Excited state nonlinear optics of quasi-one-dimensional Mott-Hubbard insulators

Ground as well as excited state nonlinear optical properties of one-dimensional Mott-Hubbard insulators are discussed in detail. One-dimensional strongly correlated materials are predicted to have several orders of magnitude larger excited state optical nonlinearities in comparison to that from the ground state. Unlike $\pi$-conjugated polymers and other classes of one-dimensional systems, strongly correlated materials such as ${\mathrm{Sr}}_2\mathrm{Cu}{\mathrm{O}}_3$, halogen-bridged Ni compounds, etc., have excited one- and two-photon allowed states almost energetically degenerate, which leads to order(s)-of-magnitude larger dipole coupling between them in comparison to that between the ground and optical states. This causes several orders of magnitude enhancement in the optical nonlinearities obtained from the first two-photon state in the wavelength region suitable for terahertz communications. Our results and conclusions are based on exact numerical calculations of the extended Hubbard model suitable for strongly correlated systems. We argue based on theoretical as well as available experimental data that one-dimensional cuprates would be a good source of terahertz radiation, to be experimentally verified. We also discuss in detail ground state nonlinear properties such as third-harmonic generation, two-photon absorption, and electroabsorption from the theoretical model and compare with experiments. Theoretical calculations of excited state nonlinearities of some $\pi$-conjugated polymers are also presented for comparison.

Figure 1

Optical-absorption spectrum for one-dimensional Mott-Hubbard insulators with $U_{\mathrm{Cu}\left(\mathrm{Ni}\right)}=10\mathrm{eV}$, $U_{\mathrm{O}\left(X\right)}=6\mathrm{eV}$. The spectrum denoted by the solid line corresponds to $V=ϵ=0.5\mathrm{eV}$, $t=0.75\mathrm{eV}$, whereas the dashed and dotted lines correspond to $V=t=2ϵ=1.0\mathrm{eV}$ and $V=t=1.0$, $ϵ=0.65$, respectively.

Figure 2

Third-order susceptibility of one-dimensional Mott-Hubbard insulators relevant to third-harmonic generation. (a) Imaginary part of the THG susceptibility, (b) real part of the THG susceptibility, and (c) magnitude of the THG susceptibility. Locations of ${\omega }_A$, ${\omega }_B$, and ${\omega }_C$ are very close to the experimentally observed values. The peak at ${\omega }_A$ is a three-photon resonant absorption, whereas those at ${\omega }_B$ and ${\omega }_C$ are two-photon resonant absorptions.

Figure 3

Theoretical prediction of third-order susceptibility of one-dimensional Mott-Hubbard insulators relevant for two-photon absorption (TPA) as well as intensity dependent refractive index $\left(n_2\right)$. Panel (a) represents the imaginary part of the third-order susceptibility, whereas (b) the real part. Both the real and imaginary parts show peaked structure around $0.88\mathrm{eV}$ (optical fiber communication length). The dashed curve in (b) corresponds to the case of higher value of linewidth parameter ${\Gamma }_a=0.4\mathrm{eV}$ compared to the solid line case, ${\Gamma }_a=0.3\mathrm{eV}$.

Figure 4

Nature of (a) real and (b) imaginary parts of third-order susceptibility ${\chi }_{xxxx}^{\left(3\right)}(-\omega ,0,0,\omega )$ in arbitrary units as a function of fundamental photon energy (in eV). $\mathrm{Im}{\chi }_{xxxx}^{\left(3\right)}(-\omega ,0,0,\omega )$ is related to electroabsorption (EA). The dip at around $1.77\mathrm{eV}$ in the EA spectra corresponds to the two-photon resonant peak seen at ${\omega }_B$ in the THG spectra.

Figure 5

Theoretical predictions of (a) THG, (b) TPA, and (c) EA. This figure conclusively proves that the third peak at ${\omega }_C$ is a two-photon resonant absorption which could be seen in the TPA spectra (b). The same should be observed in other one-dimensional Mott-Hubbard systems as well.

Figure 6

Effect of lattice constant and charge-transfer energy in isostructural one-dimensional Mott-Hubbard insulators. For the same values of on-site Coulomb repulsions, in (a) $ϵ=0.65$, $V=t=1\mathrm{eV}$; in (b) $ϵ=0.5\mathrm{eV}$, $V=t=1\mathrm{eV}$; and in (c) $ϵ=0.5\mathrm{eV}=V$, $t=0.75\mathrm{eV}$ in order to simulate situation from ${\mathrm{Sr}}_2\mathrm{Cu}{\mathrm{O}}_3$ to $\left[\mathrm{Ni}{\left(\mathrm{chxn}\right)}_2\mathrm{Cl}\right]{\mathrm{Cl}}_2$ to $\left[\mathrm{Ni}{\left(\mathrm{chxn}\right)}_2\mathrm{Br}\right]{\mathrm{Br}}_2$.

Figure 7

Theoretical prediction of enhanced excited state nonlinearity in one-dimensional Mott insulators. Panel (a) represents the ratio of the imaginary part of the THG susceptibility from the two-photon allowed state to that from the ground state. The latter is the same as that presented in Fig. 1a. Panel (b) represents the ratio of the real part of the THG evaluated from the excited state to the ground state. Panel (c) represents the ratio of the magnitudes of the THG as indicated in the axis labels. The inset figures are indicative of the same as that of the main figure but in logarithmic scale.

Figure 8

Excited state enhancement of (a) imaginary and (b) real parts of the third-order susceptibility with respect to the ground state relevant for TPA in logarithmic scale.

Figure 9

Excited state enhancement of (a) real and (b) imaginary parts of the third-order susceptibility with respect to the ground state relevant for EA in logarithmic scale.

Figure 10

(a) Third-harmonic generation (THG) susceptibility and (b) excited state THG susceptibility for poly-(para-phenylenevenylene) (PPV).