Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Unlike the three-dimensional (3D) case, theories predict that in one dimension (1D) a state with FFLO correlations occupies a major part of the phase diagram. Here we report experimental measurements of density profiles of a two-spin mixture of ultracold (6)Li atoms trapped in an array of 1D tubes (a system analogous to electrons in 1D wires). At finite spin imbalance, the system phase separates with an inverted phase profile, as compared to the 3D case. In 1D, we find a partially polarized core surrounded by wings which, depending on the degree of polarization, are composed of either a completely paired or a fully polarized Fermi gas. Our work paves the way to direct observation and characterization of FFLO pairing.

We have confirmed the existence, as first reported by Kim and Chan, of a supersolid state in solid 4 He at temperatures below 250 mK. We have employed a torsional oscillator cell with a square cross section to insure a locking of the solid to the oscillating cell. We find that NCRI signal is not a universal property of solid 4 He, but can be eliminated through an annealing of the solid helium sample. This result has important implications for our understanding of the supersolid state. He confined within the porous media of porous gold and Vycor glass. KC followed this remarkable discovery with the observation of a supersolid or non-classical rotational inertia (NCRI) signal in bulk solid helium [2]. An important goal, which we have achieved in our experiments, has been to provide an independent confirmation of the KC observations for bulk 4 He. We have also investigated the influence of annealing and sample preparation on the existence of the supersolid state. We find that the supersolid state is not a universal property of solid 4 He, but that it is possible through crystal annealing near the melting curve to create samples that show only classical rotational inertia (CRI).In these measurements we have employed the torsional oscillator technique developed at Cornell over the past several decades [4]. Oscillators with two different sample geometries were used in the experiments reported in this letter. The first had a cylindrical sample geometry with an internal volume of 2.7 cm 3 and operated at a frequency of 253 Hz, while the second had a cubic geometry with a volume of 1.4 cm 3 and operated at 185 Hz. The helium used in the experiments was commercial well-grade helium similar to that used by KC in their bulk solid helium work [2]. This helium has a stated 3 He impurity level of 0.2 -0.3 ppm.Our earliest runs were made with the cylindrical cell. Data obtained with this cell at a pressure of 27 bar showed an onset of the supersolid signal at a temperature near 0.2 K, with a maximum signal amplitude at 30 mK of 0.6 % of the total period shift seen upon forming the solid in the cell. The magnitude of this signal is in good agreement with the observations of KC made under similar conditions and provides a confirmation of their results. In an attempt to improve the size of our NCRI signal we increased the sample pressure toward 55 bar. The cell failed before reaching this pressure.A diagram of our second cell is shown in Fig. 1. The design is similar to that of our first cell with several significant modifications. First, we have converted the The torsion cell's motion is excited and detected capacitively. The AC voltage on the detection electrodes serves as reference signal for a lock-in amplifier to keep the oscillation in resonance. At 4 K, the mechanical quality factor is 9 x 10 5 , and the resonance frequency is 185 Hz.interior of the cell to a nearly cubic geometry by epoxying a Tellurium-Copper insert into the cylindrical volume of the Beryllium-Copper oscillator. The insert was machined to provide a cubic ...

We report torsional oscillator supersolid studies of highly disordered samples of solid 4 He. In an attempt to approach the amorphous or glassy state of the solid, we prepare our samples by rapid freezing from the normal phase of liquid 4 He. Less than two minutes is required for the entire process of freezing and the subsequent cooling of the sample to below 1 K. The supersolid signals observed for such samples are remarkably large, exceeding 20 % of the entire solid helium moment of inertia. These results, taken with the finding that the magnitude of the small supersolid signals observed in our earlier experiments can be reduced to an unobservable level by annealing, strongly suggest that the supersolid state exists for the disordered or glassy state of helium and is absent in high quality crystals of solid 4 He. Following the discovery by Kim and Chan (KC) [1, 2] of the supersolid or nonclassical rotational inertia (NCRI) state of bulk solid 4 He, several independent groups using the same torsional oscillator technique have confirmed the KC supersolid results. These include the Japanese groups of Shirahama et al. [3], working at Keio University, and Kubota et al. [4] at the ISSP, as well as our group [5] at Cornell University. In these early experiments, the solid samples were formed by the blocked capillary technique. In this method the fill line to the cell is first allowed to freeze ensuring that solidification in the cell occurs under a condition of constant average density. This technique is known to produce relatively disordered polycrystalline samples. The signals observed in the early experiments were small representing, at most, a few percent of the total solid helium mass. The Cornell experiments [5] also demonstrated that the supersolid signal could be substantially reduced through annealing of the sample. In some cases the annealing process appeared to eliminate the supersolid signal; i.e., it reduced the supersolid fraction below the 0.05% level of experimental detection. This signal reduction upon annealing strongly suggested that sample disorder plays an important role in supersolid phenomena. This inference is supported by more recent work by Chan's group [6] where high quality crystals were grown under conditions of constant pressure. The supersolid signals observed for these constant pressure samples were somewhat smaller in magnitude than those obtained for more disordered samples created in the same cell by the blocked capillary method.Recently, there has been a growing consensus in the theoretical community [7,8,9,10] that an ideal hcp helium crystal will not exhibit the supersolid phenomenon, but rather, some form of disorder such as vacancies, interstitials, superfluid grain boundaries [11,12], or perhaps a glassy or superglass phase [13,14] is required for the existence of the supersolid state. A summary of the current theoretical literature is given in a recent review [15]. FIG. 1: Torsional oscillator:The motion of the torsion bob is excited and detected electrostatically. A Straty...

We study the effect of confinement on solid 4He's nonclassical rotational inertia fraction (NCRIF) in a torsional oscillator by constraining it to narrow annular cells of various widths. The NCRIF exhibits an observed maximum value of 20% for annuli of approximately 100 microm width. Samples constrained to porous media or to larger geometries both have smaller NCRIF, mostly below approximately 1%. In addition, we extend the blocked-annulus experiment of Kim and Chan to solid samples with large supersolid fractions. Blocking the annulus suppresses the nonclassical decoupling from 17.1% to below the limit of our detection of 0.8%. This result demonstrates the nonlocal nature of the supersolid phenomena. At 20 mK, NCRIF depends on velocity history showing a closed hysteresis loop in different thin annular cells.

We study the role of particle transport and evaporation on the phase separation of an ultracold, spinpolarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up to 2 s.