Session Y32: Mott Phases and Novel Quantum Systems

Mott phases and superfluid-insulator transition of spin-3 bosonic atoms in an optical lattice

We present a theoretical study of the Mott phases and superfluid-insulator transition of spin-3 bosonic atoms with dipolar interactions in an optical lattice. We present the various broken symmetry states obtained and discuss the application of our results to Chromium atoms in optical traps.   

Criterion for bosonic superfluidity in an optical lattice

We show that the current method of determining superfluidity in optical lattices based on a visibly ``sharp" bosonic momentum distribution $n({\bf k})$ can be misleading, for even a {\em normal} Bose gas can have a similarly ``sharp'' $n({\bf k})$. We show that superfluidity can be detected from the so-called ``visibility'' $(v)$ of $n({\bf k})$ $-$ that $v$ must be 1 within $O(N^{-2/3})$, where $N$ is the number of bosons. Many current experiments, however, have interpreted states with $v<1$ as superfluid. Such states are in fact normal, reflecting strong temperature effects in the system. These normal states, however, allow one to explore the physics in the quantum critical regime.   

Theory of Clock-Shift Density-Profile Measurements and Applications

``Clock shifts'' -- shifts in spectroscopic line energies proportional to the local density -- provide a spectroscopic way of measuring spatial density profiles. By measuring the absorption of a probe laser at various frequencies, one can obtain a histogram of the number of particles with the associated local densities. Campbell \textit{et al.} (\textit{Science} \textbf{313}, 649 (2006)) have recently imaged the ``wedding-cake structure'' of the Mott insulator phase in trapped ultracold bosons in optical lattices, using this technique. We develop a theory of clock-shifts for these systems, making comparisons with experiment. We find qualitative agreement with experiment using the simplest strong-coupling mean-field theory with a local density approximation, and a harmonic, isotropic trap model. We show which embellishments to these approximations are best at accounting for the experimental data. We propose applications of this technique to cooling, thermometry, and measurement of correlations, giving an elementary theory of each. Finally, we highlight a \textit{superfluid} shell structure that can be particularly apparent in these experiments.   

Synchronization versus dephasing in the pairing dynamics of cold fermions

Motivated by recent experiments on degenerate Fermi gases with time-dependent interaction~[1,2], we consider the time dynamics of BCS-paired fermions with switchable interaction. Several new regimes [3] of dissipationless coupled dynamics of the collective BCS mode and individual fermion pair states are identified and explored. The system can exhibit synchronized evolution in which all pair states are fully phased-locked, trasnforming to a Landau-damped dephased behavior upon variation of coupling strength. At the synchronization-dephasing transition the amplitude of long-time persistent oscillations vanishes. A second transition is found in the dephased regime, at which the long-time asymptotic constant value of pairing amplitude vanishes. Using a combination of numerical and analytical methods we establish a continuous (type II) character of both transitions. We also propose an experiment which could probe these new dynamical states. \newline [1] C.~A.~Regal, M.~Greiner, and D.~S.~Jin, Phys. Rev. Lett. {\bf 92}, 040403 (2004). \newline [2] M.~W.~Zwierlein, C.~A.~Stan, C.~H.~Schunck, S.~M.~F.~Raupach, A.~J.~Kerman, and W.~Ketterle, Phys. Rev. Lett. {\bf 92}, 120403 (2004). \newline [3] R.~A.~Barankov and L.~S.~Levitov, Phys. Rev. Lett. {\bf 96}, 230403 (2006).   

Quantum phase transitions of polar molecules in bilayer systems

We investigate the quantum phase transitions of bosonic polar molecules in a two-dimensional double layer system. We show that an interlayer bound state of dipoles (dimers) can be formed when the dipole strength is above a critical value, leading to a zero energy resonance in the interlayer $s$-wave scattering channel. In the positive detuning side of the resonance, the strong {\it repulsive} interlayer pseudo-potential can drive the system into a maximally entangled state, where the wavefunction is a superposition of two states that have all molecules in one of the two layers and none in the other. We critically discuss how the zero-energy resonance, dimer states and the maximally entangled state can be measured in time-of-flight experiments.   

Quantum phase diagram of Polar Molecules in 1D Double Wire Systems

We study the quantum phase transitions of fermionic polar molecules loaded in a double wire potential. By tuning the magnitude and direction of external electric field we observed many interesting quantum phases in different parameter range, including an easy-plane spin density wave, a triplet superconducting phase, and a truly long range order of easy-axis ferromagnetic phase in strong interacting regime. We also discuss how these exotic quantum phases can be measured in the existing experimental techniques.   

