Evidence for superfluidity of ultracold fermions in an optical lattice

Chin, J. K.; Miller, David; Liu, Y.; Stan, C. A.; Setiawan, Widagdo; Sanner, Christian; Xu, Kuan‐Man; Ketterle, Wolfgang

doi:10.1038/nature05224

Cited by 361 publications

(398 citation statements)

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“…These experiments represent an exciting opportunity to simulate the fundamental mechanisms and models of condensed matter physics, for instance Cooper pairing of fermions and the Hubbard model, without the additional complexities presented by real materials. A number of experiments have already demonstrated the possibilities for ultra-cold atomic gases, including inducing superfluidity in fermionic systems and probing the BEC-BCS crossover [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

FFLO order in ultra-cold atoms in three-dimensional optical lattices

Rosenberg

Chiesa²,

Zhang³

2015

J. Phys.: Condens. Matter

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We investigate different ground-state phases of attractive spin-imbalanced populations of fermions in 3-dimensional optical lattices. Detailed numerical calculations are performed using Hartree-FockBogoliubov theory to determine the ground-state properties systematically for different values of density, spin polarization and interaction strength. We first consider the high density and low polarization regime, in which the effect of the optical lattice is most evident. We then proceed to the low density and high polarization regime where the effects of the underlying lattice are less significant and the system begins to resemble a continuum Fermi gas. We explore the effects of density, polarization and interaction on the character of the phases in each regime and highlight the qualitative differences between the two regimes. In the high-density regime, the order is found to be of Larkin-Ovchinnikov type, linearly oriented with one characteristic wave vector but varying in its direction with the parameters. At lower densities the order parameter develops more structures involving multiple wave vectors.

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Section: Introductionmentioning

confidence: 99%

FFLO order in ultra-cold atoms in three-dimensional optical lattices

Rosenberg

Chiesa²,

Zhang³

2015

J. Phys.: Condens. Matter

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“…phase separation. Although an FFLO-type state has been predicted to appear in these systems as well [10,11], it is likely to be difficult to observe since it appears in the edges of the trap except for large polarizations.Recent experiments [12,13] on Fermi gases confined in optical lattices have already demonstrated the potential of these systems for a multitude of studies of new phases, dimensionality effects, and dynamics. In this letter, we calculate the phase diagram for an attractively interacting Fermi gas in an optical lattice at zero and finite temperatures.…”

mentioning

confidence: 99%

“…Recent experiments [12,13] on Fermi gases confined in optical lattices have already demonstrated the potential of these systems for a multitude of studies of new phases, dimensionality effects, and dynamics. In this letter, we calculate the phase diagram for an attractively interacting Fermi gas in an optical lattice at zero and finite temperatures.…”

mentioning

confidence: 99%

Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

et al. 2007

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We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair (BP), and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.PACS numbers: 03.75. Ss, 03.75.Hh,74.25.Dw Recent advances in the experiments of ultracold Fermi gases have shown great potential for elucidating longstanding problems in many different fields of physics related to strongly correlated Fermions. For instance, in recent experiments [1,2,3,4,5] spin-density imbalanced, or polarized, Fermi gases were considered. Such systems make it possible to study pairing with mismatched Fermi surfaces, potentially leading to non-standard phases such as that appearing in FFLO-states [6,7] or BP-states [8] (Sarma-states). These possibilities have been considered extensively in condensed-matter, nuclear, and highenergy physics [9]. The experiments in trapped gases have shown clear evidence of the separation of the gas into a BCS core region and a normal state shell around it, i.e. phase separation. Although an FFLO-type state has been predicted to appear in these systems as well [10,11], it is likely to be difficult to observe since it appears in the edges of the trap except for large polarizations.Recent experiments [12,13] on Fermi gases confined in optical lattices have already demonstrated the potential of these systems for a multitude of studies of new phases, dimensionality effects, and dynamics. In this letter, we calculate the phase diagram for an attractively interacting Fermi gas in an optical lattice at zero and finite temperatures. In particular, we consider the possibility of the single mode FFLO-phase, where the order parameter is space-dependent, and of the BCS-BP phase, where compared to the standard BCS phase the excess polarization is carried by additional Bogoliubov excitations. We investigate their competition with the phase separation (PS) of the gas into normal and BCS superfluid regions. Our results reveal that a typical phase diagram as a function of polarization and temperature is as shown in Fig. 1: phase separation is expected for small polarizations and temperatures, whereas at zero temperature the FFLO state appears after some critical polarization. At a finite temperature, the FFLO-phase competes with the BCS-BP phase. As the temperature increases the BCS-BP phase becomes energetically favorable, and as the temperature is increased even further the BCS-BP phase gives way to a normal polarized Fermi gas.Furthermore, the phase diagrams reveal a Lifshitz point which is surrounded by the normal, FFLO, and BCS-BP phases. The transitions around this point are of second order, but the FFLO ph...

