Mott-insulator dynamics

The hydrodynamics of a lattice Bose gas in a time-dependent external potential is studied in a mean-field approximation. The conditions under which a Mott insulating region can melt, and the local density can adjust to the new potential, are determined. In the case of a suddenly switched potential, it is found that the Mott insulator stays insulating and the density will not adjust if the switch is too abrupt. This comes about because too rapid currents result in Bloch oscillation-type current reversals. For a stirrer moved through a Mott insulating cloud, it is seen that only if the stirrer starts in a superfluid region and the velocity is comparable to the time scale set by the tunneling will the Mott insulator be affected.

Figure 1

Time development of a 2D lattice Bose gas following the turn-on of a wide Gaussian perturbation potential. (a) Spatial distribution of the condensate density before the switch of the potential. The field of view is $64\times$64 lattice sites. (b) Final condensate density, after an evolution of duration $t=800U^{-1}$. Field of view as in (a). (c) Cross section of the final total density profile $n$ (symbols) and potential profile $V$ after the switch (line). (b) Fraction of Bose-Einstein condensed atoms (dimensionless) as a function of time. The tunneling matrix element is $J=0.03U$, the trap frequency is $\omega =0.07U$, the chemical potential is $\mu =0.5U$, and the Gaussian potential has width $W=10$ lattice sites and strength $V_1=0.5U$.

Figure 2

Time development of a 2D lattice Bose gas following the turn-on of a wide Gaussian perturbation potential. Panels and parameters are as in Fig. 1, except the height of the Gaussian potential, $V_1=1.0U$.

Figure 3

Spatial distribution of the condensate phase of a 2D lattice Bose gas in a harmonic trap plus Gaussian potential. Parameters are as in Fig. 1, featuring the weaker Gaussian potential with $V_1=0.5U$, and the panels refer to times (a) $t=20U^{-1}$, (b) $t=40U^{-1}$, (c) $t=60U^{-1}$, and (d) $t=100U^{-1}$. The field of view is $45\times$45 lattice sites.

Figure 4

Spatial distribution of the condensate phase of a 2D lattice Bose gas in a harmonic trap plus Gaussian potential. Parameters are as in Fig. 2, featuring the stronger Gaussian potential with $V_1=1.0U$, and the panels refer to times (a) $t=20U^{-1}$, (b) $t=40U^{-1}$, (c) $t=60U^{-1}$, and (d) $t=100U^{-1}$. The field of view is $45\times$45 lattice sites.

Figure 5

Final central condensate density after the turn-on of a wide Gaussian perturbation potential and subsequent evolution for a duration of $800U^{-1}$. The condensate density $n_c$ is averaged over the nine centermost points of the lattice. Pluses denote the result of simulations with a Gaussian perturbation with width $W=10$ and height $V_1$; asterisks are for a Gaussian with width $W=15$, and circles are for a Lorenzian profile with width $W=15$. In (a), the $x$ axis is the height of the perturbing potential, $V_1$; in (b), it denotes the maximum potential slope, $V_{\max }^{\prime }$.

Figure 6

Time development of a 2D lattice Bose gas following the turn-on of a wide Gaussian perturbation potential. Panels and parameters are as in Fig. 1, except $J=0.02U$, $\mu =1.5U$, and the height of the Gaussian potential is $V_1=1.0U$.

Figure 7

Time development of a 2D lattice Bose gas following the turn-on of a wide Gaussian perturbation potential. Panels and parameters are as in Fig. 1, except $J=0.02U$, $\mu =1.0U$, and the height of the Gaussian potential is $V_1=1.5U$.

Figure 8

Spatial distribution of the condensate density $n_C$ of a 2D lattice Bose gas in a harmonic trap plus Gaussian potential. Parameters are as in Fig. 7, featuring several superfluid and Mott insulating shells, and the panels refer to times (a) $t=0U^{-1}$, (b) $t=30U^{-1}$, (c) $t=60U^{-1}$, (d) $t=90U^{-1}$, (e) $t=120U^{-1}$, and (f) $t=600U^{-1}$. Field of view is $49\times$49 lattice sites.

Figure 9

Time development of a 2D lattice Bose gas as a Gaussian “spoon” potential is moved through it. The potential has width $W=3$, amplitude $V_1=5U$, and velocity $v=0.5U$. The remaining parameters are as in Fig. 1.

Figure 10

As in Fig. 9, but with velocity $v=0.025U$.

Figure 11

Fraction of Bose-Einstein condensed atoms at the end of a sweep with a Gaussian “spoon” potential, as a function of the velocity with which the spoon is moved. Dashed line: Initial condensate fraction.