A central goal in condensed matter and modern atomic physics is the exploration of manybody quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensedmatter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor BoseEinstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. 87 Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.Most ultracold atomic gases consist of atoms with nonzero total angular momentum denoted by the quantum number F , which is the sum of the total electronic angular momentum and nuclear spin. In spinor atomic gases, such as F = 1 and F = 2 gases of 23 Na [1, 2] and 87 Rb [3,4], all magnetic sublevels representing all orientations of the atomic spin may be realized [5]. The phase coherent portion of a Bose-Einsein condensed spinor gas is described by a vector order parameter and therefore exhibits spontaneous magnetic ordering. Nevertheless, considerable freedom remains for the type of ordering that can occur. For 87 Rb F = 1 spinor gases, the spindependent energy per particle in the condensate is the sum of two terms, c 2 n F 2 + q F 2 z , where F denotes the dimensionless spin vector operator. The first term describes spin-dependent interatomic interactions, with n being the number density and c 2 = (4π 2 /3m)(a 2 − a 0 ) depending on the atomic mass m and the s-wave scattering lengths a f for collisions between pairs of particles with total spin f [6,7]. Given c 2 < 0 for our system [3,4,8,9], the interaction term alone favors a ferromagnetic phase with broken rotational symmetry. The second term describes a quadratic Zeeman shift in our experiment, with q = (h × 70 Hz/G 2 )B 2 at a magnetic field of magnitude B [10]. This term favors instead a scalar phase with no net magnetization, i.e. a condensate in the |m z = 0 magnetic sublevel. These phases are divided by a second-order quantum phase transition at q = 2|c 2 |n.This article describes our observation of spontaneous symmetry breaking in a 87 Rb spinor BEC that is rapidly quenched across this quantum phase transition. Nearlypure spinor Bose-Einstein condensates were prepared in the scalar |m z = 0 phase at a high quadratic Zeeman shift (q ≫ 2|c 2 |n). By rapidly reducing the magnitude of the applied magneti...

Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 87Rb gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the non-condensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.

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.

We consider a two-component atomic gas illumined by two intersecting laser beams which induce Raman coupling between the components. This spatially periodic coupling modifies the dispersion relation of the gas. Properties of a Bose-Einstein condensate of such a gas are strongly affected by this modification. Using the quasiparticle excitation spectrum derived from a Bogoliubov transformation, the Landau critical velocity is found to be anisotropic and can be widely tuned by varying properties of the dressing laser beams.

Context. Sodium laser guide stars (LGS) are about to enter a new range of laser powers. Previous theoretical and numerical methods are inadequate for accurate computations of the return flux, hence for the design of the next-generation LGS systems. Aims. We numerically optimize the cw (continuous wave) laser format, in particular, the light polarization and spectrum. Methods. Using Bloch equations, we simulate the mesospheric sodium atoms, including Doppler broadening, saturation, collisional relaxation, Larmor precession, and recoil, taking all 24 sodium hyperfine states into account and 100-300 velocity groups. Results.LGS return flux is limited by "three evils": Larmor precession due to the geomagnetic field, atomic recoil due to radiation pressure, and transition saturation. We study their impact and show that the return flux can be boosted by repumping (simultaneous excitation of the sodium D 2 a and D 2 b lines with 10−20% of the laser power in the latter). Conclusions. We strongly recommend the use of circularly polarized lasers and repumping. As a rule of thumb, the bandwidth of laser radiation in MHz (at each line) should approximately equal the launched laser power in Watts divided by six, assuming a diffraction-limited spot size.