Interference in Floquet-Volkov transitions

Floquet states are signatured by pseudoeigenvalues which are discretely separated by the photon energy. Similarly, the laser-assisted photoemission effect (LAPE) induces electron-photon energy exchange (with momentum change), and also results in a discrete energy distribution. Both effects result from coherent interactions of electrons and photons. Here, we investigate the coherent interference between a Floquet state and the LAPE effect.

Figure 1

Schematic of Floquet-Volkov transitions where pseudoeigenvalues of Floquet and Volkov states enable multiple transition pathways despite energy conservation. $k_n$ indicates the $z$ component of the momentum of each state. Note that Volkov states collapse to free states at detection.

Figure 2

Momentum direction dependence of $\left|\gamma \right|$ for $\lambda =+$, $\beta =0.59$, and $\alpha =2.1$ and 1.5 for linear $({\theta }_{\mathbf{E}}=0)$ and circular $({\theta }_{\mathbf{E}}=\frac{\pi }{4})$ polarizations, respectively.

Figure 3

Energy spectra (without UV photoionization laser) of Floquet states for $\beta =0.59$ (scaled by 0.5946 to mimic the laser profile averaging; see Appendix pp4). The incidence of the IR pump laser is in the $xz$ plane.

Figure 4

Momentum-resolved photoemission spectra from Floquet states in $p$ polarization for ${\theta }_{\mathbf{E}}=0$, $\beta =0.59$, and $\alpha =2.1$ $(\beta$ and $\alpha$ scaled by 0.5946 to mimic the laser profile averaging; see Appendix pp4). Additional side bands are due to LAPE.

Figure 5

Momentum-resolved photoemission spectra from Floquet states in circular polarization for ${\theta }_{\mathbf{E}}=0.68$, $\beta =0.54$, and $\alpha =1.5$ $(\beta$ and $\alpha$ scaled by 0.5946 to mimic the laser profile averaging; see Appendix pp4). Note that the band gaps at $v_{F}k=0.5{\omega }_p$ are not identical because the surface electric field is elliptical due to different transmittivity coefficients for $s$- and $p$-polarization components.

Figure 6

Calculated (lines) and simulated (symbols) band gaps, $2{\Delta }_1$ at $2v_{F}k={\omega }_p$ for the orthogonal linear polarization (solid line and square) and $2{\kappa }_l$ at $2v_{F}k=l{\omega }_p$ for the circular polarization (dashed and dotted lines, and circles).