Bloch Oscillations of THz Acoustic Phonons in Coupled Nanocavity Structures

Nanophononic Bloch oscillations and Wannier-Stark ladders have been recently predicted to exist in specifically tailored structures formed by coupled nanocavities. Using pump-probe coherent phonon generation techniques we demonstrate that Bloch oscillations of terahertz acoustic phonons can be directly generated and probed in these complex nanostructures. In addition, by Fourier transforming the time traces we had access to the proper eigenmodes in the frequency domain, thus evidencing the related Wannier-Stark ladder. The observed Bloch oscillation dynamics are compared with simulations based on a model description of the coherent phonon generation and photoelastic detection processes.

Figure 1

Top: Schematic of the coupled nanocavities nanostructure. Bottom left: Phonon band structure. The central grey region (indicated with a double arrow) limited by the thicker black forbidden bands corresponds to the cavity-mode band. $L$, $U$, and WSL indicate the lower and upper minigaps, and the acoustic WSL region. Bottom right: Calculated acoustic reflectivity. Red triangles indicate the resonance energies of the isolated nanocavities.

Figure 2

Time resolved reflectivity measured on a structure formed by 15 coupled acoustic nanocavities. (a) Measured signal using a laser wavelength of 815 nm without a slowly varying background. (b) Signal after applying a bandpass filter set between 0.517 and 0.636 THz. The insets show a zoom of the time trace between 200 and 300 ps.

Figure 3

Upper panel: calculated acoustic reflectivity of the studied structure. The dips correspond to the nanophononic WSL energy levels. Lower panel: Fourier transform of the derivative of the experimental signal shown in Fig. 2 ($E\mathrm{\text{−}}FT$), simulated spectrum ($G+D$), and computed acoustic phonon generation spectrum ($G$).

Figure 4

Left panel: simulated time evolution of the generated spectrum between 0.554 and 0.585 THz. The white vertical lines indicate the positions of the acoustic spacers. Right panel: experimental signal treated with a bandpass filter between 0.554 and 0.585 THz. Horizontal lines are a guide to the eye to relate the maxima in the detected signal with the localization of maxima of acoustic deformation in the structure.