Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charge neutrality of these systems presents an apparent limitation-a wide range of intriguing phenomena arise from the Lorentz force for charged particles in a magnetic field, such as the fractional quantum Hall effect in two-dimensional electron systems. The limitation can be circumvented by exploiting the equivalence of the Lorentz force and the Coriolis force to create synthetic magnetic fields in rotating neutral systems. This was demonstrated by the appearance of quantized vortices in pioneering experiments on rotating quantum gases, a hallmark of superfluids or superconductors in a magnetic field. However, because of technical issues limiting the maximum rotation velocity, the metastable nature of the rotating state and the difficulty of applying stable rotating optical lattices, rotational approaches are not able to reach the large fields required for quantum Hall physics. Here we experimentally realize an optically synthesized magnetic field for ultracold neutral atoms, which is evident from the appearance of vortices in our Bose-Einstein condensate. Our approach uses a spatially dependent optical coupling between internal states of the atoms, yielding a Berry's phase sufficient to create large synthetic magnetic fields, and is not subject to the limitations of rotating systems. With a suitable lattice configuration, it should be possible to reach the quantum Hall regime, potentially enabling studies of topological quantum computation.

We use a two-photon dressing field to create an effective vector gauge potential for Bose-Einstein-condensed 87Rb atoms in the F=1 hyperfine ground state. These Raman-dressed states are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential whose magnitude is set by the strength and detuning of the Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to nonuniform vector potentials, giving nonzero effective magnetic fields.

Electromagnetism is a simple example of a gauge theory where the underlying potentials (the vector and scalar potentials) are defined only up to a gauge choice. The vector potential generates magnetic fields through its spatial variation and electric fields through its time dependence 1 . Here, we report experiments in which we have produced a synthetic gauge field. The gauge field emerges only at low energy in a rubidium BoseEinstein condensate: the neutral atoms behave as charged particles do in the presence of a homogeneous effective vector potential 2 . We have generated a synthetic electric field through the time dependence of an effective vector potential, a physical consequence that emerges even though the vector potential is spatially uniform.Gauge theories play a central role in modern quantum physics. In some cases, they can be viewed as emerging as the low-energy description of a more complete theory 3,4 . Electromagnetism is the best known gauge theory and its gauge fields are the ordinary scalar and vector potentials. Magnetic fields arise only from spatial variations of the vector potential, whereas electric fields arise from both time variations of the vector potential and gradients of the scalar potential. These potentials are defined only to within a gauge choice, where for a charged particle the canonical momentum (the variable canonically conjugate to position) and the mechanical momentum (the mass times the velocity) are not equal. Our experiments 2 have realized a particular version 5 of a class of proposals 6-11 to generate effective vector potentials for neutral atoms through interactions with laser light, and have created synthetic magnetic fields 12 important for simulating charged condensed-matter systems with neutral atoms 13,14 . Here we demonstrate the complementary phenomenon: a synthetic electric field generated from a time-dependent effective vector potential. Additionally, we make independent measurements of both the mechanical momentum and canonical momentum, where the latter is usually not possible.The electromagnetic vector potential A for a charged particle appears in the Hamiltonian H = (p can − qA) 2 /2m, where p can is the canonical momentum, q is the charge and m is the mass. (p can −qA = mv is the mechanical momentum for a particle moving with velocity v.) We recently demonstrated a technique to engineer Hamiltonians of this form for ultracold atoms, and prepared a Bose-Einstein condensate (BEC) at rest with an effective vector potential A = A xx constant in time and space 2 , corresponding to E = B = 0, where E and B are the synthetic electric field and synthetic magnetic field for neutral atoms, respectively. In ref. 12, we made A depend on position, giving B = ∇ × A = 0 but E = 0. Here we add time dependence to a spatially uniform vector potential A(t ) = A(t )x, generating a synthetic electric field E(t )x = −∂A/∂t . The resulting force is distinct from that arising from gradients of scalar potentials φ(r), for example, from an external trapping potential. A revealin...

