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."Comment: 29 pages, 12 figures, book will appear later this year; v2 is in improved format and includes small corrections for final versio

Superpositions in Atomic Quantum Rings

Ultracold atoms are trapped circumferentially on a ring that is pierced at its center by a flux tube arising from a light-induced gauge potential due to applied Laguerre-Gaussian fields. We show that by using optical coherent state superpositions to produce light-induced gauge potentials, we can create a situation in which the trapped atoms are simultaneously exposed to two distinct flux tubes, thereby creating superpositions in atomic quantum rings. We consider the examples of both a ring geometry and harmonic trapping, and in both cases the ground state of the quantum system is shown to be a superposition of counter-rotating states of the atom trapped on the two distinct flux tubes.Comment: 11 pages, 6 figure

Topological Winding and Unwinding in Metastable Bose-Einstein Condensates

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of grey solitons, or density notches, which serve as an experimental signature of this phenomenon.Comment: 4 pages, 3 figure

Symmetry Breaking in Bose-Einstein Condensates

A gaseous Bose-Einstein condensate (BEC) offers an ideal testing ground for studying symmetry breaking, because a trapped BEC system is in a mesoscopic regime, and situations exist under which symmetry breaking may or may not occur. Investigating this problem can explain why mean-field theories have been so successful in elucidating gaseous BEC systems and when many-body effects play a significant role. We substantiate these ideas in four distinct situations: namely, soliton formation in attractive BECs, vortex nucleation in rotating BECs, spontaneous magnetization in spinor BECs, and spin texture formation in dipolar BECs.Comment: Submitted to the proceedings of International Conference on Atomic Physics 200