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Physical Review A

Magnetic quantum phase transition of cold atoms in an optical lattice

Peng-Bin He, Qing Sun, Peng Li, Shun-Qing Shen, W. M. Liu

Published Oct 16, 2007• 56 citations
Publisher

Abstract

We propose a scheme to investigate the magnetic phase transition of cold atoms confined in an optical lattice. We also demonstrate how to get coupled two-leg spin ladders which display a phase transition from a spin liquid to magnetic ordered state in two-dimensional optical lattice. An experimental protocol is further designed for observing this phenomenon.

DOI
10.1103/physreva.76.043618

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We propose a scheme to investigate the magnetic phase transition of cold atoms confined in an optical lattice. We also demonstrate how to get coupled two-leg spin ladders which display a phase transition from a spin liquid to magnetic ordered state in two-dimensional optical lattice. An experimental protocol is further designed for observing this phenomenon.
We propose a scheme to investigate the quantum phase transition of cold atoms in the bilayer hexagonal optical lattices. Using the quantum Monte Carlo method, we calculate the ground state phase diagrams which contain an antiferromagnet, a solid, a superfluid, a fully polarized state and a supersolid. We find there is a supersolid emerging in a proper parameter space, where the diagonal long range order coexists with off-diagonal long range order. We show that the bilayer optical lattices can be realized by coupling two monolayer optical lattices and give an experimental protocol to observe those novel phenomena in the real experiments.
We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.
We propose a scheme to simulate the t–J–U model and investigate the quantum phase transitions using cold atoms confined in a two-dimensional optical lattice. By adjusting the parameters of external laser fields, we find a phase transition from antiferromagnetic phase to Gossamer superfluid. The Gossamer superfluid has a d-wave or mixed d- and s-wave symmetry, depending on the hopping parameters which can be adjusted by tuning the laser field. Experimental protocol to observe these new phenomena for future experiments has also been briefly discussed.
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
The physics of quantum degenerate cold gases in optical lattices has rapidly grown to an extremely dynamic field over the past few years. In the experimental realizations, however, mainly cubic symmetries (or their two- and one-dimensional projections) are considered. We have implemented an optical lattice with an underlying triangular symmetry in order to investigate strongly correlated ultra-cold atoms in a novel experimental geometry. Exhibiting an explicit polarization dependence (compare figure 1) the optical lattice realized here should allow for the creation and analysis of thus far unexplored magnetic phases. Experiments attending to the quantum phase transition from a superfluid to a Mott-insulating state in a three- as well as in a two-dimensional system with triangular symmetry have been performed. Similarities as well as differences to the findings obtained in cubic lattices will be discussed and can be attributed to the inherent differences in the crucial lattice parameters such as tunneling energy J and on-site interaction U.