Session V4: Bosons and Fermions in Optical Lattices

Doublon production rate by optical lattice modulation for strongly correlated Fermionic atoms

Currently lattice modulation spectroscopy technique is applied to experiments. [1] In this spectroscopy, the number of doubly occupying atom (doublon) produced by amplitude modulation of an optical lattice potential is probed. Theoretically, it allows us to access a kinetic energy correlation function. [2] We discuss doublon excitations of strongly correlated fermionic atoms in a high-temperature regime relevant to current experiments of fermionic atoms in an optical lattice. [3] We employ a slave particle representation, and the self-energy is estimated by using non-crossing approximation based on a spin-incoherent assumption. Furthermore, this formalism is applied to calculation of the doublon production rate as a function of the lattice modulation frequency, chemical potential and temperature. Using parameters given in the experiment [1], a fit to the experimental data is implemented, and quantitatively good agreement is obtained. \\[4pt] [1] D. Greif, L. Tarruell, T. Uehlinger, R. J\"ordens, and T. Esslinger, Phys. Rev. Lett. 106, 145302 (2011).\\[0pt] [2] C. Kollath, A. Iucci, I. P. McCulloch, and T. Giamarchi, Phys. Rev. A 74, 041604(R) (2006).\\[0pt] [3] A. Tokuno, E. Demler, and T. G.iamarhi, arXiv:1106.1333.   

Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions

Using quantum Monte Carlo simulations, we investigate the finite temperature phase diagrams of hardcore bosons in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trapped systems, and compare it with previously proposed approaches.   

Double occupancy as a universal probe for antiferromagnetic correlations and entropy in cold fermions on optical lattices

We study antiferromagnetic (AF) order and correlations in the half-filled Hubbard model using dynamical mean-field theory, determinantal quantum Monte Carlo (in dimensions $d=2,3$), and Bethe Ansatz (in $d=1$). We establish a low-temperature enhancement of the double occupancy $D$ at stromg coupling as a local probe of strong AF correlations accessible in cold-atom experiments [1]. As a function of entropy $s=S/(N k_{\rm B})$, $D$ is nearly universal with respect to dimensionality, with a minimum in $D(s)$ at $s\approx \log(2)$ [2]. The quantum AF Heisenberg regime at $s\la \log(2)$, driven by an abrupt gain in kinetic energy and with clear signatures also in the next-nearest neighbor correlation function, should be in immediate experimental reach. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve $s<\log(2)/2$ (on a cubic lattice) and should consider lower dimensions, for which the AF effects are larger, or even use dimensionality as a tunable parameter.\\[4pt] [1] E. V. Gorelik, I. Titvinidze, W. Hofstetter, M. Snoek, and N. Bl\"umer, Phys. Rev. Lett. {\bf 105}, 065301 (2010).\\[0pt] [2] E. V. Gorelik, T. Paiva, R. Scalettar, A. Kl\"umper, and N. Bl\"umer, arXiv:1105.3356v1.   

Tunable Phases of Fermionic Cold Atoms Systems in Mixed Dimensions

We investigate a system with two species of fermions. One species, f-fermions, moves on a two-dimensional square lattice. Another species, c-fermions, is constrained to move on a one-dimensional lattice embedded in the square lattice of f-fermions. The phases of the effective one-dimensional system whose interactions are mediated by the two-dimensional system can be tuned by manipulating the two-dimensional density. We explore effective theories, quantum phases, correlations, and relevant energy scales for various fillings of the mixed dimensional system using a functional renormalization group approach.   

Pairing and Density-Wave Phases of Population Imbalanced Fermi-Fermi Mixture on Optical Lattice

We study a two species fermion mixture with different populations on a square lattice, which can be modeled by a Hubbard Hamiltonian with on-site inter-species interaction. Such a model can be realized in a cold atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice, and with interaction strength that can be tuned by an external magnetic field. When one of the fermion species is close to half-filling, the system is highly affected by lattice effects. We find several correlated phases for this system, including spin density wave state, d-wave charge density wave state, and p-wave superfluid state for the minority species. We study this system using a functional renormalization group method, determining its phase diagram and providing an estimate for the critical temperature of each phase. These phases emerge from a combination of interaction, population imbalance, and lattice effects. Lattice effects in particular lead to a much richer phase diagram than that of a imbalanced mixture of fermionic gas.   

