Dynamical enhancement of spatial entanglement in massive particles

We discuss dynamical enhancement of entanglement in a driven Bose-Hubbard model and find an enhancement of two orders of magnitude from the ground state value which is robust against fluctuations in experimental parameters.

Figure 1

(a) The system is prepared in an entangled state. (b) The system is split into two halves by raising the intermediate barrier. $J$ is the kinetic term and $U$ the on-site interaction in the Bose-Hubbard model, (1).

Figure 2

(a) Entropy of entanglement $E$ and probability of successful postselection of evenly distributed numbers of bosons between the right and the left part of an $L=6$–well Bose-Hubbard system. The overall particle number is $N=6$ [solid (blue) line], $N=3$ [dashed (red) line], and $N=2$ [dash-dotted (green) line]. (b) Negativity $N$ of the thermal state and corresponding probability at temperature $T=0\mathrm{nK}$ (thick line) and $T=80\mathrm{nK}$ (thin line) for some systems in the left panel.

Figure 3

Entropy of entanglement $E$ and probability of successful postselection for the driven Bose-Hubbard Hamiltonian, (4), with $L=8=N$ [solid (blue) line], $L=6=N$ [dashed (red) line], and $L=4=N$ [dash-dotted (green) line]. At $t=100\mathrm{ms}$ the coherent driving is stopped and at $t=150\mathrm{ms}$ the lattice depth is increased in order to freeze the entanglement dynamics.

Figure 4

(a) Fidelity $f(t,\Delta t)$ at $t=100\mathrm{ms}$ for state preparation with imperfect timing. (b) Negativity $N$ of the mixed state, (5), resulting from the measurement of the driven Bose-Hubbard Hamiltonian with $L=6=N$ at $t_0=100\mathrm{ms}$.