Quantum Quench and Nonequilibrium Dynamics in Lattice-Confined Spinor Condensates

We present an experimental study on nonequilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized to reveal atom number distributions of an inhomogeneous system, and to study transitions from two-body to many-body dynamics. Our data also imply the nonequilibrium dynamics depend weakly on the quench speed but strongly on the lattice potential. This enables precise measurements of the spin-dependent interaction, a key parameter determining the spinor physics.

Figure 1

(a) Observed spin dynamics after Quench-Q sequences to different $q$. Lines are fits based on Eq. (2) [18]. (b) Lines denote the predicted energy $E_n=h{f}_n$ (see text).

Figure 2

(a) Triangles (circles) represent fast Fourier transformations (FFT) over the first 40 ms (80 ms) of $t_{\mathrm{hold}}$ on the $q/h=85\mathrm{Hz}$ dataset shown in Fig. 1. Vertical lines mark the predicted $f_n$ (see text). Solid lines are five-Gaussian fits. Results obtained at $t_{\mathrm{hold}}=40\mathrm{ms}$ are shifted up by 0.4 for visual clarity. (b) Atom number distributions extracted from the $t_{\mathrm{hold}}=40\mathrm{ms}$ FFT spectrum in panel (a). We define ${\chi }_n$ as the fraction of atoms localized in lattice sites having $n$ atoms, and extract ${\chi }_n$ from dividing the area below the corresponding peak in a FFT spectrum by the spin oscillation amplitude $D_n$ (see Ref. [20]). Black bars mark the predicted ${\chi }_n$ in Mott-insulator shells at $n_{\mathrm{peak}}=6$ based on Eq. (1) and the Thomas-Fermi approximation. (c) Similar to panel (b) but extracted from the $t_{\mathrm{hold}}=80\mathrm{ms}$ FFT spectrum in panel (a).

Figure 3

(a) Observed spin dynamics after Quench-L sequences at two $t_{\mathrm{ramp}}$. Lines are fits based on Eq. (2). Data taken at $t_{\mathrm{ramp}}=1.5\mathrm{ms}$ are shifted up by 0.1 for visual clarity. (b) Extracted $U_2$ and $U_2/U_0$ from fitting observed dynamics with Eq. (2) at various $t_{\mathrm{ramp}}$ [23]. The horizontal line is a linear fit. (c) Similar to panel (b) but based on our data taken under 20 different conditions. The right axis marks the corresponding ratio $a_2/a_0=(U_2+U_0)/(U_0-2U_2)$, where $a_0$ and $a_2$ are scattering lengths.

Figure 4

(a) Observed spin dynamics after Quench-Q sequences to $q/h=30\mathrm{Hz}$ at various $u_{L,z}$ while $u_{L,x}=u_{L,y}=33(3)E_R$ (see text). Results obtained at $u_{L,z}=33(3)E_R$, $25(2)E_R$, and $19(2)E_R$ are, respectively, shifted up by 0.55, 0.25, and 0.06 for visual clarity. Lines are fits based on Eq. (2). (b) FFT spectra of the dynamics shown in panel (a). Lines are two-Gaussian fits.