Ultracold fermions provide a new testbed for dynamical phases of quantum matter forbidden by equilibrium thermodynamics.

We have characterized the one-dimensional (1D) to three-dimensional (3D) crossover of a twocomponent spin-imbalanced Fermi gas of 6 Li atoms in a 2D optical lattice by varying the lattice tunneling and the interactions. The gas phase separates, and we detect the phase boundaries using in situ imaging of the inhomogeneous density profiles. The locations of the phases are inverted in 1D as compared to 3D, thus providing a clear signature of the crossover. By scaling the tunneling rate t with respect to the pair binding energy B , we observe a collapse of the data to a universal crossover point at a scaled tunneling value oftc = 0.025(7).PACS numbers: 67.85. Lm, 71.10.Pm, 37.10.Jk, 05.70.Fh Atomic Fermi gases prepared in two hyperfine sublevels realize a quasi-spin-1 /2 system, for which the two states may be denoted as |↑ and |↓ . Spinimbalanced Fermi gases, where the number of spinup atoms, N ↑ , exceeds the number of spin-down atoms, N ↓ , have been studied extensively in recent years, largely motivated by a search for exotic superfluid phases [1][2][3]. One such superfluid, the FuldeFerrell-Larkin-Ovchinnikov (FFLO) phase [4,5], has not been conclusively observed in three dimensions (3D) but is believed to occupy a large portion of the one-dimensional (1D) phase diagram [6,7]. Measurements have confirmed that the 1D phase diagram is consistent with theories exhibiting FFLO [8], but direct evidence for this phase remains elusive. Since the FFLO phase is expected to be more robust to quantum and thermal fluctuations in higher dimensions, attention has focused on the dimensional crossover [9][10][11][12].A crossover between 1D and 3D regimes may be realized by simply varying the confinement aspect ratio [13][14][15][16][17]. A complementary dimensional crossover occurs by varying the tunneling between tubes aligned in an array, as depicted in Fig. 1(a). Such a geometry, which may be achieved using ultracold atoms in an optical lattice, is more analogous to some material systems, such as carbon nanotube bundles [18] and spin-1 /2 magnet chains [19,20]. The bundle will cross over from an array of independent 1D tubes for small tunneling t, to a 3D system as t is increased [21,22]. We have employed this geometry to determine the crossover value of t for a spin-imbalanced Fermi gas with various interaction strengths and find a striking universality in the crossover location.Trapped Fermi gases with spin-imbalance have been observed to phase separate at low temperatures in both 3D [23][24][25][26][27] FIG. 1. (Color online) (a) Schematic of an array of 1Dcoupled tubes formed by a 2D optical lattice. The tunneling rate t between the tubes increases with decreasing optical lattice depth. (b) Schematic of phase separation for a trapped spin-imbalanced Fermi gas in 1D (top) and in 3D (bottom) at zero temperature. In 1D, the central region is an FFLO partially-polarized superfluid (SFP), with balanced superfluid (SF0) wings for small polarization P . In 3D, for P < P 3D c , a central SF0 core is surrounded by an SFP or ...

We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k −1 F , we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6) /m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. At unitarity, the contact rises to 0.28(3)k 2 F per particle, measuring the breaking of scaling symmetry. Our observations support the conjecture that in systems with strong scattering, the local relaxation rate is bounded from above by kBT / .Conjectured quantum bounds on transport appear to be respected and nearly saturated by quark-gluon plasmas [1, 2], unitary Fermi gases [3][4][5][6][7][8][9][10][11], and bad metals [12,13]. For many modalities of transport these bounds can be recast as an upper bound on the rate of local relaxation to equilibrium 1/τ r k B T / , where k B is the Boltzmann constant and T is temperature [14,15]. Systems that saturate this "Planckian" bound do not have well defined quasiparticles promoting transport [1,[12][13][14][15]. A canonical example is the quantum critical regime, where one expects diffusivity D ∼ /m, a ratio of shear viscosity to entropy density η/s ∼ /k B , and a conductivity that is linear in T [4, 12, 13]. These limiting behaviors can be understood by combining τ r with a propagation speed v ∼ k B T /m, for example D ∼ v 2 τ r . This argument applies to ultracold three-dimensional (3D) Fermi gases, whose behavior in the strongly interacting regime is controlled by the quantum critical point at divergent scattering length, zero temperature, and zero density [4,16,17]. In such systems, one observes D 2 /m [6-8] and η/s 0.4 /k B [3], compatible with conjectured quantum bounds.However in attractive two-dimensional (2D) Fermi gases, scale invariance is broken by the finite bound-state pair size, so the strongly interacting regime is no longer controlled by a quantum critical point [16,[18][19][20][21][22][23]. Strikingly, an extreme violation of the conjectured D /m bound has been observed in an ultracold 2D Fermi gas: a spin diffusivity of 6.3(8) × 10 −3 /m near ln(k F a 2D ) = 0 [24], where k F is the Fermi momentum and a 2D is the 2D s-wave scattering length. No similarly dramatic effect of dimensionality is observed in charge conductivity [12] or bulk viscosity [25], and such a low spin diffusivity is unexplained by theory [11,19].In this work, we recreate the conditions of Ref. [24], and study the demagnetization dynamics of ultracold 2D Fermi gases using both a coherent spin-echo sequence [8] and time-resolved spectroscopy [7]. We find a modification of th...

We have measured changes in the ground-state populations of Cs vapor induced by optical pumping at high magnetic field. The 2.7-T field of our experiments is strong enough to decouple the nuclear and electronic spins, allowing us to independently measure each population. The spatial dependence of the Cs populations in small amounts of buffer gas obeys a simple coupled diffusion model and the relative populations reveal the details of relaxation within the vapor cell. Optical pumping can produce high nuclear polarization in the Cs vapor due to perturbations of the hyperfine interaction during collisions with buffer-gas particles and depending on the pumping transition, radiation trapping can strongly influence the electronic and nuclear polarizations in the vapor.

We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of 6 Li atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the BCS and unitary regimes. We disagree with the QMC results in the BEC regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure the equation of state in the crossover regime for a gas with equal numbers of the two fermion spin states.