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arXiv:1208.3304 · Physical Review A

Mott insulators in plaquettes

J.-P. Martikainen

Published Sep 26, 2012• 2 citations
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Abstract

We study small systems of strongly interacting ultracold atoms under the influence of gauge potentials and spin-orbit couplings. We use second-order perturbation theory in tunneling, derive an effective theory for the strongly correlated insulating states with one atom per site, and solve it exactly. We find dramatic changes in the level structure and in the amount of degeneracies expected. We also demonstrate the dynamical behavior as the barriers between plaquettes are gradually removed and find potentially high overlap with the resonating valence bond (RVB) state of the larger system.

DOI
10.1103/physreva.86.033630

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We study small systems of strongly interacting ultracold atoms under the influence of gauge potentials and spin-orbit couplings. We use second-order perturbation theory in tunneling, derive an effective theory for the strongly correlated insulating states with one atom per site, and solve it exactly. We find dramatic changes in the level structure and in the amount of degeneracies expected. We also demonstrate the dynamical behavior as the barriers between plaquettes are gradually removed and find potentially high overlap with the resonating valence bond (RVB) state of the larger system.
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We study the exchange physics in high-spin Mott insulating systems with S=3∕2S=3∕2S=3∕2 which is realizable in ultracold atomic systems. The high symmetry of SO(5)\mathit{SO}(5)SO(5) or SU(4)\mathit{SU}(4)SU(4) therein renders stronger quantum fluctuations than the usual spin-1∕21∕21∕2 systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-3∕23∕23∕2 model, whose topological excitations exhibit fractionalization behavior. The generalization to the SU(N)\mathit{SU}(N)SU(N) plaquette state is also investigated.
The one-dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high-order symbolic perturbative expansion. Analytical expressions are derived for the ground-state quantities such as energy per site, variance of on-site occupation, and correlation functions: $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j+r}⟩$ and $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{j}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{j+r}⟩$. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultracold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.
The concept of valence-bond resonance plays a fundamental role in the theory of the chemical bond and is believed to lie at the heart of many-body quantum physical phenomena. Here we show direct experimental evidence of a time-resolved valence-bond quantum resonance with ultracold bosonic atoms in an optical lattice. By means of a superlattice structure we create a three-dimensional array of independent four-site plaquettes, which we can fully control and manipulate in parallel. Moreover, we show how small-scale plaquette resonating valence-bond (RVB) states with s- and d-wave symmetry can be created and characterized. We anticipate our findings to open the path towards the creation and analysis of many-body RVB states in ultracold atomic gases.
Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of 87Rb{}^{87}\mathrm{Rb}87Rb atoms. This state is stable to a small applied potential gradient (an ``electric'' field), but a resonant response was observed when the potential energy drop per lattice spacing (E),(E),(E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for $E\ensuremath{\approx}U$ via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions and to a variety of lattices should allow study of numerous other correlated quantum phases.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion UUU from a Gossamer superconductor at small UUU. At the critical value U=UcU={U}_{c}U=Uc​, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at U>UcU>{U}_{c}U>Uc​ to a Gossamer SC state at U<UcU<{U}_{c}U<Uc​ at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.