Photoinduced $\eta$-pairing at finite temperatures

We numerically prove photoinduced $\eta$-pairing in a half-filled fermionic Hubbard chain at both zero and finite temperature. The result, obtained by combining the matrix-product-state based infinite time-evolving block decimation technique and the purification method, applies to the thermodynamic limit. Exciting the Mott insulator by a laser electric field docked on via the Peierls phase, we track the time evolution of the correlated many-body system and determine the optimal parameter set for which the nonlocal part of the $\eta$-pair-correlation function becomes dominant during the laser pump at zero and low temperatures. These correlations vanish at higher temperatures and long times after pulse irradiation. In the high laser frequency strong Coulomb coupling regime we observe a remnant enhancement of the Brillouin-zone boundary pair-correlation function also at high temperatures, if the Hubbard interaction is about a multiple of the laser frequency, which can be attributed to an enhanced double occupancy in the virtual Floquet state.

Figure 1

Time evolution of pair correlations in an infinite half-filled Hubbard chain at $T=0$. Contour plots of $\tilde{P}(\pi ,t)$ are given in the ${\omega }_{\mathrm{p}}\text{−}{A}_0$ plane at $t·t_{\mathrm{h}}=10$ (a), 12 (b), and 16 (c) for $U/t_{\mathrm{h}}=8$, where the pump is parametrized by ${\sigma }_{\mathrm{p}}=2$ at $t_0·t_{\mathrm{h}}=10$. $\tilde{P}(\pi ,t), {\tilde{P}}_{r>0}(\pi ,t)$, and $2n_{\mathrm{d}}\left(t\right)$ are displayed as functions of time in (d) for the peak position $\times$ read off from (c). (e) demonstrates that the $\tilde{P}(\pi ,t)/A_0^2$ (symbols) can be rescaled to $\mathrm{Im}\chi \left(\omega \right)$ (black line) for small $A_0$, where $\mathrm{Im}\chi \left(\omega \right)$ is the imaginary part of the optical spectrum ${\chi }_{JJ}\left(\omega \right)$. iTEBD data were obtained with bond dimensions up to $\chi =2000$. For a discussion of the accuracy of the iTEBD calculations, see the Supplemental Material [35].

Figure 2

Temperature dependence of various correlation functions for the half-filled Hubbard chain without irradiation. Double occupancy $n_{\mathrm{d}}$ at different Coulomb repulsions $U/t_{\mathrm{h}}$ (a) [here, the symbols mark data obtained by a separate ground-state simulation ($T=0$)] and pair correlators $\tilde{P}\left(\pi \right), {\tilde{P}}_{r>0}\left(\pi \right)$ compared to $n_{\mathrm{d}}$ for $U/t_{\mathrm{h}}=8$ (b).

Figure 3

Pair correlations in an infinite half-filled Hubbard chain at $T>0$. Contour plots of $\tilde{P}(\pi ,t)$ (a), ${\tilde{P}}_{r>0}(\pi ,t)$ (b), and $2n_{\mathrm{d}}\left(t\right)$ (c) in the ${\omega }_{\mathrm{p}}\text{−}{A}_0$ plane at time $t·t_{\mathrm{h}}=20$ for $T/t_{\mathrm{h}}=1$, after pulse irradiation where ${\sigma }_{\mathrm{p}}=2, t_0·t_{\mathrm{h}}=10$, and $U/t_{\mathrm{h}}=8$, obtained by iTEBD with bond dimensions $\chi =800$. Time evolution of $\tilde{P}(\pi ,t), {\tilde{P}}_{r>0}(\pi ,t)$, and $2n_{\mathrm{d}}\left(t\right)$ (d) for parameters corresponding to the peak position $\times$ in (b). The dotted yellow line marks $2n_{\mathrm{d}}(t=0)$ for the pure Hubbard model with corresponding parameters. The iTEBD data are obtained for bond dimension $\chi =1600$.

Figure 4

Pair correlations at high temperatures. Contour plots of $\tilde{P}(\pi ,t)$ at $T/t_{\mathrm{h}}=8$, calculated for $U/t_{\mathrm{h}}=8$ (a) and 10 (b) by iTEBD with $\chi =800$, where the pump is parametrized as before. Time evolution of $\tilde{P}(\pi ,t), {\tilde{P}}_{r>0}(\pi ,t)$, and $2n_{\mathrm{d}}\left(t\right)$ (c), for the peak-position parameters determined from ${\tilde{P}}_{r>0}(\pi ,t·t_{\mathrm{h}}=15)$ [see Fig. S2(d) in the Supplemental Material 35] by iTEBD with $\chi =1600$.