Longitudinal Spin Diffusion in a Nondegenerate Trapped $^{87}\mathrm{Rb}$ Gas

Longitudinal Spin Diffusion in a Nondegenerate Trapped ${}^{87}{Rb}$ Gas

D. Niroomand, S. D. Graham, and J. M. McGuirk

Phys. Rev. Lett. 115, 075302 – Published 14 August 2015

Abstract

Longitudinal spin diffusion of two pseudospin domains is studied in a trapped ${}^{87}{Rb}$ sample above quantum degeneracy, and the effect of coherence in the domain wall on the dynamics of the system is investigated. Coherence in a domain wall leads to transverse-spin-mediated longitudinal spin diffusion that is slower than classical predictions, as well as altering the domains’ oscillation frequency. The system also shows an instability in the longitudinal spin dynamics as longitudinal and transverse spin components couple, and a conversion of longitudinal spin to transverse spin is observed, resulting in an increase in the total amount of coherence in the system.

Received 15 January 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.075302

Authors & Affiliations

D. Niroomand, S. D. Graham, and J. M. McGuirk

Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada

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Vol. 115, Iss. 7 — 14 August 2015

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Figure 1
(a) Schematic of the domain preparation, showing the patterning laser and accompanying spin evolution in the Bloch sphere representation (longitudinal axis ${\hat{u}}_{∥}$ and transverse equatorial plane). Applying a $π$ pulse to atoms initially in $| 1 ⟩$ while illuminating them with the masked laser transfers atoms in the unilluminated half (left) of the distribution to $| 2 ⟩$ while leaving atoms in the illuminated half unchanged (right). (b) Composite image of atoms in $| 1 ⟩$ (purple) and $| 2 ⟩$ (green) following initialization.
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Figure 2
Time evolution of spin domains with $c_{init} = 0.74$ . (a) Typical initial spin distribution of $| 1 ⟩$ (solid line) and $| 2 ⟩$ (dashed line), used to infer $S_{∥}$ . (b) Evolution of $S_{∥}$ . (c) Evolution of transverse spin amplitude $c (z, t)$ . Coherence is initially confined to the domain wall, in a region less than one third of the axial full width at half maximum of the atomic distribution, $\sim 0.3 w_{ax}$ , but rapidly spreads toward the edges of the cloud, covering a region of the size $\sim 0.7 w_{ax}$ by 200 ms. Ramsey fringes at (d) the trap center $z = 0$ and (e) $z = 0.3 w_{ax}$ as shown by arrows in (c), with a sinusoidal fit to guide the eye.
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Figure 3
(a) Time evolution of $S_{∥}$ for different initial domain wall coherences; from top (i) to bottom (iii), $c_{init} = S_{⊥} / S_{⊥}^{\max} = 0.74, 0.51, 0.28$ , respectively, in the cloud center. (b) Dipole moment time evolution calculated from (a), with a representative decaying sinusoidal fit to (iii), $c_{init} = 0.28$ . (c) Damping rate and (d) oscillation frequency of the dipole moment for different $c_{init}$ . Error bars correspond to fit uncertainties for dipole moment oscillations and $c_{init}$ measurements. The shaded band is the result of numerical simulations of Eq. (1).
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Figure 4
(a) Time evolution of $S_{⊥}$ for different domain wall coherences; from (i) top to (iii) bottom, $c_{init} = 0.71, 0.51, 0.30$ , respectively, in the cloud center. (b) Time evolution of $S_{⊥}$ in different spatial regions, denoted by $z = (0, 0.3, 0.6) \times w_{ax}$ [dotted lines in (i)]. The dashed box indicates a change in sampling rate to measure both the fast initial rise of coherence and longer relaxation to equilibrium. (c) Time evolution of total ensemble coherence for $c_{init}$ shown in (a). The solid curve is a numerical simulation of Eq. (1) for (i), showing good qualitative agreement. Quantitative agreement is limited by challenges extracting Ramsey fringe amplitudes in the presence of noise, dephasing, and a small signal in the cloud wings.
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Figure 5
Instability onset seen in the ratio of maximum ensemble coherence to initial coherence, $c_{tot}^{\max} / c_{tot}^{init}$ , from simulations of Eq. (1), plotted logarithmically to highlight the instability threshold. We vary $a$ and (a) $T$ or (b) $ℓ$ with other parameters set to the conditions of Fig. 3, panel (ii). Since $μ \propto 1 / a$ , increasing $a$ diminishes the instability, as collisional damping grows faster than exchange scattering. Decreasing $T$ or increasing $ℓ$ stabilizes the spin current as expected, through increasing adiabatic rotation during domain wall crossing. Crosses represent the experimental conditions used here.
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Physical Review Letters

Longitudinal Spin Diffusion in a Nondegenerate Trapped Rb87 Gas

D. Niroomand, S. D. Graham, and J. M. McGuirk

Phys. Rev. Lett. 115, 075302 – Published 14 August 2015

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Longitudinal Spin Diffusion in a Nondegenerate Trapped ${}^{87}{Rb}$ Gas