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Flat band modes and compact localised states using Bose-Einstein condensates with spin-orbit coupling in a 2D lattice

Alexander V. H. McPhail, Maarten D. Hoogerland

Published Dec 30, 2019• 0 citations
Publisher

Abstract

Bose-Einstein condensates (BECs) are ideal tools for exploring analogies to other physical systems, including condensed matter systems, because of the easily tunable parameters. In the realm of condensed matter physics, BECs can be used to provide insight into the super fluid-Mott insulator transition, topological insulators, and other quantum Hall effects.

DOI
10.1117/12.2541203

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Bose-Einstein condensates (BECs) are ideal tools for exploring analogies to other physical systems, including condensed matter systems, because of the easily tunable parameters. In the realm of condensed matter physics, BECs can be used to provide insight into the super fluid-Mott insulator transition, topological insulators, and other quantum Hall effects.
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The experimental and theoretical research of spin–orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin–orbit coupling parameters, we discuss the fundamental properties and general applications of spin–orbit-coupled Bose–Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin–orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin–orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin–orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.
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By loading Bose-Einstein condensates into a three dimensional optical lattice potential we are able to demonstrate several new intriguing regimes in the physics of ultracold atoms. For example by changing the lattice potential depth we have been able to induce a quantum phase transition from a superfluid to a Mott insulating ground state of the system. Furthermore, by rapidly isolating the different potential wells from each other the collapse and revival of the matter wave field of a Bose-Einstein condensate has been observed. 1