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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 $k_F^{-1}$, we find that the bare transverse spin diffusivity reaches a minimum of $1.7(6)\hbar/m$, 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 $0.28(3) k_F^2$ 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 $k_B T/\hbar$.

We demonstrate fluorescence microscopy of individual fermionic potassium atoms in a 527-nm-period optical lattice. Using electromagnetically induced transparency (EIT) cooling on the 770.1-nm D$_1$ transition of $^{40}$K, we find that atoms remain at individual sites of a 0.3-mK-deep lattice, with a $1/e$ pinning lifetime of $67(9)\,\rm{s}$, while scattering $\sim 10^3$ photons per second. The plane to be imaged is isolated using microwave spectroscopy in a magnetic field gradient, and can be chosen at any depth within the three-dimensional lattice. With a similar protocol, we also demonstrate patterned selection within a single lattice plane. High resolution images are acquired using a microscope objective with 0.8 numerical aperture, from which we determine the occupation of lattice sites in the imaging plane with 94(2)\% fidelity per atom. Imaging with single-atom sensitivity and addressing with single-site accuracy are key steps towards the search for unconventional superfluidity of fermions in optical lattices, the initialization and characterization of transport and non-equilibrium dynamics, and the observation of magnetic domains.

Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. So far, these "contact" relations have been established only for interactions with $s$-wave symmetry, i.e., without relative angular momentum. We report measurements of two new physical quantities, the "$p$-wave contacts", and present evidence that they encode the universal aspects of $p$-wave interactions through recently proposed relations. Our experiments use an ultracold Fermi gas of $^{40}$K, in which $s$-wave interactions are suppressed by polarising the sample, while $p$-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new contact relations, we infer an attractive $p$-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant $p$-wave quantum gas., Comment: Minor corrections to methods & supplements

We observe that the diffusive spin current in a strongly interacting degenerate Fermi gas of $^{40}$K precesses about the local magnetization. As predicted by Leggett and Rice, precession is observed both in the Ramsey phase of a spin-echo sequence, and in the nonlinearity of the magnetization decay. At unitarity, we measure a Leggett-Rice parameter $\gamma = 1.08(9)$ and a bare transverse spin diffusivity $D_0^\perp = 2.3(4)\,\hbar/m$ for a normal-state gas initialized with full polarization and at one fifth of the Fermi temperature, where $m$ is the atomic mass. One might expect $\gamma = 0$ at unitarity, where two-body scattering is purely dissipative. We observe $\gamma \rightarrow 0$ as temperature is increased towards the Fermi temperature, consistent with calculations that show the degenerate Fermi sea restores a non-zero $\gamma$. Tuning the scattering length $a$, we find that a sign change in $\gamma$ occurs in the range $0 < (k_F a)^{-1} \lesssim 1.3$, where $k_F$ is the Fermi momentum. We discuss how $\gamma$ reveals the effective interaction strength of the gas, such that the sign change in $\gamma$ indicates a switching of branch, between a repulsive and an attractive Fermi gas., Comment: 9 pages, 5 figures; Changed to the more conventional kF=(3 pi^2 n)^1/3, instead of the polarized definition we used in v1

Understanding the quantum dynamics of strongly interacting fermions is a problem relevant to diverse forms of matter, including high-temperature superconductors, neutron stars, and quark-gluon plasma. An appealing benchmark is offered by cold atomic gases in the unitary limit of strong interactions. Here we study the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. We observe the demagnetization of the gas, caused by diffusive spin transport. At low temperatures, the diffusion constant saturates to the conjectured quantum-mechanical lower bound $\simeq \hbar/m$, where $m$ is the particle mass. The development of pair correlations, indicating the transformation of the initially non-interacting gas towards a unitary spin mixture, is observed by measuring Tan's contact parameter., Comment: 8 pages, 6 figures. Accepted version

