Tracking ultrafast solid-state dynamics using high harmonic spectroscopy

We establish time-resolved high harmonic generation (tr-HHG) as a powerful spectroscopy method for tracking photoinduced dynamics in strongly correlated materials through a detailed investigation of the insulator-to-metal phase transitions in vanadium dioxide. We benchmark the technique by comparing our measurements to established momentum-resolved ultrafast electron diffraction, and theoretical density functional calculations. Tr-HHG allows distinguishing of individual dynamic channels, including a transition to a thermodynamically hidden phase. In addition, the HHG yield is shown to be modulated at a frequency characteristic of a coherent phonon of the equilibrium monoclinic phase over a wide range of excitation fluences. These results demonstrate that tr-HHG is capable of tracking complex dynamics in solids through its sensitivity to the band structure.

Figure 1

Atomic and band structure of the ${\mathrm{VO}}_2$ IMT. (a) Atomic arrangement of ${\mathrm{VO}}_2$ during IMT phase transitions. In the photoinduced phase transition, the $M_1 \to R$ transition occurs at high fluence, while the $M_1 \to \mathcal{M}$ occurs at low to moderate fluences. (b) Energy diagram of the band structure of ${\mathrm{VO}}_2$ in the $R, M_1$, and $\mathcal{M}$ phases.

Figure 2

Experimental geometry. (a) An 80 fs, MIR driver pulse is used to generate harmonics from a 100 nm thick epitaxial ${\mathrm{VO}}_2$ sample. The transmitted harmonic spectrum is then collected and recorded using a spectrometer or photodiode. A 50 fs, 1.5 $\mu \mathrm{m}$ pump at variable delay, $\tau$, from the driver is used to photoexcite the IMT. The fluence of the pump can be modulated using a half-waveplate, polarizer energy throttle. (b) The unpumped high harmonic (HH) spectrum driven by 10 $\mu \mathrm{m}$ in the $M_1$ phase at room temperature of 20 ${}^{\circ }\mathrm{C}$ (blue circles) and $R$ phase at 100 ${}^{\circ }\mathrm{C}$ (red circles). Blue rectangles indicate locations of expected harmonics.

Figure 3

Change in optical IR transmittance (top) and fifth harmonic yield (bottom). The time dependent change in optical IR transmittance (top) or the fifth harmonic yield (bottom) driven by 10 $\mu \mathrm{m}$ following the photoexcited IMT in ${\mathrm{VO}}_2$. Negative delays indicate the harmonic generating driver or IR probe pulse arrives before photoexcitation. The various phases of ${\mathrm{VO}}_2$ are annotated on the curves. No revival of the IR transmittance is observed for long timescales in (a) or short timescales in (b). (c) Long-term recovery and revival of the harmonics as the ${\mathrm{VO}}_2$ transitions to the $\mathcal{M}$ phase. The amplitude of $\mathcal{M}$ recovery in the HHG yield is plotted as a function of pump fluence in Fig. 4. The dashed rectangles are expanded upon with higher time-resolution in (b) and (d). The shaded green rectangles show the region of the fast dynamics for the $M_1^{*}\to M_1^{*,b}$ transition. In both (c) and (d) the suppression of the harmonics in the $R$ phase can be seen for high fluences.

Figure 4

HHG, IR transmittance, and UED comparisons. (a) and (b) Comparison of the fifth harmonic (solid lines, driven by 10 $\mu \mathrm{m}$) and third harmonic (dashed lines, driven by 7 $\mu \mathrm{m}$) dynamics for varying pump fluences. Similar dynamics are observed regardless of harmonic probed. Black oscillations indicated in (b) correspond to $M_1$ phase phonon modes (Appendix pp5). (c) Biexponential fit of a moderately pumped HHG yield where both the $M_1^{*}\to M_1^{*,b}$ and $M_1^{*,b}\to \mathcal{M}$ transitions are occurring (Appendix pp3). (d) Extracted phase fractions for the $\mathcal{M}$ phase from UED results [35, 36] for different pump fluences, and the corresponding change in amplitude for the IR transmittance and HHG yield. Note the UED results were pumped with 800 nm, and the tr-HHG was pumped with 1.5 $\mu \mathrm{m}$.

