Physics Colloquium: Johannes Hofmann, "Exact results for interacting dipolar quantum gases"

Exact results for interacting dipolar quantum gases
 

Johannes Hofmann
Senior Lecturer
Department of Physics
University of Gothenburg, Sweden

Abstract

Helium-4 at low temperatures becomes a superfluid, where part of the liquid flows without dissipation. Over 50 years ago, it has been conjectured that such a superflow could exist even in a crystal, which is then dubbed a supersolid — a counter-intuitive state of matter that retains superfluid properties even though the atoms are arranged in a fixed crystalline lattice. A natural example for this is the solid phase of Helium-4, but experiments have not been conclusive: Our current understanding is that the ground state of Helium at high pressure forms a regular, commensurate crystal (number of atoms equal to the number of lattice cells) with no superfluidity present. Part of the problem is that the superfluid fraction in a crystalline supersolid is expected to be very small and any effects would thus be very hard to detect.

This dire experimental situation has changed within the last two years with experiments on ultracold quantum gases in which the atoms have a permanent magnetic dipole moment. While these systems do not form a crystal in its standard meaning with a single atom for each unit cell, the ground state exhibits a periodic mass-density wave along a weakly confined direction if the dipole interaction strength is tuned beyond a critical value. Crucially, the system remains a Bose-Einstein condensate (here, a superfluid) and thus forms a supersolid. It is, however, of a very different nature compared to a crystalline supersolid, with a small density modulation on top of a homogenous superfluid background density. A detailed theoretical understanding of this recently discovered state in dipolar gases is still lacking. Quite generally, the description of interacting dipolar many-body systems beyond simple many-body approximation (such as the Gross-Pitaevskii description or a Bogoliubov approach) has been a challenge to date.

In my talk, I will discuss recent progress in the theoretical description of dipolar quantum gases, focusing on exact theoretical results that are independent of any many-body approximation. In particular, I will discuss how a detailed understanding of the short-distance structure of the dipolar potential gives rise to an exact universal description of the gas [i.e., a description that does not rely on microscopic details of the interaction beyond effective parameters such as the scattering length]. I will then present results on the transition between homogenous superfluid and supersolid phase and show that the transition point is determined by a criterion on the static structure factor formulated by Hansen and Verlet in the context of freezing transition in classical fluids. Moreover, I argue that the supersolid phase of dipolar gases may be understood as a superfluid version of a smectic-A liquid crystal, which is a classical state of molecules ordered in layers. Based on this, I present a hydrodynamic description of the supersolid, which only involves conserved quantities and broken-symmetry parameters.

 

Last Updated: 04/20/2021 11:11