Experiments on solid-state materials and atomic quantum gases are increasingly investigating similar concepts in many-body quantum physics. Yet, the flavor of experiments on the gaseous atomic materials is different from that of conventional materials research. Here, we summarize some aspects of atomic physics and some of the common technical elements of cold-atom experiments which underlie the investigations described in the remaining chapters of this volume., Comment: 20 pages, 6 figures; to be printed as a Chapter the forthcoming volume "Ultracold Bosonic and Fermionic Gases", (Contemporary Concepts of Condensed Matter Science (Elsevier)), edited by Alexander Fetter, Katherine Levin, and Dan Stamper-Kurn

We report the laser cooling and trapping of neutral potassium on an open transition. Fermionic 40K is captured using a magneto-optical trap (MOT) on the closed 4S-4P transition at 767 nm and then transferred, with unit efficiency, to a MOT on the open 4S-5P transition at 405 nm. Because the 5P state has a smaller line width than the 4P state, the Doppler limit is reduced. We observe temperatures as low as 63(6) microkelvin, the coldest potassium MOT reported to date. The density of trapped atoms also increases, due to reduced temperature and reduced expulsive light forces. We measure a two-body loss coefficient of 2 x 10^-10 cm^3/s, and estimate an upper bound of 8x10^-18 cm^2 for the ionization cross section of the 5P state at 405 nm. The combined temperature and density improvement in the 405 nm MOT is a twenty-fold increase in phase space density over our 767 nm MOT, showing enhanced pre-cooling for quantum gas experiments. A qualitatively similar enhancement is observed in a 405 nm MOT of bosonic 41K., Comment: 8 pages, 8 figures, 1 table

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed., Comment: 8 pages, 7 figures; v3: Journal reference added, minor changes to text

Pauli blocking of spontaneous emission by a single excited-state atom has been predicted to be dramatic at low temperature when the Fermi energy $E_\mathrm{F}$ exceeds the recoil energy $E_\mathrm{R}$. The photon scattering rate of a ground-state Fermi gas can also be suppressed by occupation of the final states accessible to a recoiling atom, however suppression is diminished by scattering events near the Fermi edge. We analyze two new approaches to improve the visibility of Pauli blocking in a trapped Fermi gas. Focusing the incident light to excite preferentially the high-density region of the cloud can increase the blocking signature by 14%, and is most effective at intermediate temperature. Spontaneous Raman scattering between imbalanced internal states can be strongly suppressed at low temperature, and is completely blocked for a final-state $E_\mathrm{F} > 4 E_\mathrm{R}$ in the high imbalance limit., Comment: 12 pages, 8 figures. v4: to appear in Journal of Physics B: Atomic, Molecular, and Optical Physics

We study ferromagnetism in a repulsively interacting two-component Fermi gas in a harmonic trap. Within a local density approximation, the two components phase-separate beyond a critical interaction strength, with one species having a higher density at the trap center. We discuss several easily observable experimental signatures of this transition. The mean field release energy, its separate kinetic and interaction contributions, as well as the potential energy, all depend on the interaction strength and contain a sharp signature of this transition. In addition, the conversion rate of atoms to molecules, arising from three-body collisions, peaks at an interaction strength just beyond the ferromagnetic transition point. We then go beyond the local density approximation, and derive an energy functional which includes a term that depends on the local magnetization gradient and acts as a `surface tension'. Using this energy functional, we numerically study the energetics of some candidate spin textures which may be stabilized in a harmonic trapping potential at zero net magnetization. We find that a hedgehog state has a lower energy than an `in-out' domain wall state in an isotropic trap. Upon inclusion of trap anisotropy we find that the hedgehog magnetization profile gets distorted due to the surface tension term, this distortion being more apparent for small atom numbers. We estimate that the magnetic dipole interaction does not play a significant role in this system. We consider possible implications for experiments on trapped Li-6 and K-40 gases., Comment: 10 pgs, 5 figs: Added discussion of suppression of atom loss rate with onset of ferromagnetism; Added fig showing separate kinetic/potential/interaction energy signatures of ferromagnetism

