Figure 1

(a) Dipolar particles, trapped in a quasi-2D geometry with a radial confinement $\omega$. When the external magnetic field $\mathit{B}$ is tuned in resonance, dipolar interactions $V_{\mathrm{dd}}$ can induce spin relaxation processes, leading to a net angular momentum increase of $1\hslash$ per particle. (b) Energy levels of a 2D harmonic oscillator. (c) One of the possible spin-flip processes, bringing both particles to higher angular momentum states. (d) Eventually, after repeated application of the driving scheme, all particles occupy the lowest Landau level.Reuse & Permissions

Figure 2

Exact ground state energy (dots) for $N=10$ particles at fixed angular momentum $L$, compared to the approximate expression (solid line) as given in Eq. (3). For $L>L^{\star }=45\hslash$, the energy increases linearly. Inset shows $L$ as a function of the rotation frequency $\Omega$ in the analytic model. $L$ diverges at the critical rotation frequency $\Omega =\omega$, when the rotation exceeds the trap frequency.Reuse & Permissions

Figure 3

(a) Description of the transfer in the analytical model with $N=100$ particles for decreasing energy splitting $\Delta$ between the two components $\uparrow$ and $\downarrow$. The transfer starts at $\Delta =E_{\mathrm{F}}$ with particles continuously being transferred into the $\downarrow$ state as $\Delta$ is lowered to $-E_{\mathrm{F}}$. Notice that during the transfer, both components rotate in the same direction. The crossing $N_{\uparrow }=N_{\downarrow }$ is not precisely at $\Delta =0$ due to the initial bias. (b) Full simulation of the transfer scheme for $N=4$, 6, and 8 particles in the adiabatic limit $\gamma \to 0$. As the Zeeman splitting $\Delta$ is tuned through zero, the angular momentum increases in steps of $2\hslash$, indicating the transfer of two particle at a time. The interaction strength is given by ${\widehat{C}}_{\mathrm{dd}}=0.1$. (c) Angular momentum at the end of the transfer for $N=6$ particles at different values of the Landau-Zener parameter $\lambda ={\widehat{C}}_{\mathrm{dd}}^2/\widehat{\gamma }$. The data points for different rates collapse onto a single curve. The solid line is a probabilistic model, fitted to the data points.Reuse & Permissions