Figure 5

$M_1$ vs $R$ phase harmonic generation. High harmonic spectra in the forward (top) and backward (bottom) direction for the $M_1$ phase (blue) at 20 ${}^{\circ }\mathrm{C}$ and $R$ phase (red) at 100 ${}^{\circ }\mathrm{C}$. Blue shaded rectangles show location of expected harmonics. HH: high harmonic.

Figure 6

Slow timescale. The slow timescale retrieved from third harmonic tr-HHG (blue curve) is in good agreement with results from UED measurements (data: red circles; fit: red dashed curve).

Figure 7

Fast timescale. (b) Fast time dynamics for the $M_1^{*}\to M_1^{*,b}$ transition of $t_{\mathrm{fast}}=300\pm 24\mathrm{fs}$ and $245\pm 68\mathrm{fs}$ retrieved from the third and fifth tr-HHG measurements respectively. Each measurement was pumped with only 3 mJ ${\mathrm{cm}}^{-2}$ where this is the only transition present. (b) Absolute change in harmonic yield plotted on a semilogarithmic scale to show the single exponential timescale present HH: high harmonic.

Figure 8

Two timescales. (a) Initiating the IMT with moderate pump fluences of 20 and 12 mJ ${\mathrm{cm}}^{-2}$ (at 1.5 $\mu \mathrm{m}$) (HH3, blue squares and HH5, yellow diamonds respectively) presents both the $M_1^{*}\to M_1^{*,b}$ and $M_1^{*,b}\to \mathcal{M}$ timescales in the changing harmonic yield for both the third and fifth tr-HHG measurements. Fast dynamics of $t_{\mathrm{fast}}=322\pm 34\mathrm{fs}$ and $400\pm 108\mathrm{fs}$ (purple curves), and slow dynamics of $t_{\mathrm{slow}}=1.45\pm 0.34\mathrm{ps}$ and $1.10\pm 0.37\mathrm{ps}$ (green curves) are retrieved from the third and fifth harmonic curves respectively. (b) Absolute change in harmonic yield plotted on a semilogarithmic scale showing the biexponential fit as two intersecting linear lines corresponding to timescales in the phase transition HH: high harmonic.

Figure 9

Calculated tr-HHG traces. Calculated tr-HHG traces for a semiconductor system with a band gap of 0.68 eV photoexcited with 1.5 $\mu \mathrm{m}$, and with HHG driven by 10 $\mu \mathrm{m}$ (top) or 7 $\mu \mathrm{m}$ (bottom). Negative delays indicate the harmonic generating driver pulse arrives before photoexcitation. (a) and (c) show the harmonic spectra for various pump delays. (b) and (d) show the tr-HHG traces for the third, fifth, and seventh harmonic orders for each driver frequency. An increase in harmonic yield is observed for positive delays in this semiconductor system, contrasting with the decrease in yield observed for ${\mathrm{VO}}_2$.

Figure 10

Phonon mode analysis. (a) Fast Fourier transform of the oscillations observed in Fig. 4. (b) Oscillation frequencies retrieved from (a) added to the fast timescales found in Appendix pp3 (solid curves) are overlaid with the tr-HHG data (circles).

Figure 11

Harmonic yield in the backwards direction. These curves show the change in harmonic yield for harmonics generated in the backwards direction. We can still see the same double timescale that is observed in transmission.

Figure 12

$1.3\mu \mathrm{m}$ pump, $4.0\mu \mathrm{m}$ probe. Complementary measurements with a 1.3 $\mu \mathrm{m}$ pump and 4.0 $\mu \mathrm{m}$ probe show similar dynamics to the IR transmissivity results presented in the paper.