Terahertz Electron-Hole Recollisions in $\mathrm{GaAs}/\mathrm{AlGaAs}$ Quantum Wells: Robustness to Scattering by Optical Phonons and Thermal Fluctuations

Electron-hole recollisions are induced by resonantly injecting excitons with a near-IR laser at frequency $f_{\mathrm{NIR}}$ into quantum wells driven by a $10\mathrm{kV}/\mathrm{cm}$ field oscillating at $f_{\mathrm{THz}}=0.57\mathrm{THz}$. At $T=12\mathrm{K}$, up to 18 sidebands are observed at frequencies $f_{\text{sideband}}=f_{\mathrm{NIR}}+2n{f}_{\mathrm{THz}}$, with $-8\le 2n\le 28$. Electrons and holes recollide with total kinetic energies up to 57 meV, well above the $E_{\mathrm{LO}}=36\mathrm{meV}$ threshold for longitudinal optical (LO) phonon emission. Sidebands with order up to $2n=22$ persist up to room temperature. A simple model shows that LO phonon scattering suppresses but does not eliminate sidebands associated with kinetic energies above $E_{\mathrm{LO}}$.

Figure 1

PL and absorption measurements for $T=12\text{}$ and $T=294\mathrm{K}$. The absorption spectra are offset for clarity. The heavy hole peaks in both measurements at low temperature agree very well. The second, minor peaks denoted with asterisks in the absorption spectra are assigned to the light hole exciton.

Figure 2

Measured high-order sideband strengths compared with theoretical calculations. The observed sideband conversion efficiencies versus sideband energy offset $(=h{f}_{\text{sideband}}-h{f}_{\mathrm{NIR}})$ and sideband order for the 5 nm QW sample at $T=12\mathrm{K}$ (top left) and $T=294\mathrm{K}$ (bottom left) and for the 10 nm QW sample at $T=12\mathrm{K}$ (top right) and $T=294\mathrm{K}$ (bottom right) are plotted as black circles. For each sideband, the conversion efficiency is calculated by integrating the individual sideband peak and then dividing by the photomultiplier tube’s response to the NIR laser with no sample. Calculated sideband strengths, normalized to the conversion efficiency for the $n=1$ sideband, are plotted as blue squares connected by a line to guide the eye. The vertical red lines at 0 meV denote $h{f}_{\mathrm{NIR}}$. The dashed line represents the noise floor of detection. The arrows indicate the threshold at which, within the three step model [21], the total kinetic energy of the colliding electron and hole is larger than the longitudinal optical phonon energy.

Figure 3

Classical calculation of electron-hole dynamics associated with 28th order sideband. Top: trajectories of the electron (black) and hole (red) show electron-hole separation reaches a maximum of 60 nm between tunnel ionization (0 ps) and recollision (flash). Bottom: total kinetic energy of the electron and hole. The total kinetic energy exceeds the threshold for LO phonon emission $E_{\mathrm{LO}}$ (short dashed line) for only $\sim 50\mathrm{fs}$ before emitting a sideband with sideband offset energy $E_{\mathrm{SB}}$ $(\text{long vertical arrow})=\text{Total kinetic energy}+\text{detuning}\mathrm{\Delta }(\text{double arrow})$. The long dashed horizontal lines denote 0 nm (top) and 0 meV (bottom). See text and Supplemental Material [20] for details.

Figure 4

Calculations of the effects of longitudinal optical phonon scattering. HSG calculations at (a) $T=12$ and (b) $T=294\mathrm{K}$ with (black circles) and without (red triangles) LO phonon scattering. An arrow denotes the threshold for emitting a LO phonon in the 5 nm QW sample. Excitonic dephasing is included in all calculations. The inset is the calculated total energy-dependent scattering rate given by [25].