Spin liquid phases of large spin Mott insulating ultracold atoms

Bhuvanesh Sundar, Todd C. Rutkowski, Michael J. Lawler +1 more

Markus Greiner, Olaf Mandel, Tilman Esslinger +2 more

Bhuvanesh Sundar, Todd C. Rutkowski, Michael J. Lawler +1 more

Todd C. Rutkowski, Michael J. Lawler

Mott insulating ultracold gases possess a unique whole-atom exchange interaction which enables large quantum fluctuations between the Zeeman sublevels of each atom. By strengthening this interaction---either through the use of large-spin atoms or by tuning the particle-particle interactions via optical Feshbach resonance---one may enhance fluctuations and facilitate the appearance of the long-sought-after quantum spin liquid phase---all in the highly tunable environment of cold atoms. To illustrate the relationship between the spin magnitude, interaction strength, and resulting magnetic phases, we present and solve a mean-field theory for bosons optically confined to the one-particle-per-site Mott state, using both analytic and numerical methods. We find on square and triangular lattices for bosons of hyperfine spin $f>2$ that making the repulsive $s$-wave scattering length through the singlet channel small---relative to the higher-order scattering channels---accesses a short-range resonating valence bond (s-RVB) spin liquid phase.

Markus Greiner, Olaf Mandel, Tim Rom +4 more

Todd C. Rutkowski

This thesis investigates the plausibility of producing a quantum spin liquid (QSL) with ultracold bosonic atoms optically confined to the Mott insulating state. QSLs have received a great deal of attention for being an antiferromagnetic groundstate with many exotic properties, including the absence of local order, long-range entanglement, and fractionalized excitations. However, the identification and characterization of these phases in solid state systems remains a great challenge. Here we outline an alternate route to uncovering the QSL phase, which from the nature of spin angular momentum for ultracold atoms encounters many properties unique to these systems along the way. This proposal is possible because the magnetic exchange interactions for Mott insulating ultracold atoms are mediated by the hopping of whole atoms. Whole-atom exchange—a unique property of cold atoms—allows large fluctuations between the quantized Zeeman sublevels of each atomic spin. As we demonstrate, these fluctuations increase when large-spin atoms are used, or when interactions are tuned via optical Feshbach resonance (OFR). These strong quantum spin fluctuations inhibit classical magnetic ordering, and lead to a QSL ground state. To illustrate the relationship between the spin magnitude, interaction strength, and QSL ground state, we present two distinct approaches to solving the relevant Hamiltonian. With mean field theory we find that for large spin (f > 2), and strong scattering through the spin-singlet channel, that magnetically-ordered Bose-Einstein condensates are unstable to the formation of a QSL. We then utilize Rayleigh-Schodinger perturbation theory to derive an effective Hamiltonian for our system in the Hilbert space of nearest-neighbor singlet coverings. At large spin this Hamiltonian produces a type of quantum dimer model (QDM), which are known to possess QSL phases. We derive the QDM parameters t, t′ and V as a function of spin on several lattices, finding they scale with the inverse number of Zeeman sublevels. We then determine the proximity of the physically accessible states to the QSL phase, and discuss how other regions of the phase diagram may be accessed. We then conclude by highlighting several advantages to studying QSLs and QDMs with ultracold bosons.