Multiphoton Spectroscopy of a Dynamical Axion Insulator

Abstract

The unusual magnetoelectric transport present in Weyl semimetals and 3D topological insula- tors can be compactly understood as manifestations of a background axion field, which itself is determined by the microscopic band structure. In the presence of correlations, an additional axion quasiparticle may emerge as the collective excitations on top of the mean background field. Such modes couple nonlinearly to electric and magnetic fields, giving rise to a dynamical magnetoelectric response. However, unambiguous identification of this collective axion mode is challenging due to its inherent nonlinear dynamics. Here, we propose an all-optical protocol that utilizes a pump-probe setup for verifying and characterizing the transient dynamics of axion fields in three-dimensional insulator systems. In particular, we show that nonlinear Raman processes induce dynamical oscillations of the axion field that depend on the geometry of the incident electromagnetic fields. These oscillations manifest in the polarization and magnetization of the material, hence, can be subsequently measured using time-resolved Kerr rotation spectroscopy. Our results open a pathway towards using multi-photon and quantum pair spectroscopies to identify new correlated phases of quantum matter.

Figures (4)

• Figure 1: Schematic of the general excitation and detection set-up (a) Excitation scheme: two incident linearly polarized beams, $A^{(1)}(\omega_1, \boldsymbol{q}_1)$ and $A^{(1)}(\omega_2, \boldsymbol{q}_2)$, come in at a relative angle of $\pi - 2\varphi$, with respective linear polarizations $\boldsymbol{\hat{\varepsilon}}_1,\boldsymbol{\hat{\varepsilon}}_2$; frequencies $\omega_1,\omega_2$; and momenta $\boldsymbol{q}_1, \boldsymbol{q}_2$. The two beams are used to induce finite $\boldsymbol{E}\cdot\boldsymbol{B}$, exciting an axionic collective mode using a multiphoton absorption event. (b) Detection scheme: a linearly polarized probe beam, with polarization $\boldsymbol{\hat{\varepsilon}}_I$, at normal incidence; upon reflection the beam's polarization $\boldsymbol{\hat{\varepsilon}}_R$ will in general be elliptically polarized at a polarization angle that oscillates in phase with the induced axion oscillations.
• Figure 2: Schematic depiction of different axion excitation pathways. (a) Two photons can be absorbed in order to produce an axion excitation, which is most efficient when $\omega_1,\omega_2 \sim \Omega_0/2$. (b) Stimulated Raman can excite the axion when an incoming photon inelastically scatters and emits an axion collective mode, leaving the sample with a different energy. (c) Parallelpiped volume generated by triple product in Eq. \ref{['eq:main_theta_soln']}.
• Figure 3: This figure illustrates two distinct axion excitation pathways: two-photon absorption (upper half-plane) and stimulated Raman scattering (lower half-plane), with excitation amplitude $|\delta \theta|^2$ shown via color bars. The amplitude is plotted against normalized beam frequencies $\omega_1 / \Omega_0$ and $\omega_2 / \Omega_0$, with $\Omega_0 = 1$, and beam geometries indicated atop each subfigure. (a) For $\varphi = 0$ (anti-parallel beams), two-photon absorption dominates. (b) At $\varphi = \pi/2$ (parallel incidence), two-photon absorption is suppressed, and Raman excitation is maximal. (c) For $\varphi = \pi/4$ (orthogonal beams), both channels are present, with Raman excitation strongly enhanced. The grey line at $y = 0$ separates the two excitation regimes.
• Figure 4: Transient Kerr rotation reveals signatures of excited axion modes. Using a pump profile $\boldsymbol{E}\cdot\boldsymbol{B} \propto e^{(t/\sigma)^2} \cos(\Omega_D t)$ tuned to two-photon resonance ($\Omega_D = \Omega_0$), we drive out-of-phase axion oscillations $\delta\theta(t)$ with relative phase $\pi/2$ set by damping $\gamma$. These oscillations are reflected in the time-dependent Kerr angle $\Theta_K(t)$, which closely follows the axion dynamics. Amplitudes are illustrative and not to scale.