Phases of Bosons or Fermions in confined optical lattices

Phases of Bose or Fermi atoms in optical lattices confined in harmonic traps are studied within the Thomas-Fermi approximation. Critical radii and particle number for onset of Mott insulator states are calculated and phase diagrams shown in 1D, and estimated for 2 and 3D. Methods to observe these and novel phases such as d-wave superconductivity is discussed. Specifically the collective modes are calculated.Comment: Revised and extended. To appear in PR

Confinement induced molecules in a 1D Fermi gas

We have observed two-particle bound states of atoms confined in a one-dimensional matter wave guide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.Comment: 4 page

1D Bose Gases in an Optical Lattice

We report on the study of the momentum distribution of a one-dimensional Bose gas in an optical lattice. From the momentum distribution we extract the condensed fraction of the gas and thereby measure the depletion of the condensate and compare it with a theorical estimate. We have measured the coherence length of the gas for systems with average occupation $\bar{n}>1$ and $\bar{n}<1$ per lattice site.Comment: 4 pages, 3 figure

A scanning microcavity for in-situ control of single-molecule emission

We report on the fabrication and characterization of a scannable Fabry-Perot microcavity, consisting of a curved micromirror at the end of an optical fiber and a planar distributed Bragg reflector. Furthermore, we demonstrate the coupling of single organic molecules embedded in a thin film to well-defined resonator modes. We discuss the choice of cavity parameters that will allow sufficiently high Purcell factors for enhancing the zero-phonon transition between the vibrational ground levels of the electronic excited and ground states.Comment: 8 page

1D Bose gases in an optical lattice

We report on the study of the momentum distribution of a one-dimensional Bose gas in an optical lattice. From the momentum distribution we extract the condensed fraction of the gas and thereby measure the depletion of the condensate and compare it with a theoretical estimate. We have measured the coherence length of the gas for systems with average occupation n̄>1 and n̄<1 per lattice sit

Repulsively bound atom pairs in an optical lattice

Throughout physics, stable composite objects are usually formed via attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report on the first observation of such an exotic bound state, comprised of a pair of ultracold atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under collisions with one another. Signatures of the pairs are also recognised in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, due to the presence of strong decay channels. These results exemplify on a new level the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose-Hubbard model, a correspondence which is vital for future applications of these systems to the study of strongly correlated condensed matter systems and to quantum information.Comment: 5 pages, 4 figure

Superfluid to Mott insulator transition in one, two, and three dimensions

No Heading: We have created one-, two-, and three-dimensional quantum gases and study the superfluid to Mott insulator transition. Measurements of the transition using Bragg spectroscopy show that the excitation spectra of the low-dimensional superfluids differ significantly from the three-dimensional cas

Superfluid, Mott-Insulator, and Mass-Density-Wave Phases in the One-Dimensional Extended Bose-Hubbard Model

We use the finite-size density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional ($d = 1$) extended Bose-Hubbard model for density $\rho = 1$ in the $U-V$ plane, where $U$ and $V$ are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density Wave (MDW). For small values of $U$ and $V$, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional-Ising characters. For large values of $U$ and $V$ we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase boundaries join at a bicritical point at ($U, V) = (8.5 \pm 0.05, 4.75 \pm 0.05)$.Comment: 10 pages, 15 figure

Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.Comment: 44 pages, 15 figures, contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge