Session W3: Ultracold Atoms in Reduced Dimensions

Realization of a Super-Tonks-Girardeau gas with strong attractive interactions

We realize a 1D quantum gas with strong attractive interactions. For this, we load a Bose-Einstein condensate of Cs atoms into an array of ``tube-like" 1D traps generated by a 2D optical lattice and exploit the tunability of the interaction strength near a Feshbach resonance. When the 3D scattering length is increased towards and beyond the length scale set by the tight transversal confinement, we observe a confinement-induced resonance (CIR) that allows us to tune the effective 1D-interaction parameter $g_{\mathrm{1D}}$ to large positive and negative values. By tuning to large positive values of $g_{\mathrm{1D}}$, we first observe the transition from a 1D mean field system to a Tonks-Girardeau (TG) gas as evidenced by a change of the breathing mode frequency $\omega_B$ along the weakly confining direction from $\sqrt{3}$ to $2$ in units of the (bare) dipole oscillation frequency $\omega_D$. When the CIR is crossed to enter the strong attractive interaction regime, $\omega_B$ increases beyond 2 (in units of $\omega_D$), giving evidence of the regime of hard-rod interactions known as the super-Tonks-Girardeau (sTG) regime$^{1}$. We find, in contrast to the TG regime, that the release energy strongly depends on $g_{\mathrm{1D}}$, and that the sTG gas is surprisingly stable despite the fact that the interaction is strongly attractive. \newline $^{1}$ G. Astrakharchik et al., Phys. Rev. Lett. {\bf 95}, 190407 (2005).   

Studying integrability in the 1D Bose gas using atom chips, RF dressing and interference

The repulsively interacting one-dimensional (1D) Bose gas is the simplest example of a integrable system, exactly solvable by the (thermodynamic) Bethe Ansatz (BA), a key method in many- body condensed-matter theory. We have recently performed the first experimental test of the thermodynamic BA for the 1D Bose gas, employing $^{87}$Rb on an atom chip [PRL 100, 090402 (2008)]. We are now extending these experiments to $(i)$ interferometric studies of both phase-coherent and independent 1D Bose gases, employing RF-dressing to create double-well potentials and $(ii)$ the two-component 1D Bose gas. For the latter system, the BA yields exact results {\em only} for the case of component-{\em in}dependent interactions. RF dressing allows experimental control over the effective 1D interaction strengths, enabling the tuning of the system towards and away from integrability. Our latest results will be presented at the conference.   

Spin-incoherent Luttinger liquid regime of trapped Fermi gases

The Luttinger liquid phase has been the paradigm of low-energy physics in 1D systems for about half a century. This phase is characterized by the absence of fermionic quasiparticles even in the presence of well defined Fermi surfaces with the relevant modes of dispersion represented by bosonic spin and charge excitations propagating at different velocities. Very recently the so-called spin-incoherent Luttinger liquid has become an active area of research. In contrast with the spin-coherent Luttinger liquid, here the spin-incoherence results from the induced spin-spin interaction being the smallest energy scale in the system. Recent success in manipulating ultracold atomic systems allows one to realize such different strongly correlated regimes by tuning the inter atomic interaction strength and trap parameters. We show, while the spin-incoherent regime is hard to achieve in solid state setups, it is almost unavoidable in trapped atom configurations. Further, for probing such states, we identify the noise correlations of density fluctuations as a robust observable uniquely suitable in the context of trapped atomic gases to discriminate between these two regimes. Finally, we address the prospects of realizing and probing these phenomena experimentally using optical lattices.   

FFLO vs Bose-Fermi mixture in a two channel model of a 1D Fermi gas: a 3-body study

We study three fermions with a 1D two-channel model of a Feshbach resonance in order to gain insight into how the FFLO-like state at small negative scattering lengths evolves into a Bose-Fermi mixutre at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture the correlations are monotonic. This behavior is is already present at the 3-body level. We present an exact study of the 3-body problem, and compare the results to scalable quantum Monte-Carlo calculations.   

Probing the FFLO phase of a spin imbalanced 1D Fermi gas

The search for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a polarized superfluid with a spatially varying order parameter, has generated large interest in both condensed matter and cold atoms communities. To date, there has been only indirect experimental evidence of FFLO in the heavy fermion superconductor CeCoIn5. In a 1D polarized Fermi gas, the FFLO phase is predicted to occupy a large region of the phase diagram\footnote{G. Orso, Phys. Rev. Lett. 98, 070402 (2007), Hu et al., Phys. Rev. Lett. 98, 070403 (2007).}. We have implemented a 2D optical lattice in order to explore experimental signatures of FFLO, for example in-situ density distributions or time of flight imaging. In this talk, we will present the experimental progress on both methods.   

Excitation spectrum and effective interactions of highly-elongated Fermi gas

Full 3D calculations of small two-component Fermi gases under highly-elongated confinement, in which unlike fermions interact through short-range potentials with variable atom-atom s-wave scattering length, are reported. The 3D excitation frequencies are compared with those determined from atomic and molecular 1D model Hamiltonian. Our numerical results suggest that the effective 1D atom-dimer and dimer-dimer interactions are to a good approximation determined by simple analytical expressions. Implications for the description of quasi-1D Fermi gases within strict 1D frameworks are discussed.   

Finite-size and confinement effects in spin-polarized trapped Fermi gases

We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different-species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization. Our findings contribute to understanding some experimental discrepancies in spin-polarized Fermi gases as finite-size and confinement effects.   

Phase Diagram of A One Dimensional Spin-Imbalanced Fermi Gas

We study a 1D polarized Fermi gas by confining a two spin-component Fermi gas of $^{^{6}}$Li atoms in a 2D optical lattice. The lattice forms an array of tubes with weak axial confinement. Polarization is varied by changing the relative spin populations. In 3D, we observed phase separation in which an unpolarized superfluid core was surrounded by a normal polarized gas\footnote{G. B. Partridge et al., Science 311, 503-505 (2006); G. B. Partridge {\it et al.}, {\it Phys. Rev. Lett.} {\bf 97}, 190407 (2006).}. In 1D, however, theory predicts an inverted phase separation, where a central partially polarized (FFLO) superfluid is surrounded by wings that are either fully polarized or an unpolarized superfluid depending on the spin imbalance\footnote{G. Orso, Phys. Rev. Lett. 98, 070402 (2007); H. Hu et. al, Phys. Rev. Lett. 98, 070403 (2007)}. We will present our results and compare with the theoretical phase diagram.