We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.

Helical spin textures in a 87Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. The formation of this modulated phase is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. The reduction of dipolar interactions by a sequence of rf pulses results in a suppression of the modulated phase, thereby confirming the role of dipolar interactions in this process. This study demonstrates the significance of magnetic dipole interactions in degenerate 87Rb F=1 spinor gases.

We demonstrate a precise magnetic microscope based on direct imaging of the Larmor precession of a 87Rb spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of 8.3 pT/Hz1/2 over a measurement area of 120 microm2, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The achieved phase sensitivity is close to the atom shot-noise limit, estimated as 0.15 pT/Hz1/2 for a unity duty cycle measurement, suggesting the possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.

Dynamical instabilities due to spin-mixing collisions in a 87 Rb F = 1 spinor Bose-Einstein condensate are used as an amplifier of quantum spin fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in quantitative agreement with mean-field calculations. We quantify the microscopic spin fluctuations of the initially paramagnetic condensate by applying this amplifier and measuring the resulting macroscopic magnetization. The magnitude of these fluctuations is consistent with predictions of a beyond-mean-field theory. The spinor-condensate-based spin amplifier is thus shown to be nearly quantum-limited at a gain as high as 30 dB.Accompanied by a precise theoretical framework and created in the lab in a highly controlled manner, ultracold atomic systems serve as a platform for studies of quantum dynamics and many-body quantum phases. Among these systems, gaseous spinor Bose Einstein condensates [1,2,3,4,5], in which atoms may explore all sub-levels of a non-zero hyperfine spin F , provide a compelling opportunity to access the static and dynamical properties of a magnetic superfluid [6,7,8,9,10].We previously identified a quantum phase transition in an F = 1 spinor Bose Einstein condensate between a paramagnetic and ferromagnetic phase [9]. This transition is crossed as the quadratic Zeeman energy term, of the form qF 2 z , is tuned through a critical value q = q 0 ; here, F z is the longitudinal (ẑ axis) projection of the dimensionless vector spin operator F. Accompanying this phase transition is the onset of a dynamical instability in a condensate prepared in the paramagnetic ground state, with macroscopic occupation of the |m z = 0 magnetic sublevel [11,12,13]. This instability causes transverse spin perturbations to grow exponentially, producing atoms into the |m z = ±1 sublevels. In contradiction with the mean-field prediction that the paramagnetic state should remain stationary because it lacks fluctuations by which to seed the instability, experiments revealed the spontaneous magnetization of such condensates after they were rapidly quenched across the phase transition.In this Letter, we investigate the spin fluctuations that become amplified by the spin-mixing instability. In particular, we test whether these fluctuations correspond to quantum noise, i.e. to the zero-point fluctuations of quantized spin excitation modes that become unstable. For this, we use the spin-mixing instability as an amplifier, evolving microscopic quantum fluctuations into measurable macroscopic magnetization patterns. We present two main results. First, we characterize the spin-mixing amplifier and demonstrate its spectrum to be tunable by varying the quadratic Zeeman shift. This spectrum compares well with a theoretical model that accounts for the inhomogeneous condensate density and for magnetic dipole interactions. Second, we measure precisely the transverse magnetization produced by this amplifier at various stages of amplification, up to a gain of 30 dB in the magnetization variance. This magnetization sig...