Low-energy photoexcitations inside the Mott gap in doped Hubbard and t-J ladders

TL;DR

This study addresses how ultrafast, low-energy pump pulses affect the Drude and mid-infrared absorptions in doped Mott insulators. Using time-dependent density matrix renormalization group on a hole-doped two-leg Hubbard ladder and a four-leg $t$-$J$ ladder, the authors show that monocycle pulses resonant with Drude absorption reduce the Drude weight and can modestly boost mid-IR spectral weight, with the mid-IR enhancement diminishing at higher pulse intensities. Pumping at mid-IR energies mainly reduces the Drude weight, since mid-IR excitations originate from magnetic processes that do not couple directly to photons. These insights provide experimentally testable predictions for cuprates and highlight distinct driving pathways for manipulating low-energy charge dynamics in strongly correlated electron systems.

Abstract

We investigate changes in the optical conductivity of doped Mott insulators by tuning ultrashort pump pulses to target either the Drude or low-energy absorption regions. Using a hole-doped two-leg Hubbard ladder and a four-leg t-J ladders, we calculate the optical conductivity after pump by employing the time-dependent density matrix renormalization group. We find that a monocycle electric field pulse tuned to the Drude absorption reduces the Drude weight, accompanied by a slight enhancement in the mid-infrared (mid-IR) spectral weight. However, this enhancement diminishes as the pulse intensity increases. In contrast, a pump pulse tuned to the mid-IR absorption only affects the Drude weight. This behavior arises because the mid-IR absorption originates from magnetic excitations that do not couple directly to photons. These predictions can be tested experimentally by applying ultrashort low-energy pump pulses to cuprate materials.

Figures (5)

• Figure 1: $\mathrm{Re}\,\sigma(\omega,\tau)$ for the $x_\mathrm{h} = 1/8$ hole-doped two-leg Hubbard ladder of size $L = 16 \times 2$ with $U = 10$. (a) Equilibrium case before pump at $\tau = -10$ (black solid line). For comparison, $\mathrm{Re}\,\sigma(\omega,\tau = -10)$ at half filling ($x_\mathrm{h} = 0$) is shown as the black dashed line. Inset: Pump pulse $A_\mathrm{pump}(t)$ with $t_0 = 10$ and $t_\mathrm{d} = 2$ used in panels (b) and (c), where $\Omega = 0$ (red line) and $\Omega = 1$ (blue line). (b) $\mathrm{Re}\,\sigma(\omega,\tau)$ above $\omega = 6$ and (c) below $\omega = 2.5$ at $\tau = 10$. The red and blue solid lines correspond to $\Omega = 0$ and $\Omega = 1$, respectively, with $A_0 = 0.5$. The red dashed line represents the case of $\Omega = 0$ with $A_0 = 1.43$. The black solid line shows $\mathrm{Re}\,\sigma(\omega,\tau = -10)$, whose high-resolution behavior for the broadening factor of $\gamma=0.1$ is shown in the inset of (c), where small weight around $\omega\sim 1$ to 2 is evident. In panel (c), the downward red and blue arrows indicate the position of pump frequency $\Omega$.
• Figure 2: Low-energy part of $\mathrm{Re}\,\sigma(\omega,\tau = 10)$ for the $x_\mathrm{h} = 1/8$ hole-doped four-leg $t$-$J$ ladder with $L = 12 \times 4$, pumped by the $\Omega = 0$ pulses. The equilibrium result at $\tau = -10$ is shown as the black line. (a) $J = 0.4$: The red solid and red dashed lines correspond to $A_0 = 0.5$ and $A_0 = 1.43$, respectively. (b) $J = 1$: The red line represents the case of $A_0 = 0.5$. Downward red arrows indicate the position of pump frequency $\Omega$.
• Figure 3: Charge distribution and spin correlations in the $x_\mathrm{h} = 1/8$ hole-doped four-leg $t$-$J$ ladder with $L = 12 \times 4$ and $J = 0.4$. (a) Hole density $n_\mathrm{h}(i)$ for each rung $i$. (b) Static spin structure factor $S_z(q_\mathrm{leg}, q_\mathrm{rung} = \pi)$. Red circles and blue upward triangles represent the results at $\tau = 10$ for the $\Omega = 0$ pulse with $A_0 = 0.5$ and $A_0 = 1.43$, respectively. The equilibrium case before pumping ($\tau = -10$) is shown by black squares. Solid lines are guides to the eye.
• Figure 4: Low-energy part of $\mathrm{Re}\,\sigma(\omega,\tau = 10)$ for the $x_\mathrm{h} = 1/8$ hole-doped four-leg $t$-$J$ ladder with $L = 12 \times 4$ and $J = 0.4$. The equilibrium result before pump ($\tau = -10$) is shown as the black line. The red and blue lines correspond to $\Omega = 1$ and $\Omega = 2$, respectively. The inset displays the electric field profile $E_\mathrm{pump}(t)$ for the pump pulse. The amplitude of the electric field is identical for all values of $\Omega$. Downward red and blue arrows indicate the position of pump frequency $\Omega$.
• Figure 5: Charge distribution and spin correlations in the $x_\mathrm{h} = 1/8$ hole-doped four-leg $t$-$J$ ladder with $L = 12 \times 4$ and $J = 0.4$. (a) Hole density $n_\mathrm{h}(i)$ for each rung $i$. (b) Spin structure factor $S_z(q_\mathrm{leg}, q_\mathrm{rung} = \pi)$. Red circles and blue upward triangles represent the results at $\tau = 10$ for pump pulses with $\Omega = 1$ and $\Omega = 2$, respectively, under identical electric field amplitudes (see the inset of Fig. \ref{['Fig4']}). The equilibrium case before pump ($\tau = -10$) is shown by black squares. Solid lines are guides to the eye.