Laser-driven Ultrafast Dynamics of a Fractional Quantum Hall System

Abstract

Fractional quantum Hall (FQH) systems are strongly interacting electron systems with topological order. These systems are characterized by novel ground states, fractionally charged and neutral excitations. The neutral excitations are dominated by a low-energy collective magnetoroton mode. Here we derive and use a quasi-one-dimensional model to investigate the ultrafast nonequilibrium dynamics of a laser-driven FQH system within a two-Landau-level approximation. As opposed to the traditional and synthetic bilayers, our model accounts for interactions where electrons can scatter from one Landau-level to another. By performing exact time evolution of the system, we create an out-of-equilibrium state following the laser pulse that shows rich physics. Our calculations show the presence of non-trivial excited modes. One of these modes is electromagnetically active and represent density oscillations of \emph{magnetoplasmon} mode. Another mode is identified by evaluating the overlap of the initial state and the out-of-equilibrium state following the laser pulse with a quadrupole operator. This mode is analogous to the chiral-graviton mode for FQH systems recently measured in experiments [Nature {\bf 628}, 78 (2024)]. Our results show that a linearly-polarized pulse field can excite the graviton mode when inter-Landau level scattering occurs.

Figures (4)

• Figure 1: (a) Torus with lengths $L_x$ and $L_y$. Magnetic field is pointing along $\hat{z}$. (b) A schematic of a two-level FQH system. Initially, the system is in fractional $\nu=1/3$ state occupying the LLL ($n=0$). This state is then laser-driven creating excitations to the first Landau level ($n=1$). The energy difference between the two levels is $\omega_c$. (c) and (d) are the two-electron scattering processes that do not conserve Landau level index. (c) describes two electrons transitioning from one Landau level to another. (d) a two-electron process where only one electron scatters to another Landau level.
• Figure 2: Color online. Structure factor in frequency domain ${\mathcal{S}}_{\mathbf q}(\omega)$ for different system sizes. The torus dimensions is taken $L_x=L_y=\sqrt{6\pi N}\ell_B$. The laser-frequency is $\omega_0=0.7\omega_c$. The intensity is set to $eA_0/\sqrt{2}m^*\ell_B=0.2E_c$ and $t_d=10/E_c$. The units of time is the inverse of $E_c$. The usual values of $E_c$ is around $14\; {\rm meV}$inelastic1/3 which gives $47$ femto-seconds as the unit of time. The structure factor spectrum is normalized such that $\int {\mathcal{S}}_{\mathbf q}(\omega)d\omega=1$.
• Figure 3: Color online. (a) $I_n=|\langle\Psi_0| \hat{O}^{(2)}|n\rangle|$ for $N=7$ for $L_y=\sqrt{2\pi 21} \ell_B$. Where $|\Psi_0\rangle$ is the FQH-1/3 state and $|n\rangle$ is the $n$-th excited state of Hamiltonian in Eq. (\ref{['eq:Model']}). The inset of (a) gives the transition matrix element between FQH-1/3 state and the eigen-states of LLL. (b) Same as (a) but for $N=6$ and $L_y=\sqrt{2\pi 18}\ell_B$. The level-spacing is set to $0.5E_c$. Grey vertical line on plots is at energy $0.14 E_c$.
• Figure 4: The structure factor $S_\mathbf{q}(\omega)$ (unnormalized) for $\mathbf{q}=(2\pi/L_x,0)$, $\omega=0.7\omega_c$ and $N=6$ electron system. All parameters are set according to the Fig. \ref{['fig:sq']}. Without the two-particle chiral excitations (Fig. \ref{['fig:excite']} (c)) the intra-LL mode is suppressed. Inset gives the strength of the main peak of the low-energy (graviton) and plasmon mode against the intensity of the laser-pulse. Quadratic dependence and linear dependence is evident for the low energy mode and plasmon mode respectively. The peak value of the plasmon mode is divided by 5 for better fit.