Triangular Optical Lattice Research Articles

Defect solitons in triangular optical lattices

We report the existence and stability of solitons in triangular optical lattices with a defect in saturable nonlinearity. With the changes of defect intensity, defect solitons may exist in different gaps. For a positive defect, solitons only exist in the semi-infinite gap and can be stable in the low power region. For a negative defect, solitons can exist in the semi-infinite gap and in the first gap. With the increasing of the negative defect depth, solitons will be stable only in the moderate power region in the first gap, and the stable region will become more and more narrow.

Cold atoms in a two-dimensional triangular optical lattice as an artificial frustrated system

We investigate the strongly correlated effect of cold atoms in a triangular optical lattice using the dynamical cluster approximation combined with the continuous-time quantum Monte Carlo method. When the interaction increases, the Fermi surface evolves from a circular ring into a flat plane, and the system transitions from a Fermi liquid into a Mott insulator. The transition between the Fermi liquid and a pseudogap shows a reentrant behavior due to the Kondo effect. We give an experimental protocol to observe these phenomena in future experiments by varying the lattice depth and the atomic interaction via the Feshbach resonance.

Ultracold quantum gases in triangular optical lattices

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.

Fermionic superfluidity and spontaneous superflows in optical lattices

We studied the superfluidity of strongly repulsive fermionic atoms in optical lattices. Atoms are paired through a correlated tunneling mechanism, which induces superfluidity when repulsive nearest-neighbor interactions are included in the Hubbard model. This paired superfluid is a metastable state, which persists for a long time as the pair-broken process is severely suppressed. The mean-field phase diagram and low-energy excitations are investigated in a square lattice system. Intriguingly, spontaneous superflows may appear in the ground state of a triangular optical lattice system due to antiferromagnetic frustration.

Frustration effects in rapidly rotating square and triangular optical lattices

We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing \mathrm{U}\left(1\right) quantum rotor approach and the topologically constrained path integral that includes a summation over \mathrm{U}\left(1\right) topological charge. We derive an effective quantum action for the BH model, which enables a non-perturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f=0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.

Polarization plateau in an atomic Fermi gas loaded on a three-leg triangular optical lattice

In order to demonstrate that atomic Fermi gas is a good experimental reality in studying unsolved problems in frustrated interacting-spin systems, we numerically examine the Mott core state emerged by loading two-component atomic Fermi gases on triangular optical lattices. Consequently, we find that plateau like structures are observable in the Mott core polarization as a function of the population imbalance. These plateau states are caused by a flexibility that the surrounding metallic region absorbs the excess imbalance to keep the plateau states inside the Mott core. We also find spin patterns peculiar to the plateau states inside the Mott core.

Hofstadter's butterfly energy spectrum of ultracold fermions on the two-dimensional triangular optical lattice

We study the energy spectrum of ultracold fermionic atoms on the two-dimensional triangular optical lattice subjected to a perpendicular effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations and numerically solve them, then we obtain the Hofstadter's butterfly-like energy spectrum, which has a novel fractal structure. The observability of the Hofstadter's butterfly spectrum is also discussed.

Exotic superconducting phases of ultracold atom mixtures on triangular lattices

We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in the work of Mathey et al. [Phys. Rev. Lett. 97, 030601 (2006)]. Using functional renormalization-group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-1/2 fermions on an isotropic lattice we find a competition of s-, p-, extended d-, and f-wave symmetries, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between p- and f-wave symmetries. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.

Quantum Stripe Ordering in Optical Lattices

We predict the robust existence of a novel quantum orbital stripe order in the p-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.

THREE-SPIN INTERACTIONS AND ENTANGLEMENT IN OPTICAL LATTICES

The entanglement properties of some novel quantum systems are studied that are inspired by recent developments in cold-atom technology. A triangular optical lattice of two atomic species can be employed to generate a variety of spin-1/2 Hamiltonians including effective three-spin interactions. A variety of one- or two-dimensional systems can thus be realized that possess multi-degenerate ground states or non-vanishing chirality. The properties of these ground states and their phase transitions are probed with appropriate measures such as the entropic entanglement and the spin chirality.

Effective three-body interactions in triangular optical lattices

We demonstrate that a triangular optical lattice of two atomic species, bosonic or fermionic, can be employed to generate a variety of novel spin-1/2 Hamiltonians. These include effective three-spin interactions resulting from the possibility of atoms tunneling along two different paths. Such interactions can be employed to simulate particular one or two dimensional physical systems with ground states that possess a rich structure and undergo a variety of quantum phase transitions. In addition, tunneling can be activated by employing Raman transitions, thus creating an effective Hamiltonian that does not preserve the number of atoms of each species. In the presence of external electromagnetic fields, resulting in complex tunneling couplings, we obtain effective Hamiltonians that break chiral symmetry. The ground states of these Hamiltonians can be used for the physical implementation of geometrical or topological objects.

Quantum Information and Triangular Optical Lattices

The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or fermionic, can be employed to generate a variety of novel spin-1/2 models that include effective three-spin interactions. Such interactions can be employed to simulate specific one or two dimensional physical systems that are of particular interest for their condensed matter and entanglement properties. In particular, connections between the scaling behaviour of entanglement and the entanglement properties of closely spaced spins are drawn. Moreover, three-spin interactions are well suited to support quantum computing without the need to manipulate individual qubits. By employing Raman transitions or the interaction of the atomic electric dipole moment with magnetic field gradients, one can generate Hamiltonians that can be used for the physical implementation of geometrical or topological objects. This work serves as a review article that also includes many new results.