Session N2: Magnetism in Optical Lattices

Bose-Hubbard model on a checkerboard superlattice

We study the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and charge-density-wave insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--charge-density-wave insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.   

Quantum Magnetism in an Optical Lattice: Antiferromagnetic Ising Chain in Transverse and Longitudinal Fields

Understanding the behaviors of strongly-interacting spin systems is one of the central objectives of condensed matter physics. Solid-state realizations of such systems can be quite difficult to control and observe, and do not often admit description with simple models due to their complex structure and myriad interactions and dissipation channels. Ultracold gases in optical lattices offer an elegant alternative, providing exquisite control over interactions, and structure, and recently, site-resolved read-out. Here we present the first realization of quantum magnetism within an optical lattice. Using ultracold Rubidium atoms, we study an Ising spin chain in both transverse and longitudinal fields. By mapping the spin degree of freedom onto dipolar excitations of a Mott Insulator in a tilted optical lattice, we achieve strong spin-spin interactions, and fast dynamics. By sweeping the lattice tilt, we demonstrate a phase-transition from a paramagnetic phase to an anti-ferromagnetic phase. We observe anti-ferromagnetic ordering both \emph{in-situ}, taking advantage of the single-site resolution of our quantum gas microscope, and via a 1D quantum noise correlation measurement.   

Simulation of magnetism in a triangular optical lattice

We have realized a quantum simulator for magnetism with scalar bosons in a triangular optical lattice. To this end, we identify the local superfluid phase with a classical spin. By tuning the tunneling matrix elements between neighboring lattice sites in magnitude and sign, we can emulate a large variety of magnetic phases in this lattice geometry. We could confirm all the expected magnetic phases, ranging from ferromagnetic via parallel- and staggered-spin-chains to mixed anitferromagnetic-ferromagnetic phases and fully antiferromagneitc systems. In the latter case, we could even observe spin frustration which leads to spontaneous symmetry breaking.\\ We will present the experimental results obtained for the relevant regions of the spin-phase diagram together with a discussion on the technical realization of the spin-emulator. These results open the perspective to extremely complex and yet not well understood phases like the spin-liquid in a quantum xy-model and the dynamics of different types of phase transitions.   

Quantum simulation of the transverse field Ising model with trapped atomic ions

We simulate an fully-connected ferromagnetic Ising model in a transverse magnetic field using a chain of spins, each represented by the ground states within the hyperfine manifold of a 171-Yb+ ion. ~We observe the transition from paramagnetic to ferromagnetic ground state spin order as the ratio of the transverse field to Ising couplings is varied. The crossover curves get `sharper' as the system size is increased, from N=2 to 9 ions, heralding the expected quantum phase transition in an infinite size system. Sources of error and insight from numerical simulations will be discussed and we expect these results will guide future experiments that will simulate quantum magnetic models that are intractable using classical computers.   

Quantum magnetic phases in harmonically trapped two-component bosons

We consider a two-component bosonic system trapped in a harmonic potential. We use large scale Quantum Monte Carlo simulations to study under which experimental conditions magnetic phases, e.g. Ising antiferromagnet (checkerboard solid), can be observed in the trap.   

Nearest-neighbor correlations of fermions in optical lattices as a tool to study the approach to magnetic order

Fermionic atoms in optical lattices constitute an almost ideal realization of the Fermi-Hubbard model, a key model in the study of strongly correlated electron systems. This Hamiltonian incorporates the transition from a metallic to a Mott insulating phase, where the suppression of transport results from strong interactions. We have studied this transition in a gas of ultracold fermionic potassium atoms through measurements of the lattice site occupation. Observing magnetically ordered phases will require the detection of spin correlations over several lattice sites. We have developed a method for probing nearest-neighbor density and spin correlations in the system [1]. We show that in the paramagnetic phase it gives access to the number of defects of the Mott-insulating core and is well suited for thermometry. Furthermore, its sensitivity to short range magnetic correlations opens interesting prospects for studying the approach to magnetic order.\\[4pt] [1] Daniel Greif \emph{et al.}, arXiv:1012.0845v1 (2010)   

