High-Harmonic Generation Approaching the Quantum Critical Point of Strongly Correlated Systems

By employing the exact diagonalization method, we investigate the high-harmonic generation (HHG) of the correlated systems under the strong laser irradiation. For the extended Hubbard model on a periodic chain, HHG close to the quantum critical point (QCP) is more significant compared to two neighboring gapped phases (i.e., charge-density-wave and spin-density wave states), especially in low frequencies. We confirm that the systems in the vicinity of the QCP are supersensitive to the external field and more optical-transition channels via excited states are responsible for HHG. This feature holds the potential of obtaining high-efficiency harmonics by making use of materials approaching QCP. Based on the two-dimensional Haldane model, we further propose that the even- or odd-order components of generated harmonics can be promisingly regarded as spectral signals to distinguish the topologically ordered phases from locally ordered ones. Our findings in this Letter pave the way to achieve ultrafast light source from HHG in strongly correlated materials and to study quantum phase transition by nonlinear optics in strong laser fields.

Figure 1

(a) Contour plots of the optical conductivity Re $\sigma (\omega )$ as a function of $\omega$ and the NN interactions $V$. Contour plots of HHG spectrum $|⟨j{⟩}_{\omega }{|}^2$ as a function of $\omega /{\omega }_0$ and $V$, with ${\omega }_0=0.1$ and $A_0=10.0$ in (b) as well as ${\omega }_0=1.2$ and $A_0=0.5$ in (c). Other parameters of the Hamiltonian (1) and the external laser are set to be $U=10.0$ and $t_d=50.0$.

Figure 2

The HHG spectrum $|⟨j{⟩}_{\omega }{|}^2$ as a function of $\omega /{\omega }_0$ with $V=0.0$ (a), $V=5.0$ (b), and $V=6.0$ (c). The third and fifth harmonics are plotted in red to emphasize the difference in intensity. Time profiles of $A(t)$ (red lines) and $⟨j{⟩}_t$ (blue lines) with $V=0.0$ (d), $V=5.0$ (e), and $V=6.0$ (f). Other parameters of the Hamiltonian (1) and the external laser are set to be $U=10.0$, ${\omega }_0=1.2$, $A_0=0.5$, and $t_d=50.0$.

Figure 3

Contour plots of HHG spectrum $|⟨j{⟩}_{\omega }{|}^2$ as a function of $\omega /{\omega }_0$ and $V$, with ${\omega }_0=0.1$ in (a) and ${\omega }_0=0.2$ in (b). Other parameters of the Hamiltonian (2) and the external laser are set to be $t_2=0.2$, $A_{0,x}=10.0$, $A_{0,y}=10.0$, and $t_d=50.0$.

Figure 4

The HHG spectrum $|⟨j{⟩}_{\omega }{|}^2$ as a function of $\omega /{\omega }_0$ with $V=0.0$ (a), $V=2.0$ (b), and $V=4.0$ (c). Time profiles of $A_x(t)$ (red lines) and $⟨j_x{⟩}_t$ (blue lines) with $V=0.0$ (d), $V=2.0$ (e), and $V=4.0$ (f). Other parameters of the Hamiltonian (2) and the external laser are set to be $t_2=0.2$, ${\omega }_0=0.1$, $A_0=10.0$, and $t_d=50.0$.