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“…For a p-component quantum gas in a single trap, we have α = p. If the quantum gas is in the lowest band of a cubic lattice with hopping integral t and lattice spacing d, then α = p(λ/d) 3 [I 0 (2t /k B T )] 3 , where I 0 (x) is the Bessel function of the first kind (see the Methods section). The corresponding column densityñ(x,y) = n(x,y,z)dz (with r = (x,y)) is n(x,y) = α k B T hω z e (µ−V (r))/kBT λ 2…”

mentioning

confidence: 99%

“…n(x) = αe (µ−V (x))/kBT /λ 3 (1) where λ = h/ √ 2πMk B T is the thermal wavelength and k B is the Boltzman constant. For a p-component quantum gas in a single trap, we have α = p. If the quantum gas is in the lowest band of a cubic lattice with hopping integral t and lattice spacing d, then α = p(λ/d) 3 [I 0 (2t /k B T )] 3 , where I 0 (x) is the Bessel function of the first kind (see the Methods section).…”

mentioning

confidence: 99%

Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases

2009

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Experiments that use cold atoms in optical lattices to simulate the behaviour of strongly correlated solid-state systems promise to provide insight into a range of longstanding problems in many-body physics 1-10 . The goal of such 'quantum simulations' is to obtain information about homogeneous systems. Cold-gas experiments, however, are carried out in spatially inhomogeneous confining traps, which leads inevitably to different phases in the sample. This makes it difficult to deduce the properties of homogeneous phases with standard density imaging, which averages over different phases. Moreover, important properties such as superfluid density are inaccessible by standard imaging techniques, and will remain inaccessible even when systems of interest are successfully simulated. Here, we present algorithms for mapping out several properties of homogeneous systems, including superfluid density. Our scheme makes explicit use of the inhomogeneity of the trap, an approach that might turn the source of difficulty into a means of constructing solutions.To deduce the bulk properties of homogeneous systems from the observed properties of non-uniform systems, local density approximation (LDA) naturally comes to mind. In this approximation, the properties of a non-uniform system at a given point are deduced from their bulk values assuming an effective local chemical potential. To the extent that LDA is valid, determining bulk thermodynamic quantities as functions of chemical potentials amounts to determining their spatial dependencies in confining traps. In present experiments with ultracold atomic gases, column-integrated density (or density for two-dimensional (2D) experiments) is the only local property that can be accessed. No other thermodynamic quantities have been measured because there are no clear ways to access them. Here, we show that by studying changes in density caused by external perturbations, one can access the quantities mentioned above from density data. The deduction of superfluid density is particularly important, as it is a fundamental quantity that has eluded measurement since the discovery of Bose-Einstein condensation.Our first step is to use the density near the surface of the quantum gas as a thermometer. Within LDA, the density is n(x) = n(µ(x),T ), where n(µ, T ) is the density of a homogeneous system with temperature T and chemical potential µ, µ(x) = µ − V (x); V (x) = 1/2 M i=x,y,z ω 2 i x 2 i is a harmonic trapping potential with frequencies ω i and M is the mass of the atom. Near the surface, the density is sufficiently low that one can carry out a fugacity expansion to obtain(1) where λ = h/ √ 2πMk B T is the thermal wavelength and k B is the Boltzman constant. For a p-component quantum gas in a single trap, we have α = p. If the quantum gas is in the lowest band of a cubic lattice with hopping integral t and lattice spacing d, then α = p(λ/d) 3 [I 0 (2t /k B T )] 3 , where I 0 (x) is the Bessel function of the first kind (see the Methods section). The corresponding column densityñ(x,y) = ...

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Evidence for superfluidity of ultracold fermions in an optical lattice

Cited by 361 publications

References 30 publications

FFLO order in ultra-cold atoms in three-dimensional optical lattices

FFLO order in ultra-cold atoms in three-dimensional optical lattices

Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases

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