First-order phase transition in the bosonic Kondo-Hubbard model

Recent experimental progress in populating the excited bands of an optical lattice gives rise to the exciting possibility of simulating multi-band condensed matter Hamiltonians. The Kondo lattice model (KLM), in which tightly bound electrons act as spinful scattering centers for electrons in a conduction band, is a typical example of the type of model one would like to simulate. In the KLM, the orbital (band) degree of freedom gives rise to a complex phase diagram, which includes magnetically ordered states, a heavy Fermi liquid, and unconventional superconductors [1]. Here we consider a version of the KLM first proposed in [2], in which the electrons are replaced by spin-$\frac{1}{2}$ bosons, which in turn are realized physically by bosonic alkali atoms in an optical lattice. As we demonstrate, the interplay between spin, charge, and orbital degrees of freedom can drive the Mott insulator to superfluid transition to be first order, without explicit breaking of SU(2) symmetry. The observability of such behavior in the context of current experiments will also be discussed. \\[4pt] [1] H. Tsunetsugu, M. Sigrist, and K. Ueda, Rev. Mod. Phys. 69, 809 (1997).\\[0pt] [2] L. Duan, Europhys. Lett. 67, 721 (2004).   

High Resolution Control of Magnetism in a Tilted Optical Lattice

Mott Insulators in tilted optical lattices form a rich platform for the study of strongly correlated phases of matter. When the tilt per lattice site approaches the onsite interaction energy, each atom is localized to two adjacent lattice sites and is further constrained by the behaviour of neighboring atoms, thus producing strong nearest-neighbor interactions. We have recently employed such a system to observe a quantum phase transition from a paramagnetic phase to an antiferromagnetic phase. Using a spatial light modulator we are now able to tailor the lattice topography with very high resolution. Local tailoring at the single-site level enables us to generate site-resolved spin flips for potential studies of spin diffusion, and domain-wall-quasiparticle interactions. High resolution potentials applied over large regions enable investigations of dynamical frustration, and more generally the timescale for a quantum phase transition in the presence of various types of controlled disorder. We will discuss both results and prospects for future studies.   

Realizing models of magnetism with long-range interactions via cavity QED

Optical cavity photons provide a natural channel for mediating long-range interatomic interactions; such interactions are known to drive, e.g., the Dicke phase transition of a BEC in a cavity [1]. In the present work, we consider a general scheme for realizing models of quantum magnetism in which the spin- spin interactions are infinite-ranged. The proposed scheme uses three-level atoms confined in a standing-wave or a ring cavity, with their positions fixed by an external potential; depending on the distribution of atomic positions in the cavity, one can realize models of ferromagnetism, antiferromagnetism, or disordered magnetism, including models that exhibit glassy phases. The models with glassy phases are of particular interest as they are solvable, owing to the infinite range of the interactions, yet exhibit nontrivial properties; such models are, however, impossible to realize in conventional condensed matter. We explore the phase structure of the realizable models, as well as possible experimental probes of the various realizable phases.\\[4pt] [1] K. Baumann et al., Nature 464, 1301 (2010)   

Time-of-flight imaging method to observe signatures of antiferromagnetically ordered states of ultracold fermionic atoms in an optical lattice

Currently, the antiferromagnetic (AF) transition in the optical lattice system is attracting much interest in the field of atomic physics and also in condensed matter physics. Here, we theoretically propose a simple method to detect such AF states of fermionic atoms in an optical lattice by combining a time-of-flight (TOF) imaging method and a Feshbach resonance [1]. In this scheme, the nontrivial dynamics of fermionic atoms during the imaging process works as a probe with respect to the breaking of the translational symmetry in the AF state. Precise numerical simulations demonstrate that the characteristic oscillatory dynamics appears in TOF images, which can be easily observed experimentally. Our basic idea is to detect the artificially induced excitations of atoms which transfer the ordering vector Q in the momentum space, where Q characterizes the breaking of translational symmetry. Therefore, our proposal provides a general experimental idea for detecting translational symmetry broken states in optical lattices, which is largely unavailable in traditional condensed matter systems. \\[4pt] [1] K. Inaba and M. Yamashita, \textit{Phys. Rev. Lett.} \textbf{105}, 173002 (2010) .