Density redistribution effects in fermionic optical lattices

We simulate a one-dimensional fermionic optical lattice to analyze heating due to nonadiabatic lattice loading. Our simulations reveal that, similar to the bosonic case, density redistribution effects are the major cause of heating in harmonic traps. We suggest protocols to modulate the local-density distribution during the process of lattice loading in order to reduce the excess energy. Our numerical results confirm that linear interpolation of the trapping potential and/or the interaction strength is an efficient method of doing so, bearing practical applications relevant to experiments.

Figure 1

Local-density distribution of the target states integrated over each unit cell.

Figure 2

Local-density distribution of the initial state $(V_i=0)$ and the metallic target state $(V_f=V_0=8E_r)$ integrated over each unit cell.

Figure 3

Dependence on the ramp time of (a) excess energy and (b) fidelity for a metallic target state.

Figure 4

Evolution of the density profile during the ramp up for ramp time $t_R=256\hslash /E_r$ for a metallic target state.

Figure 5

Local-density distribution of the initial state $(V_i=0)$ and the Mott insulator with bulk band-insulator target state $(V_f=V_0=8E_r)$ integrated over each unit cell.

Figure 6

Dependence of the (a) excess energy and (b) fidelity on ramp time for the case of a central band insulator.

Figure 7

Evolution of the density profile during the ramp up for ramp time $t_R=256\hslash /E_r$ for the case of a central band insulator.

Figure 8

Local-density distribution of the initial state $(V_i=0)$ and the Mott-insulator target state $(V_f=V_0=8E_r)$ integrated over each unit cell. The blue curve shows the density distribution of the optimal state when linearly modulating the trap frequency $\omega$.

Figure 9

Dependence of the fidelity on ramp time for a Mott-insulator target state in the (a) trapped case and (b) homogenous case.

Figure 10

Evolution of the density profile during the ramp up for a Mott-insulator target state with ramp time $t_R=256\hslash /E_r$ (a) without tuning the trap frequency and (b) with linear modulation of the frequency for the optimal value of initial frequency $[w_i=0.16{(\hslash /E_r)}^{-1}]$. The black line corresponds to the target state.

Figure 11

Variation of (a) excess energy and (b) fidelity as a function of the initial frequency for a Mott-insulator target state. The different colors correspond to different ramp times.

Figure 12

Local-density distribution of the initial state $(V_i=0)$ and the Mott insulator with a metallic core target state $(V_f=V_0=8E_r)$ integrated over each unit cell.

Figure 13

Evolution of the density profile during the ramp up for the case of a Mott insulator with a metallic core at ramp time $t_R=256\hslash /E_r$ (a) without tuning the trap frequency and (b) with linear modulation of the frequency for the optimal value of initial frequency $[w_i=0.19{(\hslash /E_r)}^{-1}]$. The red line corresponds to the target state.

Figure 14

Variation of (a) excess energy and (b) fidelity as a function of the initial frequency for the case of a Mott insulator with a metallic core. The different colors correspond to different ramp times.

Figure 15

Variation of the fidelity as a function of the interaction strength for the case of a Mott insulator with a metallic core. The different colors correspond to different ramp times. The color scheme is the same as in Fig. 14.

Figure 16

Mott insulator with a metallic core. (a) Local-density distribution profiles for the optimal initial states obtained from all lattice loading protocols. The target state is shown for reference. (b) Dependence of the fidelity on ramp time (starting from the optimal state) for all lattice loading methods.