Stable spin domains in a nondegenerate ultracold gas

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Stable spin domains in a nondegenerate ultracold gas

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

Phys. Rev. A 97, 051603(R) – Published 8 May 2018

Abstract

We study the stability of two-domain spin structures in an ultracold gas of magnetically trapped ${}^{87}{Rb}$ atoms above quantum degeneracy. Adding a small effective magnetic field gradient stabilizes the domains via coherent collective spin rotation effects, despite negligibly perturbing the potential energy relative to the thermal energy. We demonstrate that domain stabilization is accomplished through decoupling the dynamics of longitudinal magnetization, which remains in time-independent domains, from transverse magnetization, which undergoes a purely transverse spin wave trapped within the domain wall. We explore the effect of temperature and density on the steady-state domains, and compare our results to a hydrodynamic solution to a quantum Boltzmann equation.

Received 2 March 2018

DOI:https://doi.org/10.1103/PhysRevA.97.051603

Physics Subject Headings (PhySH)

Decoherence in quantum gases

Bose gases Quantum fluids & solids Ultracold gases

Boltzmann theory Hydrodynamics

Atomic, Molecular & OpticalNonlinear DynamicsFluid Dynamics

Authors & Affiliations

S. D. Graham¹, D. Niroomand¹, R. J. Ragan², and J. M. McGuirk¹

¹Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
²Department of Physics, University of Wisconsin–La Crosse, La Crosse, Wisconsin 54601, USA

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Issue

Vol. 97, Iss. 5 — May 2018

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Images

Figure 1
Spatiotemporal evolution of radially averaged $M_{∥}$ for $T = 650$ nK and peak density $n_{0} = 1.4 \times 10^{13} {cm}^{- 3}$ at (a) $G = 0$ , (b) 54, and (c) $- 19$ Hz/mm. The initial domain undergoes dipole oscillations at $G = 0$ , which increase in frequency and damping rate for $G < 0$ . Positive gradients stabilize the initial domain-wall configuration. The domain wall drifts toward the $M_{∥} = 1$ domain over time, as $| 2 〉$ decays via dipolar relaxation. (d) Time evolution of the spin dipole moment $〈 z M_{∥} 〉$ in different effective-field gradients. $〈 z M_{∥} 〉$ oscillates for $G \leq 0$ , but stabilizes for positive gradients. Larger $G$ also leads to faster damping, through decoherence from the inhomogeneous applied field.
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Figure 2
(a) Normalized distribution of atoms in $| 1 〉$ [ $N_{1} (z)$ , $▾$ ] and $| 2 〉$ [ $N_{2} (z)$ , $▴$ ] at $T = 650$ nK and $n_{0} = 2.8 \times 10^{13} {cm}^{- 3}$ . A Gaussian is fit to the sum ( $•$ ) to extract temperature. The difference $M_{∥} = N_{2} - N_{1}$ ( $▪$ ) is fit with the same Gaussian multiplied by $tanh z / λ$ to determine domain-wall width $λ$ . (b) Time dependence of $λ$ immediately after application of $G$ (given in Hz/mm), exhibiting linear relaxation at short times. (c) Initial domain-wall relaxation rate $\dot{λ}$ for three densities as a function of effective-field gradient $G$ . Uncertainties represent a statistical uncertainty in fitting $\dot{λ}$ due to shot-to-shot temperature and density fluctuations. A linear fit is performed to determine the gradient $G_{0}$ that stabilizes the initial domain wall $λ_{0}$ .
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Figure 3
Stabilizing gradient $G_{0}$ as a function of peak density and temperature for $λ_{0} = 73 μ m$ . Points at $n_{0} = 1.4 \times 10^{13} {cm}^{- 3}$ have been offset slightly for clarity. The data span the crossover from collisionless to hydrodynamic regimes, as indicated by the Knudsen number for $λ_{0} = 73 μ m$ . The data are described by $G_{hydro}$ at high density for $T = 650$ nK (dashed) and 425 nK (dashed-dotted). Dotted lines show $G_{hydro}$ for $λ_{eq} = ℓ_{3 D}$ ( $Kn = 1$ ), demarking the region where the hydrodynamic model's prediction of a steady-state solution for some $λ_{0}$ is expected to be valid.
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Figure 4
(a) Initial transverse spin magnitude $M_{⊥}$ as measured from Ramsey fringe amplitudes. Also shown are $M_{∥}$ and $| \vec{M} |$ . Minimal decoherence is expected during the short preparation sequence. Any discrepancies in $| \vec{M} | ≃ \sqrt{M_{∥}^{2} + M_{⊥}^{2}}$ are attributed to noise-degrading Ramsey fringe fits. Solid lines are fits to a Gaussian ( $| \vec{M} |$ ), and the same Gaussian multiplied by $sech z / λ$ ( $M_{⊥}$ ) and $tanh z / λ$ ( $M_{∥}$ ). (b) Spatiotemporal evolution of the orientation of ${\vec{M}}_{⊥} (z, t)$ , from the shaded region in (a). (c) The time evolution of $ϕ$ exhibits dipolar spin-wave oscillations, highlighted for two locations in the domain wall [dotted lines in (b)].
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