Abstract
Over recent years, exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand experimental environments with non-cubic lattice geometries. In this paper, we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step, the superfluid–Mott insulator (SF–MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this, we study the physics of spinor Bose–Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF–MI transition. Our results suggest that, below the SF–MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly, this opens up new perspectives for a lattice-driven tuning of a spin dynamics resonance occurring through the interplay of the quadratic Zeeman effect and spin-dependent interaction. Finally, we discuss further lattice configurations that can be realized with our setup.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Periodic systems constitute very important structures in nature. Solids of various symmetries play a particularly key role as they, for example, exhibit intriguing magnetic phases or show semi- or superconducting properties, which are of great interest for scientific and technical applications. However, many physical aspects of solids are difficult to analyze, in particular because of the lack of direct controllability of such systems. Ultracold atoms confined in optical lattices have proven to provide almost ideal model systems, with excellent control, and allow the study and simulation of problems known from other fields, such as condensed matter physics. In magnetism, interesting phenomena, for example the occurrence of spin-frustration, are known to occur in environments with non-cubic lattice geometries, such as triangular or hexagonal. Therefore, the experimental realization of such geometries in the field of ultracold atoms opens a new and exciting testing ground for a whole class of physical problems.
Main results. We present for the first time a detailed study of the superfluid–Mott insulator (SF–MI) quantum phase transition in a triangular optical lattice, which occurs at lower lattice depth in direct comparison to a cubic lattice. Moreover, we investigate the spin exchanging dynamics of spinor Bose–Einstein condensates (BEC) across the point of the SF–MI transition in this lattice configuration. In the regime below the SF–MI phase transition point our results are described within a mean-field model. Finally, we discuss further lattice configurations which can be realized with our setup.
Wider implications. Our results suggest a lattice-depth-driven tuning of the spin dynamics through the interplay of the quadratic Zeeman effect and the spin-dependent interaction. Future perspectives include loading and investigation of spinor BEC in a spin-dependent hexagonal lattice including a Graphene-like potential. Moreover, the setup allows the sign of the tunneling matrix element, J, to be changed by slight modulation of the relative phases of the lattice laser beams. This allows investigation of model systems known from solid state physics, giving rise to effects like Néel-ordering and the creation of a spin liquid phase.