A new program, PHI, with the ability to calculate the magnetic properties of large spin systems and complex orbitally degenerate systems, such as clusters of d-block and f-block ions, is presented. The program can intuitively fit experimental data from multiple sources, such as magnetic and spectroscopic data, simultaneously. PHI is extensively parallelized and can operate under the symmetric multiprocessing, single process multiple data, or GPU paradigms using a threaded, MPI or GPU model, respectively. For a given problem PHI is been shown to be almost 12 times faster than the well-known program MAGPACK, limited only by available hardware.

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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Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature of the interactions in this system. We use Faraday rotation spectroscopy to make a continuous and minimally destructive measurement of the dynamics over multiple spin oscillations on a single evolving condensate. This method provides a sharp signature to locate a magnetically tuned separatrix in phase space which depends on the net magnetization. We also observe a phase transition from a two- to a three-component condensate at a low but finite temperature using a Stern-Gerlach imaging technique. This transition should be preserved as a zero-temperature quantum phase transition.