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arXiv:1005.4076 · Physical Review Letters

Observation of a Two-Dimensional Fermi Gas of Atoms

Kirill Martiyanov, Vasiliy Makhalov, Andrey V. Turlapov

Published Jul 15, 2010• 198 citations
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Abstract

We have prepared a degenerate gas of fermionic atoms which move in two dimensions while the motion in the third dimension is "frozen" by tight confinement and low temperature. In situ imaging provides direct measurement of the density profile and temperature. The gas is confined in a defect-free optical potential, and the interactions are widely tunable by means of a Fano-Feshbach resonance. This system can be a starting point for exploration of 2D Fermi physics and critical phenomena in a pure, controllable environment.

DOI
10.1103/physrevlett.105.030404

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We have prepared a degenerate gas of fermionic atoms which move in two dimensions while the motion in the third dimension is "frozen" by tight confinement and low temperature. In situ imaging provides direct measurement of the density profile and temperature. The gas is confined in a defect-free optical potential, and the interactions are widely tunable by means of a Fano-Feshbach resonance. This system can be a starting point for exploration of 2D Fermi physics and critical phenomena in a pure, controllable environment.
We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.
Quasi-2D degenerate Fermi gases provide a rich physical environment to explore since many effects that are present do not exist in 3D. This thesis describes the first experiments carried out in a quasi-2D Fermi gas across the broad 6Li Feshbach resonance at 834 G. A description of the apparatus used to form molecular Bose-Einstein condensates and degenerate Fermi gases in the two lowest hyperfine states of 6Li, |F = 1/2,mf = 1/2i and |F = 1/2,mf = −1/2i, is presented. An anisotropic 2D optical potential is formed by an elliptical Gaussian beam produced by tightly focusing a circular Gaussian beam in one direction with a cylindrical lens. The trapping frequencies are ∼3 kHz in the axial direction and ∼50 Hz in the radial direction giving an aspect ratio of ∼60. For a non-interacting Fermi gas this allows ∼1700 atoms to populate the lowest transverse harmonic oscillator state and to be considered as quasi-2D. We present the transition from a three dimensional gas to a two dimensional gas at ∼2000 atoms agreeing within experimental uncertainty with the non-interacting atom number. The observations are made through measuring the radial and axial widths of the gas at three different magnetic fields, 810 G, 834 G, and 991 G. The widths σ are then plotted against the atom number N. The curve, log σ(N) = n logN+a, is then fit to the data in the 3D regime and in the 2D regime. The expansion of a non-interacting Fermi gas in the 2D regime changes from a scaling of N1/4 to N1/6 in the 3D regime and for a Bose gas it changes to N1/5. A value for n is extracted in each of these regimes. For each magnetic field we then obtain in the 2D regime: n = 0.27(0.04) at 810 G, n = 0.23(0.02) at 834 G and n = 0.26(0.01) at 991 G. In the 3D regime we obtain: n = 0.195(0.01) at 810 G, n = 0.154(0.01) at 834 G and n = 0.175(0.01 at 991 G. We also observe a change in the aspect ratio as we approach the 2D regime which is not present in our 3D single beam optical dipole trap and is absent in any 3D system. These first results indicate that we have a quasi-2D Fermi gas. The main experimental results are the first indications of a confinement induced resonance in a 6Li Fermi gas through the measurement of the cloud width in the tightly confined direction after a fixed expansion time. We observe a significant deviation in the transverse width of the 2D interacting Fermi gas from the 3D case due to the increased tight confinement. The confinement induced resonance should appear when the 3D scattering length approaches the transverse harmonic oscillator length, az = p~/mωz, where m is the mass and ωz is the tight transverse trapping frequency. For our experimental parameters this leads to a 3D scattering length of 1.03 μm, where the observation is at 819(1) G. In the weakly confined direction there is no such increase in the width due to the free motion in the xy plane. Instead the cloud width across the Feshbach resonance increases monotonically, similar to that of a 3D gas and as described theoretically for a quasi-2D Fermi gas by Lin et al. [1].
We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.
Ultracold atomic gases can be prepared in laboratory environments with unrivaled control and purity. In one and a half decades the field has evolved from the first Bose condensates in dilute alkali gases to multiple species mixtures and degenerate Fermi systems. Combining quantum degenerate fermions and optical lattices enables the simulation of relevant condensed matter systems. By observing the final state of an atomic sample in a tailored optical potential the system can be used as an analog quantum computer to evaluate Hamiltonians that are computationally impossible to tackle on classical computers. A versatile optical dipole trap has been constructed and characterized. The trap can be converted to an optical lattice, allowing for the investigation of the phase diagram of the two-component, one-dimensional, imbalanced Fermi gas.