We examine single-frequency optical schemes for species-selective trapping of ultracold alkali-metal atoms. Independently addressing the elements of a binary mixture enables the creation of an optical lattice for one atomic species with little or no effect on the other. We analyze a "tune-in" scheme, using near-resonant detuning to create a stronger potential for one specific element. A "tune-out" scheme is also developed, in which the trapping wavelength is chosen to lie between two strong transitions of an alkali-metal atom such that the induced dipole moment is zero for that species but is nonzero for any other. We compare these schemes by examining the trap depths and heating rates associated with both. We find that the tune-in scheme is preferable for Li-Na, Li-K, and K-Na mixtures, while the tune-out scheme is preferable for Li-Cs, K-Rb, Rb-Cs, K-Cs and 39K-40K mixtures. Several applications of species-selective optical lattices are explored, including the creation of a lattice for a single species in the presence of a phononlike background, the tuning of relative effective mass, and the isothermal increase of phase space density., Comment: 10 pages, 4 figures; v3: published version

In this article we review our recent experiments with a 40K-87Rb mixture. We demonstrate rapid sympathetic cooling of a 40K-87Rb mixture to dual quantum degeneracy on an atom chip. We also provide details on efficient BEC production, species-selective magnetic confinement, and progress toward integration of an optical lattice with an atom chip. The efficiency of our evaporation allows us to reach dual degeneracy after just 6 s of evaporation - more rapidly than in conventional magnetic traps. When optimizing evaporative cooling for efficient evaporation of 87Rb alone we achieve BEC after just 4 s of evaporation and an 8 s total cycle time., Comment: 8 pages, 4 figures. To be published in the Proceedings of the 20th International Conference on Atomic Physics, 2006 (Innsbruck, Austria)

Neutral fermions present new opportunities for testing many-body condensed matter systems, realizing precision atom interferometry, producing ultra-cold molecules, and investigating fundamental forces. However, since their first observation, quantum degenerate Fermi gases (DFGs) have continued to be challenging to produce, and have been realized in only a handful of laboratories. In this Letter, we report the production of a DFG using a simple apparatus based on a microfabricated magnetic trap. Similar approaches applied to Bose-Einstein Condensation (BEC) of 87Rb have accelerated evaporative cooling and eliminated the need for multiple vacuum chambers. We demonstrate sympathetic cooling for the first time in a microtrap, and cool 40K to Fermi degeneracy in just six seconds -- faster than has been possible in conventional magnetic traps. To understand our sympathetic cooling trajectory, we measure the temperature dependence of the 40K-87Rb cross-section and observe its Ramsauer-Townsend reduction., Comment: 5 pages, 4 figures (v3: new collision data, improved atom number calibration, revised text, improved figures.)

We demonstrate the loading of a Bose-Fermi mixture into a microfabricated magnetic trap. In a single-chamber vacuum system, laser-cooled atoms are transported to the surface of a substrate on which gold wires have been microfabricated. The magnetic field minimum formed near these current-carrying wires is used to confine up to $6\times10^4$ neutral $^{40}$K atoms. In addition, we can simultaneously load $2 \times 10^5$ $^{87}$Rb atoms, demonstrating the confinement of two distinct elements with such a trap. In a sequence optimized for $^{87}$Rb alone, we observe up to $1 \times 10^7$ trapped atoms. We describe in detail the experimental apparatus, and discuss prospects for evaporative cooling towards quantum degeneracy in both species., Comment: 10 pages, 6 figures. To appear in Journal of Low Temperature Physics, Vol 140, Nos. 5/6, September 2005. (v4: proof corrections, references updated.)