Hidden order in one dimensional Bose insulators

We investigate the phase diagram of spinless bosons with long range ($\propto 1/r^3$) repulsive interactions, relevant to ultracold polarized atoms or molecules, using DMRG. Between the two conventional insulating phases, the Mott and density wave phases, we find a new phase possessing hidden order revealed by non local string correlations analogous to those characterizing the Haldane gapped phase of integer spin chains. We develop a mean field theory that describes the low energy excitations in all three insulating phases. This is used to calculate the absorption spectrum due to oscillatory lattice modulation. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase.   

Phase-locking transition of coupled low-dimensional superfluids

We study the phase-locking transition of two coupled low-dimensional superfluids, either two-dimensional superfluids at finite temperature, or one-dimensional superfluids at zero temperature. We find that these superfluids have a strong tendency to phase-lock. The phase-locking is accompanied by a sizeable increase of the transition temperature ($T_{KT}$ in 2D) of the resulting double-layer superfluid, which suggests a plausible way of observing the Kibble-Zurek mechanism in two-dimensional cold atom systems by rapidly changing the ratio $T/T_{KT}$ varying the tunneling rate between the superfluids. When the two superfluids interact with each other, which is the case for polar condensates or for radio frequency induced double well potentials, further phases can be realized. We also extend the discussion to more than two coupled superfluids.   

Quantum quenches in a spinor condensate

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing magnetic field. We first elucidate the nature of the equilibrium quantum phase transition, which has a multicritical point when the magnetization in the direction of the field vanishes. Quenching rapidly through this transition reveals XY ordering either at a specific wavevector, or the `light-cone' correlations familiar from relativistic theories, depending on the endpoint of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long time dynamics again depends on the endpoint, conserving the order parameter in zero field, but not at finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler \emph{et al.}   

Absorption of microwave radiation by an array of vortices in a p-wave superfluid of fermionic cold atoms

We propose an experiment to identify the weak-pairing (``non-abelian'') phase of a two-dimensional $p$-wave superfluid of cold atoms by microwave absorption. We consider transitions between two atomic hyperfine states, where atoms in the ground state form a rotated $p$-wave superfluid, and atoms in the excited state are subject to a rotation and a periodic potential. We focus our calculations on absorption originating from zero energy Majorana states present in cores of vortices of the weakly- paired superfluid, and identify van-Hove type singularities in the absorption spectrum. The absorption peaks are unique to the weak-pairing phase, and their appearance in the spectrum may serve as a demonstration of the phase transition into the weak pairing phase. We discuss how these results can be extended to three dimensional superfluids, and explore extensions of non-abelian statistics to multiple two-dimensional layers.   

Time-dependent electromagnetic wave dynamics in ultracold, high-density Rb vapor

Recent experiments and theoretical results on light localization in condensed samples show that diffusive transport is strongly suppressed and that a regime of anomalous diffusion develops dynamically. Proximity of the light localization threshold can be detected through time evolution of either forward or diffusely scattered light. We report in this paper experimental and theoretical results on time-dependent light scattering in the spectral vicinity of the F = 2 - F$'$ = 3, and the F = 1 - F$'$ = 0 optical transitions in dense, ultracold atomic $^{87}Rb$ samples formed in an optical dipole trap.   

Correlated Wavefunction for the Li Atom

Accurate wavefunctions are extremely valuable as tools for gaining understanding of quantum systems. Here we use a wavefunction explicitly containing all the interparticle distances to obtain a highly precise description of the ground state of the Li atom. In contrast to the widely used Hylleraas approach (in which the interelectron distances enter the wavefunction only as integer powers), our wavefunction exhibits an exponential dependence on all the interparticle distances, with a spatial dependence (before imposing spin and symmetry restrictions) of the form $\sum_{n=1}^N c_n \exp(-w_1r_1-w_2r_2-w_3r_3-u_1r_{23} -u_2r_{13}-u_3r_{12})$, where $r_i$ are electron-nuclear distances, $r_{ij}$ are electron-electron distances, and $w_i$ and $u_i$ are parameters. When the nonlinear parameters are carefully optimized (a nontrivial task), this type of basis causes a far more rapid convergence (with $N$) than the Hylleraas basis. We will survey the results we have obtained and compare with other studies of the Li atom.   

Diabolic Topology , Berry Phase and Optical Phase Shifts of Light in Mobius-Type Strips

We compute the optical phase shifts between the left and the right-circularly polarized light after it traverses non-planar cyclic loops describing the boundary curves of twisted strips. These optical results expressed in quantum-mechanical language in fact illustrate the phenomenon of Berry phase. Equation for the evolution of the fields described by Fermi-Walker formulation is mapped to Schroedinger equation with Hamiltonian whose eigenvalues are equal to the $\pm kappa$ where $\kappa$ is the curvature of the path. The inflexion points underlying the twisted strips manifest as the diabolic crossings of the quantum Hamiltonian. For the Mobius loops, the critical width where the diabolic geometry resides also correspond to the characteristic width where the optical phase shift is minimal.