Figure 1

Excitation probability $p_k$ as a function of the wave vector $k$, following a shortcut to adiabaticity in the $1d$ quantum Ising model. (a) The crossing of the critical point is assisted by a truncated Hamiltonian ${\tilde{\mathcal{H}}}_1(M)$ ($s_m=1$), (b) and a modified truncation where the expansion coefficients are modulated by a raised cosine Fourier filter. The range of the interaction increases from right to left with cutoff $M=4$, 8, 16, 32, 64 ($N=1600$). Above, the system evolves from $g_i=10$ to $g_f=0$ across QCP at $g_c=1$ at quench rate $\upsilon =50$ using $\mathcal{H}={\mathcal{H}}_0+{\tilde{\mathcal{H}}}_1(M)$. The insets show the scaling of $p_k$ as a function of $k/k_M\sim Mk$.Reuse & Permissions

Figure 2

Suppression of the total number of excitations $n_{\mathrm{ex}}$ as a function of the quench rate $\upsilon$ of the transverse field in a $1d$ Ising chain following a quench through the QCP ($g=1$). The dynamics is assisted by a truncated auxiliary Hamiltonian ${\tilde{\mathcal{H}}}_1(M)$, with a cutoff $M=0$, 1, 2, 4, 8, 16, 32, 64 from top to bottom. The numerics for ${\mathcal{H}}_0$ ($M=0$) is the reference case where the KZM dictates a power-law scaling of $n_{\mathrm{ex}}$ for $\upsilon \ll 1$. This scaling is recovered at slow quench rates in a passage through the QCP assisted by ${\tilde{\mathcal{H}}}_1(M)$, while at faster rates there is an efficient suppression of excitations. As the range of the interactions is increased, the dynamics in all modes is driven through the instantaneous eigenbasis of ${\mathcal{H}}_0$, a complete suppression of excitations is achieved. In all simulations $N=1600$, and we evolve from $g_i=10$ to $g_f=0$, and no filtering is applied ($s_m=1$).Reuse & Permissions