We demonstrate that emission-induced self-organization of two-level atoms can effect strong damping of the sample's center-of-mass motion. When illuminated by far-detuned light, cold cesium atoms assemble into a density grating that efficiently diffracts the incident light into an optical resonator. We observe random phase jumps of pi in the emitted light, confirming spontaneous symmetry breaking in the atomic self-organization. The Bragg diffraction results in a collective friction force with center-of-mass deceleration up to 1000 m/s(2) that is effective even for an open atomic transition.

Laser cooling by coherent scattering inside an optical cavity, a method proposed for cooling the motion of arbitrary particles that scatter light, is analyzed in terms of the modified emission spectrum. In contrast to conventional Doppler cooling, this method invokes the two-photon Doppler effect along the direction of the momentum transferred in the scattering process. Three-dimensional cooling can therefore be achieved with a single optical cavity. Both in the free-particle regime ͑cavity Doppler cooling͒ and in the strong-confiment regime ͑cavity sideband cooling͒ the minimum temperature is determined by the resonator linewidth and independent of the atomic level structure. The cooling efficiency and volume are significantly enhanced in resonators with transverse-mode degeneracy, such as the confocal resonator.

We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts anharmonic oscillations near a critical magnetic field. Measurements of the magnetic phase diagram agree with predictions made in the approximation of a single spatial mode. The oscillation period yields the best measurement to date of the sodium spin-dependent interaction coefficient, determining that the difference between the sodium spin-dependent s-wave scattering lengths a f =2 −a f =0 is 2.47 ± 0.27 Bohr radii. [3,4] in which the population oscillates between different Zeeman sublevels. We present the first observation of coherent spin oscillations in a spin-1 condensate with antiferromagnetic interactions (in which the interaction energy of colliding spin-aligned atoms is higher than that of spin-antialigned atoms.)Spinor condensates have been a fertile area for theoretical studies of dynamics [5,6,7,8] At low magnetic fields, spin interactions dominate the dynamics. The different sign of the spin dependent interaction causes the antiferromagnetic F=1 case to differ from the ferromagnetic one both in the structure of the ground-state magnetic phase diagram and in the spinor dynamics. Both cases can exhibit a regime of slow, anharmonic spin oscillations; however, this behavior is predicted over a wide range of initial conditions only in the antiferromagnetic case [8]. The spin interaction energies in sodium are more than an order of magnitude larger than in 87 Rb F = 1 for a given condensate density [3], facilitating studies of spinor dynamics.The dynamics of the spin-1 system are much simpler than the spin-2 case [4,15,16], having a well-developed analytic solution [8]. This solution predicts a divergence in the oscillation period (not to be confused with the amplitude peak observed in 87 Rb F=2 [4] oscillations).This Letter reports the first measurement of the ground state magnetic phase diagram of a spinor condensate, and the first experimental study of coherent spinor dynamics in an antiferromagnetic spin-1 condensate. Both show good agreement with the single-spatialmode theory [10]. To study the dynamics, we displace the spinor from its ground state, observing the resulting oscillations of the Zeeman populations as a function of applied magnetic field B. At low field the oscillation period is constant, at high field it decreases rapidly, and at a critical field it displays a resonance-like feature, all as predicted by theory [8]. These measurements have allowed us to improve by a factor of three the determination of the sodium F = 1 spin-dependent interaction strength, which is proportional to the difference a f =2 − a f =0 in the spin-dependent scattering lengths.The state of the condensate in the single-mode approximation (SMA) is written as the product φ(r)ζ of a spin-independent spatial wavefunction φ(r) and a spinor ζ = ( √ ρ − e iθ− , √ ρ 0 e iθ0 ,...

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