We describe an apparatus for quickly and simply producing 87 Rb Bose-Einstein condensates. It is based on a magnetic quadrupole trap and a red detuned optical dipole trap. We collect atoms in a magneto-optical trap (MOT) and then capture the atom in a magnetic quadrupole trap and force rf evaporation. We then transfer the resulting cold, dense cloud into a spatially mode-matched optical dipole trap by lowering the quadrupole field gradient to below gravity. This technique combines the efficient capture of atoms from a MOT into a magnetic trap with the rapid evaporation of optical dipole traps; the approach is insensitive to the peak quadrupole gradient and the precise trapping beam waist. Our system reliably produces a condensate with N ≈ 2 × 10 6 atoms every 16 s.

We observe the dynamics of a single magnetic vortex in the presence of a random array of pinning sites. At low excitation amplitudes, the vortex core gyrates about its equilibrium position with a frequency that is characteristic of a single pinning site. At high amplitudes, the frequency of gyration is determined by the magnetostatic energy of the entire vortex, which is confined in a micron-scale disk. We observe a sharp transition between these two amplitude regimes that is due to depinning of the vortex core from a local defect. The distribution of pinning sites is determined by mapping fluctuations in the frequency as the vortex core is displaced by a static in-plane magnetic field.PACS numbers: 75.75.+a,75.40.Gb The excitation spectrum of a sub-micron ferromagnetic particle is influenced profoundly by its shape. An example of considerable interest is the vortex state of a soft ferromagnetic disk, in which the lowest frequency excitation is a translational mode of the vortex core. This mode, in which the vortex core gyrates about its equilibrium position, has been studied in several recent experiments [1,2,3,4,5,6]. Although the core has a diameter of the order of the exchange length (∼10 nm) [7,8], the eigenfrequency of the gyrotropic mode is determined only by the geometrical aspect ratio (diameter over thickness) of the disk in which it is confined [9,10]. In particular, the gyrotropic frequency should be independent of the location of the vortex core in the disk [5]. As demonstrated recently, however, the vortex core can be pinned by defects in a patterned thin film [11,12,13]. In the case of intrinsic defects, the range of the effective pinning potential appears to be on the order of ten nanometers [13]. This raises the question of how a nanoscale defect influences the vortex gyrotropic motion.In this Letter, we report that pinning has a pronounced effect on magnetic vortex dynamics at small amplitudes. The vortex gyrotropic frequency in 50 nm thick permalloy (Py) disks with diameters from 600 nm to 2 µm fluctuates by a factor of at least two as the core is displaced by a static magnetic field over length scales ∼ 10 nm. The dependence on core location indicates that the smallamplitude dynamics are influenced strongly by the characteristics of a particular pinning site. Each site has a critical excitation amplitude above which the vortex becomes depinned and gyrates at the frequency determined by the aspect ratio of the disk. We image the spatial distribution of pinning sites in a disk by displacing the vortex core in two dimensions while monitoring the gyrotropic frequency. Using this approach, we find a density of up to ∼ 2×10 11 cm −2 for the pinning sites in our films. Although this density cannot be correlated directly with the physical morphology of the permalloy films, the extreme sensitivity to core displacement indicates that the magnetic microstructure fluctuates strongly on nanometer scales.The samples were patterned from 50 nm thick films of Py (Ni 0.81 Fe 0.19 ), which has negligible mag...

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Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.

Single-crystal thin films of the antiferromagnet FeF 2 have been used to exchange bias overlayers of Fe. An unexpected coercivity enhancement is observed at temperatures above the Néel temperature of the FeF 2. This coercivity reaches a peak value of over 600 Oe close to the Néel temperature and persists to above 300 K. The coercivity is correlated with the growth of an anisotropy in the ferromagnet, the increase of the antiferromagnetic susceptibility and the increase of the ferromagnetic resonance linewidth. We argue that the growth of spin fluctuations in the antiferromagnet leads to an enhanced ferromagnetic anisotropy, and therefore coercivity, above the Néel temperature.