Finite-temperature Properties of the Fermi-Hubbard Model on the Honeycomb Lattice

We study thermodynamic properties of the Fermi-Hubbard model on the honeycomb lattice utilizing the numerical linked-cluster expansion, which is exact in the thermodynamic limit, and quantum Monte Carlo simulations. We obtain the equation of state, double occupancy, entropy and spin correlations for a wide range of temperatures, chemical potentials, and interaction strengths. Employing a local density approximation, we study properties of the system in the presence of a harmonic trapping potential and compare the efficiency of various adiabatic cooling schemes to those obtained for such model on the square lattice.   

Realizing a fermionic superfluid state from a band insulator in an optical lattice

We propose a route to realizing a fermionic superfluid state in an optical lattice starting from a band insulator. We show that by increasing the strength of attractive interaction between the fermions in the singlet channel, a band insulator can be driven to a superfluid state in an optical lattice. The band structure is suitably designed to avoid other competing states. We estimate the Kosterlitz-Thouless transition temperature of such a superfluid. The proposal could help the realization of a superfluid state of fermions in an optical lattice circumventing the cooling problem.   

A Boson Core Compressibility Measure for Optical Lattices

Trapping in experiments on cold atomic gases in optical lattices leads to in homogeneity and different phases within the trap. We model a global measure, the boson core compressibility, that can be used to access local properties of a single phase at the center of the trap using observations of double occupancy. We test this measure on the trapped Bose-Hubbard model using mean field theory and quantum Monte Carlo. We find that the boson core compressibility focuses on the core region of the system and eliminates edge effects. We use the core compressibility to identify the transition from Mott insulator to superfluid and show that it is essentially the same as local compressibility in the core region when the system has doubly occupied sites. We generalize the definition of core compressibility to study systems with large densities at the trap center.   

Numerical studies of exotic paired states in optical lattices

Ultracold atoms are a unique tool that allows the exploration of phases of matter not easily accessible in condensed matter systems. Two interesting possibilities are spin-imbalanced systems and spin dependent optical lattices with Fermi surfaces that differ for the two hyperfine species. We use mean-field theory and quantum Monte Carlo simulations of Hubbard-like models with an attractive contact interaction to study the FFLO state and, by rotating the two Fermi surfaces by 90 degrees with respect to each other, a recently proposed exotic paired state [Feiguin and Fisher, 2009].   

Competing instabilities in a two band Hubbard model on a square lattice

We study a two band Hubbard model on a two dimensional square lattice. In particular, we focus on the cases wherein one band is doped to have a small electron pocket while the other band is doped to have a hole pocket and the Fermi lines of these two pockets are nearly nested. Similar models have been studied extensively in the context related to the Iron-based material where the interactions between electrons are always repulsive. Here we investigate the generalized cases that the interactions between the fermions within the same band $U_1$ and $U_2$ and the interactions between electrons in different bands $U_{12}$ can be tuned independently. Such models can potentially be realized in a cold atom system where the manipulation of the interaction is possible by taking advantage of the Feshbach resonance. The freedom of tuning the strength and the sign (repulsive or attractive) of the interactions, combined with the nearly nested Fermi lines, allows both the density wave phases and the pairing phases to be potential candidates for the ground state. We employ the functional renormalization group approach so that we can investigate the competition between these possible instabilities on an equal footing.   

Condensate Properties for Strongly Repulsive Bosons in a Double Well

We present path integral ground state (PIGS) quantum Monte Carlo calculations for the ground state (T = 0) properties of repulsively interacting bosons in a three-dimensional external double well potential over a range of interaction strengths and potential parameters. We focus on calculation of ground state number statistics in order to understand the level of squeezing that the system may exhibit as a function of interaction strength. For weak interactions (i.e. where the standard two-mode model of a BEC in a double well is applicable) we produce results consistent with the two-more model. However, for stronger interactions, we find a novel and somewhat surprising relationship between squeezing and interaction strength. We find that these new features are qualitatively consistent with squeezing calculations carried out using an improved, recently-proposed eight-mode model, although this model is insufficient to quantititively predict the results of the full quantum Monte Carlo simulation.   

A Quantum Plasmonic Circuit for Cold Atoms

We propose a new architecture for quantum simulation with atoms using a two dimensional lattice of plasmonic nanoparticles to both trap the atoms and mediate interactions between them. This proposal combines existing technologies from ultracold atoms and plasmonics to exploit the unique coherence properties of atoms and the strong light-matter interaction and subwavelength confinement provided by plasmonic systems. We first show that this system allows to increase the energy scales of Hubbard models by two orders of magnitude compared to optical lattices. We then show how this system can realize a dissipative quantum simulator to prepare a wide range of many-body entangled states.