Metastable Quantum Phase Transitions in a One-Dimensional Bose Gas

This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude, using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian, from the weakly- to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N, is quantized under rotation. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of \textit{metastable quantum phase transitions} (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems."