Keldysh Space Control of Charge Dynamics in a Strongly Driven Mott Insulator

The fate of a Mott insulator under strong low frequency optical driving conditions is a fundamental problem in quantum many-body dynamics. Using ultrafast broadband optical spectroscopy, we measured the transient electronic structure and charge dynamics of an off-resonantly pumped Mott insulator ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$. We observe coherent bandwidth renormalization and nonlinear doublon-holon pair production occurring in rapid succession within a sub-100-fs pump pulse duration. By sweeping the electric field amplitude, we demonstrate continuous bandwidth tuning and a Keldysh crossover from a multiphoton absorption to quantum tunneling dominated pair production regime. Our results provide a procedure to control coherent and nonlinear heating processes in Mott insulators, facilitating the discovery of novel out-of-equilibrium phenomena in strongly correlated systems.

Figure 1

Resolving Keldysh tuning using pump-probe spectroscopy. (a) $\mathrm{\Gamma }$ calculated across Keldysh space using the Landau-Dykhne method. (b) Constant energy cuts along the red lines shown in (a) plotted on a logarithmic scale. Black dots mark the Keldysh crossover. Gray dashed lines show the scaling relation in the multiphoton regime. Schematics of the multiphoton and tunneling processes are shown above. (c) Equilibrium reflectivity (top) and conductivity (bottom) spectra of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ at 20 K. The 0.3 and 0.56 eV pump energies are marked by vertical red lines. The probe energy range is shaded gray. (d) Select 0.3 eV pump 1.77 eV probe $\mathrm{\Delta }R/R$ traces at fluences of 3, 9, 15, 22, and $30\mathrm{mJ}/{\mathrm{cm}}^2$ (top to bottom). Dashed lines are fits detailed in Ref. [40]. Inset: peak $\mathrm{\Delta }R/R$ versus fluence showing nonlinearity. (e),(f) Experimental cuts through the same regions of parameter space as in (b). Error bars are smaller than data markers. Scaling relations for multiphoton and tunneling behavior are overlaid as red and blue dashed lines, respectively.

Figure 2

Nonthermal pair distribution through the Keldysh crossover. (a) Calculated $P_p$ for conditions (i)–(iii) using the Landau-Dykhne method. (b) Simulated nonequilibrium reflectivity spectra for subgap pumping. (c),(d) Analogs of (a) and (b) but simulated for above-gap pumping. Fluence increases from (i) to (iii). Black curves in (b) and (d) are the equilibrium spectra. Arrows in (b) mark the crossing points between the nonequilibrium and equilibrium curves. Experimental $\mathrm{\Delta }R/R$ maps of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ for (e) 0.3 eV pump (fluence $30\mathrm{mJ}/{\mathrm{cm}}^2$) and (f) 1 eV pump (fluence $7\mathrm{mJ}/{\mathrm{cm}}^2$). Two representative constant energy cuts (yellow, 1.77 eV; purple, 0.56 eV) are overlaid. (g) Enlargement of $\mathrm{\Delta }R/R$ maps for 0.3 eV pump using three pump fluences [marked in Fig. 1] corresponding to conditions (i)–(iii) in (a). (h) Enlargement of $\mathrm{\Delta }R/R$ maps for 1 eV pump using three pump fluences indicated above. White dashed lines mark $t=0.1\mathrm{ps}$. Red dashed lines are guides to the eye for the $\hslash {\omega }_{\text{probe}}$ where $\mathrm{\Delta }R/R$ changes sign at $t=0.1\mathrm{ps}$.

Figure 3

Nonequilibrium conductivity transients. (a) Conductivity spectra of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ in the unpumped equilibrium state at 80 K and the 0.3 eV pumped nonequilibrium state at $t=0.5\mathrm{ps}$ (fluence $26\mathrm{mJ}/{\mathrm{cm}}^2$). (b) Comparison of differential conductivity spectra between 0.3 eV pump ($\mathrm{\Delta }{\sigma }_{0.3\mathrm{eV}}$) and scaled 1 eV pump ($A\mathrm{\Delta }{\sigma }_{1\mathrm{eV}}$) cases at $t=0.1\mathrm{ps}$ and (c) $t=0.5\mathrm{ps}$. Red and blue shades indicate error estimated from the ${\omega }_{\text{probe}}$-dependent fluctuations of the experimental $\mathrm{\Delta }\sigma$ spectra.

Figure 4

Ultrafast coherent bandwidth renormalization. (a) $\mathrm{\Delta }(\mathrm{\Delta }\sigma )$ map obtained by subtracting scaled $\mathrm{\Delta }{\sigma }_{1\mathrm{eV}}$ from $\mathrm{\Delta }{\sigma }_{0.3\mathrm{eV}}$ spectra. (b) A constant probe energy cut at 1.65 eV [dashed horizontal line in (a)] plotted together with $\mathrm{\Delta }{\sigma }_{0.3\mathrm{eV}}$. (c) A constant time cut at $t=0$ [dashed vertical line in (a)]. (d) DFT simulation of the spectrum change induced by bandwidth broadening. ${\sigma }_W$ (${\sigma }_{W_{\mathrm{eq}}}$) is conductivity with (without) bandwidth broadening. (e) (left) Quantitative extraction of pump-induced bandwidth modification versus $t$ (with $E_{\mathrm{pump}}=0.12\mathrm{V}/\AA$) and (right) versus $E_{\mathrm{pump}}$ (with $t=0\mathrm{ps}$) based on fitting to DFT calculations. Red shaded region: error bar. Blue shaded region: Floquet theory prediction based on a periodically driven two-site cluster Hubbard model. Upper and lower bounds assume $U=3\mathrm{eV}$ [37] and $U=3.5\mathrm{eV}$ [34], respectively, where $U$ is the on-site Coulomb energy, with no other adjustable parameters. (f) Chronology of nonthermal processes following an impulsive subgap drive.