Model of nonadiabatic-to-adiabatic dynamical quantum phase transition in photoexcited systems

We study the ultrafast dynamic process in photoexcited systems and find that the Franck-Condon or Landau-Zener tunneling between the photoexcited state and the ground state is abruptly blocked with increasing the state coupling from nonadiabatic to adiabatic limits. The blockage of the tunneling inhibits the photoexcited state from decaying into the thermalized state and results in an emergence of a metastable state, which represents an entanglement of electronic states with different electron-phonon coupling strengths. Applying this model to the investigation of photoexcited half-doped manganites, we show that the quantum critical transition is responsible for more than a three-order-of-magnitude difference in the ground-state recovery times following photoirradiation. This model also explains some elusive experimental results, such as photoinduced rearrangement of orbital order by the structural rather than electronic process and the structural bottleneck of a one-quarter period of the Jahn-Teller mode. We demonstrate that in the spin-boson model there exist unexplored regions not covered in the conventional phase diagram.

Figure 1

Schematic photoinduced charge transfer from $3x^2/3y^2-r^2$ orbitals at $\mathrm{Mn}{}^{3+}$ to $3z^2-r^2$ and/or $x^2-y^2$ (not shown) orbitals at their neighboring ${\mathrm{Mn}}^{4+}$ sites in half-doped manganites. The (green) line indicates a ferromagnetic zigzag chain. Before the pump pulse, $3z^2-r^2$ orbitals at ${\mathrm{Mn}}^{4+}$ sites are empty. Oxygen orbitals are not shown for clarity.

Figure 2

The time evolution of photodriven state probabilities for $V=0.125$ (a), $V=0.291$ (b), and $V=V_c=0.292$ (c). When the electronic coupling $V$ is less than a critical value $V_c$, the excited state 2 returns to the ground state 1. While $V\ge V_c$, the relaxed state represents a strong entanglement of both the state 1 and the state 2. The slower oscillation period refers to the phonon mode of 69 fs, while the faster oscillation period of about $9\text{–}10$ fs is expected from the energy gap $\sqrt{{\Delta }^2+4V^2}$. Here, we set $\Delta =\varepsilon$ and $\varepsilon =0.4\mathrm{eV}$ as the energy unit.

Figure 3

Schematic free energy as a function of the configuration coordinate for two energy levels, coupled to the harmonic phonon mode. The parabolic curves are nonadiabatic free-energy surfaces in the weak-coupling limit. The splitting at the cross point caused by electronic coupling is neglected. The photoexcited state reaches the ground state by Franck-Condon or Laudau-Zener tunneling. The solid anticrossing curves refer to the adiabatic free-energy surfaces, and the energy gap (about $2V$) at the avoided crossing point blocks the tunneling and separates the photoexcited states from the thermalized states on the lower potential-energy curve. Consequently, the photoinduced states (red dots) relax to the bottom of the higher curves (green dots with energy $E_c$). Here, $\Delta$ and $\varepsilon$ are the energy gap and electron-phonon self-energy difference between the two levels, respectively.

Figure 4

The photoinduced metastable state phase diagram. The energies of the photoinduced quantum metastable state $E_q$ are located below the energies $E_c$ at the bottom of the upper adiabatic curves, shown in Fig. 3, and above the energy gap $\Delta$. $E_x$ is the free energy at the cross point of the nonadiabatic curves. Inset: Critical strength of the state coupling $V_c$ for the formation of the metastable state. The (red) straight line indicates the electron-phonon coupling $\lambda$.