest in ultralight dark matter models, such as Fuzzy Dark Matter.We consider a massive complex scalar field with contact interactions with a source and show that, upon Bose-Einstein condensation, there is an emergent long-range interaction between sources. This interaction becomes long-range in the limit of vanishing self-interaction between Bose-Einstein constituents. More generally, the range is given by ${\ensuremath{\ell}}^{\ensuremath{-}1}\ensuremath{\propto}\sqrt{\ensuremath{\lambda}n/m}$, with $\ensuremath{\lambda}$ being the 2-body self-interaction coupling constant, $n$ the particle number density in the condensate, and $m$ the mass of the condensed particles. Naively this may sound surprising since in $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit gapless excitations of the condensate have dispersion relation ${\ensuremath{\omega}}_{k}={k}^{2}/2m$, yet for the mediated force we have $F\ensuremath{\propto}1/{r}^{2}$. The reason behind this seemingly counterintuitive result lies in the fact that the force is being mediated by the phonon, which happens to acquire a nontrivial derivative interaction with the source. We discuss the potential ramifications of this observation for dark matter models. In particular, we show that this force can compete with gravity on galactic scales for a wide range of dark matter mass, provided that the interaction with baryons allows the presence of an extended dark matter condensate core. The effect could be of particular interest in ultralight dark matter models, such as Fuzzy Dark Matter.

arXiv:1812.09332Physical review. D/Physical review. D.Apr 5, 201920 citations

Bilayers of Rydberg Atoms as a Quantum Simulator for Unconventional Superconductors

J. P. Hague, C. MacCormick

In condensed matter, it is often difficult to untangle the effects of competing interactions, and this is especially problematic for superconductors. Quantum simulators may help: here we show how exploiting the properties of highly excited Rydberg states of cold fermionic atoms in a bilayer lattice can simulate electron-phonon interactions in the presence of strong correlation--a scenario found in many unconventional superconductors. We discuss the core features of the simulator, and use numerics to compare with condensed matter analogues. Finally, we illustrate how to achieve a practical, tunable implementation of the simulation using "painted spot" potentials.In condensed matter, it is often difficult to untangle the effects of competing interactions, and this is especially problematic for superconductors. Quantum simulators may help: here we show how exploiting the properties of highly excited Rydberg states of cold fermionic atoms in a bilayer lattice can simulate electron-phonon interactions in the presence of strong correlation--a scenario found in many unconventional superconductors. We discuss the core features of the simulator, and use numerics to compare with condensed matter analogues. Finally, we illustrate how to achieve a practical, tunable implementation of the simulation using "painted spot" potentials.

arXiv:1111.5594Physical Review LettersNov 28, 201232 citations

Between Rigor and Reality: Many-Body Models in Condensed Matter Physics

Axel Gelfert

The frontiers collectionJan 1, 20151 citation

n

the particle number density in the condensate, and

m

the mass of the condensed particles. Naively this may sound surprising since in $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit gapless excitations of the condensate have dispersion relation ${\ensuremath{\omega}}_{k}={k}^{2}/2m$, yet for the mediated force we have $F\ensuremath{\propto}1/{r}^{2}$. The reason behind this seemingly counterintuitive result lies in the fact that the force is being mediated by the phonon, which happens to acquire a nontrivial derivative interaction with the source. We discuss the potential ramifications of this observation for dark matter models. In particular, we show that this force can compete with gravity on galactic scales for a wide range of dark matter mass, provided that the interaction with baryons allows the presence of an extended dark matter condensate core. The effect could be of particular interest in ultralight dark matter models, such as Fuzzy Dark Matter.