We have measured the momentum distribution of an elongated BEC (aspect ratio of 152), for temperatures below the critical temperature. The corresponding coherence length is significantly smaller than the condensate length in a wide range of temperature, in quantitative agreement with theoretical predictions. The Lorentzian shape of the momentum spectrum supports the image of a phase fluctuating quasicondensate., Comment: Proceedings of the International Conference on Laser Spectroscopy (ICOLS 03), Cairns, Australia, july 2003

We study the properties of elongated Bose-Einstein condensates. First, we show that the dimensions of the condensate after expansion differs from the 3D Thomas-Fermi regime. We also study the coherence length of such elongated condensates., Comment: proceeding of Quantum Gases in Low Dimension, Les Houches 2003, 8 pages, 5 figures

We measure the axial momentum distribution of Bose-Einstein condensates with an aspect ratio of 152 using Bragg spectroscopy. We observe the Lorentzian momentum distribution characteristic of one-dimensional phase fluctuations. The temperature dependence of the width of this distribution provides a quantitative test of quasi-condensate theory. In addition, we observe a condensate length consistent with the absence of density fluctuations, even when phase fluctuations are large., Comment: 4 pages, 3 figures; submitted to Phys. Rev. Lett

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate, in a trap and in free expansion. We take the inhomogeneous density profile into account {\it{via}} a local density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate., Comment: 5 pages, 2 figures; final version, references updated

We report on the measurement of the momentum distribution of an elongated Bose-Einstein condensate. A broadening of the distribution with increasing temperature is observed, which is clear evidence for phase fluctuations in the sample., Comment: to be published in the proceedings of "Cool Interactions 2002", Heidelberg, 9-13 september 2002 (Wiley)

We demonstrate the use of frequency-encoded light masks in neutral atom lithography. We demonstrate that multiple features can be patterned across a monotonic potential gradient. Features as narrow as 0.9 microns are fabricated on silicon substrates with a metastable argon beam. Internal state manipulation with such a mask enables continuously adjustable feature positions and feature densities not limited by the optical wavelength, unlike previous light masks., Comment: 4 pages, 4 figures

We measure the angular divergence of a quasi-continuous, rf-outcoupled, free-falling atom laser as a function of the outcoupling frequency. The data is compared to a Gaussian-beam model of laser propagation that generalizes the standard formalism of photonic lasers. Our treatment includes diffraction, magnetic lensing, and interaction between the atom laser and the condensate. We find that the dominant source of divergence is the condensate-laser interaction., Comment: 5 pages, 3 figures. V3: as will appear in Phys. Rev. Lett.; RevTeX 4.0

We show that the conductance of neutral atoms through a tightly confining waveguide constriction is quantized in units of lambda_dB^2/pi, where lambda_dB is the de Broglie wavelength of the incident atoms. Such a constriction forms the atom analogue of an electron quantum point contact and is an example of quantum transport of neutral atoms in an aperiodic system. We present a practical constriction geometry that can be realized using a microfabricated magnetic waveguide, and discuss how a pair of such constrictions can be used to study the quantum statistics of weakly interacting gases in small traps., Comment: 5 pages with 3 figures. To appear in Phys. Rev. Lett

Cryogenically cooled microelectromagnet mirrors were used to reflect a cloud of free-falling laser-cooled 85Rb atoms at normal incidence. The mirrors consisted of microfabricated current-carrying Au wires in a periodic serpentine pattern on a sapphire substrate. The fluorescence from the atomic cloud was imaged after it had bounced off a mirror. The transverse width of the cloud reached a local minimum at an optimal current corresponding to minimum mirror roughness. A distinct increase in roughness was found for mirror configurations with even versus odd number of lines. These observations confirm theoretical predictions., Comment: Physical Review A, in print; 11 pages, 4 figures

We demonstrate the guiding of neutral atoms by the magnetic fields due to microfabricated current-carrying wires on a chip. Atoms are guided along a magnetic field minimum parallel to and above the current-carrying wires. Two waveguide configurations are demonstrated: one using two wires with an external magnetic field, and a second using four wires without an external field. These waveguide geometries can be extended to integrated atom optics circuits, including beamsplitters., Comment: 11 pages, 4 figures