Characterizing biexciton coherences with quantum spectroscopy

The biexciton resonance in the absorption spectra of semiconductor quantum wells is analyzed with quantum-optical spectroscopy by projecting experimental pump-probe measurements into quantum-optical absorption spectra. More specifically, the measurements are converted into phase-space distributions using the cluster-expansion transformation. The quantum-optical responses can then be projected with full convergence, despite the unavoidable experimental noise. The calculations show that classical and quantum excitations produce significantly different results for the biexciton resonance. In particular, quantum-optical spectroscopy monitors the excitation-induced broadening of the biexciton resonance as a function of pump intensity much more sensitively than classical spectroscopy does.

Figure 1

Input data for CET. (a) The measured ten QW absorption ${\alpha }_{\mathrm{QW}}(E,\Delta t=12\mathrm{ps},|{\beta }_0\rangle )$ (defined in absolute units) is shown for six representative pump intensities. The vertical line denotes the spectral position of the biexciton resonance. (b) The corresponding low-pass filtered ten QW absorption ${\alpha }_{\mathrm{QW}}^{\mathrm{filt}}(E,\Delta t=12\mathrm{ps},|{\beta }_0\rangle )$. (c) The measured ten QW absorption ${\alpha }_{\mathrm{QW}}(E_{\mathrm{BiX}},\Delta t=12\mathrm{ps},|{\beta }_0\rangle )$ (shaded area) as function of pump amplitude $|{\beta }_0|$ is compared with the CET-constructed absorption ${\alpha }_{\mathrm{CET}}(E_{\mathrm{BiX}},\Delta t=12\mathrm{ps},|{\beta }_0\rangle )$ for $C=40$ (black line), $C=77$ (cyan line), and $C=103$ (dashed line). The measurement is performed at the biexciton resonance that is 2.2 meV below $E_{1s}$.

Figure 2

Projected classical and quantum-optical differential absorption. (a) The normalized classical differential-absorption spectrum $\Delta {\overline{\alpha }}_{\mathrm{cl}}(E,\Delta t=12\mathrm{ps},|{\beta }_0\rangle )$ is shown for $1\mathrm{M}$ (shaded area), $2\mathrm{M}$ (red line), $3\mathrm{M}$ (cyan line), and $4\mathrm{M}$ (black line) photon-number excitation. The corresponding 3-M photon excitation result, projected from the unprocessed measured QW absorption [Fig. 1], is presented as a dashed line. The spectral position of the biexciton resonance is indicated by a vertical line. (b) The corresponding squeezing-cat differential absorption spectra.

Figure 3

Excitation-induced dephasing of the biexciton resonance. (a) The strength of the biexciton resonance $\Delta {\overline{\alpha }}_{\mathrm{strength}}$ is presented as a function of pump photon number for classical (black line) and squeezing-cat differential spectroscopy (red line). The pump-probe delay is 12 ps. The confidence interval is indicated as a shaded area. The corresponding $\Delta {\overline{\alpha }}_{\mathrm{strength}}$, resulting from the projection from the raw data, is shown as squares (classical spectroscopy) and circles (squeezing-cat spectroscopy). (b) The corresponding results for the half-width ${\gamma }_{\mathrm{half}}$ of the biexciton resonance.

Figure 4

Dynamics of the biexciton resonance. (a) The strength $\Delta {\overline{\alpha }}_{\mathrm{strength}}$ of the biexciton resonance as a function of pump-probe delay for classical (black line) vs squeezing-cat differential spectroscopy (red line) projected from the low-pass filtered data. The pump has 3 M photons. The corresponding (b) half-width and (c) position of the biexciton resonance. In all frames, the shaded area defines the confidence interval of the projection and the raw-data projection results are shown for classical (squares) and quantum (circles) spectroscopy.