Session X3: Optical Lattices III

Artificial Relativity with Optical Lattices

A driving force behind the study of ultracold atoms is the idea of ``quantum simulation" of other physical systems, including systems which may not be accessible in their original manifestations. In this talk, we discuss how to use optical lattice setups to generate a variety of effective Hamiltonians which resemble the Dirac Hamiltonian for a relativistic electron. Engineering such Hamiltonians suggests the possibility of a variety of experiments, including cold atom versions of \emph{Zitterbewegung} \footnote{J. Y. Vaishnav, Charles W. Clark. \emph{Phys. Rev. Lett.}, {\bf 100}, 153002 (2008).}, spintronic transistors \footnote{J. Y. Vaishnav, Julius Ruseckas, Charles W. Clark, Gediminas Juzeliunas. \emph{Phys. Rev. Lett.}, {\bf 101}, 265302 (2008).}, and topological insulators \footnote{T. D. Stanescu, V. Galitski, J. Y. Vaishnav, Charles W. Clark. Preprint.}.   

Solving the mystery of the missing superfluid shells: radio-frequency spectroscopy of a homogeneous Bose gas in an optical lattice yields a bimodal line shape

We show that near the Mott transition a uniform gas of bosons in an optical lattice should display a bimodal radio-frequency (RF) spectrum. This behavior is very different from the lineshapes in both the deep superfluid and deep Mott limit where we find a single sharp peak. The basic physics, known from studies of the single particle spectrum, is that the intermediate regime can be thought of as a Mott state with a few delocalized particles added. This yields two types of single particle excitations: a low energy ``phonon" in the gas of delocalized particles, and a higher energy particle-hole excitation of the Mott state. RF photons couple to each of these excitations. We discuss the role of symmetries in the spectrum: in particular we describe how the vertex corrections are structured in order to satisfy the Ward identities which encode the relevant conservation laws. This may account for and suggest ways to circumvent the experimental difficulties in spectroscopically distinguishing the superfluid from the Mott insulating state.   

Long-lived quantum coherence in a 1D optical lattice investigated using 2D pump-probe spectroscopy

We observe a surprising plateau in the decay of pulse-echo amplitude measured for quantum vibrational states in a 1D optical lattice, indicating a long-lived component of the coherence. We present a hypothesis for the origin of the plateau in the decay, and develop a 2D pump-probe spectroscopy technique to test this model. In our 1D lattice, atoms are free to move in the transverse directions with thermal velocities about 3 cm/s. Although the intrinsic decoherence time is expected to be of the order of 50 ms, this transverse drift through the spatially inhomogeneous laser beam leads to a finite frequency decorrelation time, degrading the echo in about 1 ms. Modeling suggests that initial position-velocity correlations, which build up during state preparation, can lead to echo amplitude which plateaus after an initial fast decay. To probe the atoms' frequency drift directly, we have developed a pump-probe spectroscopy technique, essentially a version of spectral hole-burning for these vibrational states. This allows us to directly measure the frequency-frequency correlation as function of time, which can be used to make predictions about the echo decay and develop techniques to better preserve coherence.   

Optical Microscope for Quantum Gases in a 2D Trap

Ultracold quantum gases are used to experimentally realize and quantitatively study fundamental models of condensed matter physics. When combined with optical lattice potentials, ultracold quantum gases allow for a large scale implementation of quantum materials with ultra cold atoms playing the role of electrons or cooper pairs in real materials. We create a new type of quantum simulator by combining a quantum gas in a deeply 2D surface trap with a high numerical aperture microscope. We describe the current status of the experiment which enables optical imaging with an exceptionally large numerical aperture of up to $NA=0.8$. This microscope access allows us to efficiently collect fluorescence photons for low- background imaging and very high optical resolution on the 500\,nm scale. Optical lattice potentials are generated by direct projection of the lattice potentials using a novel trapping approach with a hologram generation of the lattice geometry.   

