Spinor Dynamics in an Antiferromagnetic Spin-1 Thermal Bose Gas

Abstract

We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 23 Na atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field.Although Bose-Einstein condensates (BECs) are often thought of for sensitive measurements, their spatial coherence is not always necessary. Thermal atomic collisions are often mistakenly thought to be incoherent but, while keeping track of the spatial coherence is difficult, coherence can sometimes more easily be followed in the internal degrees of freedom. Thus, cold thermal clouds are often just as sensitive for use in spin measurements. In this work, we demonstrate collisionally-driven coherent spin population oscillations that can be interpreted as zero-momentum spin waves in a cold thermal cloud of spin-1 atoms. Such oscillations were previously only seen in the context of BECs [1-5] and two-atom, singlespatial-mode systems [6,7]. The spin oscillations that we observe in a highly multi-spatial-mode thermal gas are remarkable in that they can be described by a theory that is independent of the spatial degrees of freedom.Well-known examples of thermal spin systems that preserve internal spin states include optically-pumped dilute gases used for magnetometry [8] and spin-polarized noble gas imaging [9]. The spin polarization can be maintained even while the gas is trapped in glass cells, or by living tissues like lungs. Hydrogen masers are based on interrogating the free precession of a spin superposition of a thermal gas in a glass cell. Less well-known, collisionally-driven spin-wave effects were predicted in 1982 [10,11], and observations of such effects were reported soon thereafter in low-temperature spin-polarized hydrogen [12]. Bosonic and fermionic alkali pseudo-spin-1/2 systems have also been studied [13][14][15], and spin domain formation has been observed in these systems [16][17][18]. Due to the spindependent interaction that is absent in the pseudo-spin-1/2 system, a spin-1 gas is predicted to have additional interesting coherent collisional (spinor) dynamics which give rise to spin waves or population oscillations [19,20].The dynamics of spinor BECs have been widely investigated in spin-1 Na and Rb gases, as reviewed in Refs. [21,22]. Rb in the F = 1 state is ferromagnetic (spin-aligned collisions having the lowest energy), whereas Na is considered antiferromagnetic. Both o...

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