Spectrum of spin waves in cold polarized gases
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Spectrum of Spin Waves in Cold Polarized Gases T. L. Andreeva* Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia *e-mail: [email protected] Received June 4, 2016
Abstract—The spin dynamics of cold polarized gases are investigated using the Boltzmann equation. The dispersion relation for spin waves (transverse component of the magnetic moment) and the spin diffusion coefficient of the longitudinal component of the magnetic moment are calculated without using fitting parameters. The spin wave frequency and the diffusion coefficient for rubidium atoms are estimated numerically. DOI: 10.1134/S1063776117010010
Until recently, a single propagating collective mode (acoustic waves) has been observed in gases including paramagnetic ones. Since 1980s, spin waves in polarized gases (H, 3H, and the 3He–4He mixture) have been investigated theoretically and experimentally. The experiments were carried out at temperatures near 1 K and gas densities on the order of 1018 cm–3. Spin waves detected in these gases were strongly damping (see the literature cited in [1, 2]). The situation has radically changed only when laser cooling of gases to temperatures on the order of 1 μK has become possible. Anomalously strong spin waves observed in 2002 in rubidium vapor in the S state at gas temperature T ≈ 0.6 μK and number density n = 1.8 × 1013 cm–3 led to almost complete spatial separation of particles with opposite spins in a magnetic trap [3]. In later publications, cold Ga, In, I, and other atoms in the P states were investigated; however, spin waves in these gases were not detected [4]. It should be noted that the separation of particles with opposite spins was observed earlier in liquid solutions of 3He in 4He and in pure 3He [5]. The last (to our knowledge) work on spin waves also concerns rubidium vapor with the same values of parameters and was carried out at the same institution (Joint Institute for Lab Astrophysics, JILA) in 2010 (see [6]). In that publication, the corrections to the Boltzmann collision integral were calculated for describing experimental data on spin waves. In theoretical descriptions of spin waves in gases, either cumbersome forms of the Boltzmann collision integral are used (which strongly hampers analysis of the dispersion relation for spin waves [7]), or model versions of the collision integral are employed [2]. In this communication, we are using the Boltzmann equation taking into account the specific form of the scattering amplitude for slow particles. Our aim is to obtain the spectrum of spin waves and the spin diffu-
sion coefficient for the longitudinal component of the magnetic moment without using fitting parameters. Let us first consider the criterion of applicability of the Boltzmann approximation for gases: 3/2
⎛ 2 ⎞ n ⎜ ⎟ 1. ⎝ mT ⎠ Physically, this condition corresponds to a rarefied gas in which there is not more than one particle in each quantum state. Here, n is the number density of the gas and T is the temperature
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