The Effects of Disorder in Systems of Neutral Atoms Confined in Optical Lattices

The precise control available in systems of neutral atoms confined in optical lattices makes them an ideal place to investigate the effects of disorder on crystal structure. We will report on experiments to study how atoms in an optical lattice respond to a disordered potential. Even small amounts of disorder can have a profound impact on the energy scales in the system, leading to observable changes in both the dynamic and static properties of the system. Dynamically, disorder introduces new timescales for system response to external perturbations. Statically, even the equilibrium properties of measurable quantities such as the momentum distribution can exhibit large changes. This work is partially supported by the ARO.   

Effects of interactions on an Anderson insulator in a disordered lattice

Anderson localization of ultracold atoms in disordered optical lattices, i.e. the transition from extended to exponentially localized states, was recently demonstrated for non-interacting samples. With the addition of atomic interactions, the system becomes more complicated and more difficult to describe theoretically. The effects of the disorder are expected to be gradually suppressed, and the possibility of different quantum phases arises. In our system, we employ a ${}^{39}$K Bose gas, where the interaction can be tuned from negligible to large values via a Feshbach resonance. We employ a one-dimensional incommensurate bichromatic optical lattice as a model of a controllable disordered system. In this talk, we present recent experimental results showing a transition from the Anderson-insulator phase to a superfluid phase.   

Hexatic, Wigner crystal and superfluid phases of dipolar bosons

The finite temperature phase diagram of two-dimensional dipolar bosons versus dipolar interaction is discussed for different values of short range repulsions. We identify the stable phases as superfluid, dipolar Wigner crystal (DWC), dipolar hexatic liquid crystal (DHLC), and normal fluid. In particular, we show that the DWC exists at low temperatures for large dipolar interactions, but it melts into a DHLC at higher temperatures, where translational lattice order is destroyed, but orientational order is preserved. Upon further increase in temperature the DHLC phase melts into the normal fluid, where both orientational and translational lattice order are absent. We also find that the supersolid phase has always higher energy than the superfluid or Wigner crystal phases at low temperatures, but the supersolid is metastable, having an energy minimum that may be accessed through thermal quenching. Lastly, we calculate the static structure factor for each of the stable phases and show that each phase can be identified uniquely in an optical Bragg scattering experiment.   

Two-dimensional FFLO vortex lattices and vortex liquids

We consider fermionic atoms with attractive interactions in two dimensions, and time-reversal symmetry removed by fast rotation. The phase diagram of this system has a remarkably rich structure due to the competition between superfluidity, Landau quantization and Zeeman effect (introduced by a number imbalance of the two atom species which form Cooper pairs). Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states and vortex liquids are found and sharply distinguished at zero temperature, in addition to the usual superfluid with an Abrikosov vortex lattice and quantum Hall states. The FFLO states are stabilized by the presence of a vortex lattice, and come in two varieties: FFLO-metals and FFLO-insulators, depending on whether the ``spin-polarized'' vortex core states form a Fermi surface or a band insulator. The vortex liquid phases exist at zero temperature alongside quantum Hall insulators of unpaired atoms when the attractive interactions between atoms are not too strong. We discuss how to observe this rich phase diagram in trapped ultra-cold atom experiments, as well as connections to high magnetic field superconductivity and pseudo-gap physics in condensed matter.   

Repulsively Interacting Fermi-Fermi Mixtures in 3D Optical Lattices

Fermionic atoms in optical lattices can model quantum systems known from condensed matter physics: They form an implementation of the Hubbard model with high experimental control of the relevant parameters. In our experiment we study the properties of ultracold Fermions in different regimes, ranging from metallic and band-insulating states in the non-interacting case, to complex metals and the fermionic Mott-insulator for strongly repulsive interactions. In the experiment, spin mixtures of fermionic ${}^{40}$K at $T/T_{F}$ of about $0.15$ are loaded into a combination of a blue-detuned three dimensional optical lattice and a red-detuned optical dipole trap. With this combination of potentials we gain independent control of lattice depth and harmonic confinement. Together with in-situ phase contrast imaging this allows us to measure the response of the system to varying external confinement. In addition to measurements of the in-situ cloud size, the compressibility and the fraction of doubly occupied lattice sites we report on the current status of our efforts.