Observation of bound and antibound states of two excitons in GaAs single quantum well by two-dimensional coherent spectroscopy

We study the bound and antibound states of two excitons in a GaAs single quantum well by two-dimensional coherent spectroscopy. We also propose a method to directly observe the amplitude and phase (real and imaginary parts) of optical fields by using a heterodyne interference technique and through synchronized detection of the interference signals. In this scheme, the mechanical fluctuation of an unstabilized interferometer does not affect the measurement. In addition, the amplitude and phase of the optical fields, resulting from the coherent interactions between light and matter, are directly obtained by comparing a reference heterodyne beating signal by using a two-phase lock-in amplifier. By using this method, the bound and antibound states of two excitons are observed. It is expected that the excitons are localized to the quantum islands and the lateral confinement induces the large repulsive energy between the two excitons.

Figure 1

(a) Experimental setup to obtain the amplitude and phase of the reflected light field of a sample. LIA: lock-in amplifier; AOM: acousto-optic modulator; M: monochromator; PMT: photomultiplier. AOM shifts the frequency of the laser pulses by ${\omega }_1$ and ${\omega }_2$, respectively. ${\omega }_{21}={\omega }_2-{\omega }_1$ is the beat frequency of the heterodyne interference. (b) Reflectance and phase of a GaAs SQW with a well thickness of 15 nm at 4 K. $X_H$ and $X_L$ indicate heavy- and light-hole excitons, respectively.

Figure 2

(a) Experimental setup for 2DFT spectroscopy. LIA: lock-in amplifier; AOM: acousto-optic modulator; M: monochromator; PMT: photomultiplier. AOM shifts the frequency of the laser pulses by ${\omega }_1, {\omega }_2$, and ${\omega }_3$. ${\omega }_{21}={\omega }_2-{\omega }_1$ and ${\omega }_{31}={\omega }_3-{\omega }_1$ are the beat frequencies of the heterodyne interference, and a mixer generates the sum frequency ${\omega }_{21}+{\omega }_{31}$. LIA1 detects the amplitude and phase of the heterodyne interference between the third-order nonlinear signal and ${\omega }_1$ pulse, and LIA2 detects the amplitude of the heterodyne interference between ${\omega }_1$ and ${\omega }_3$ pulses. (b) Pulse sequence, with corresponding delay time $\tau$ and $T$. The third-order nonlinear signal is generated after the irradiation of ${\omega }_3$ pulse, and the frequency is shifted by $-{\omega }_1+{\omega }_2+{\omega }_3$ that corresponds to the $-{\mathit{k}}_1+{\mathit{k}}_2+{\mathit{k}}_3$ signal in conventional FWM measurements. Undesired signals, such as ${\omega }_1-{\omega }_2+{\omega }_3$ (${\mathit{k}}_1-{\mathit{k}}_2+{\mathit{k}}_3$), are removed from the frequency differences. (c) Complex FWM spectrum of a GaAs SQW at 4 K. The real and imaginary parts are denoted as Re and Im, respectively. Delay time $\tau =0$ ps and $T=0$ ps. ${\omega }_1, {\omega }_2$, and ${\omega }_3$ were set to 40.000, 40.005, and 40.009 MHz, respectively. The reference frequency ${\omega }_{21}+{\omega }_{31}$ is 14 kHz. Solid lines are corrected using the phase shift of the reference pulse due to the reflection at the sample. Cross symbols ($\times$) are uncorrected signals. $B_H$ and $B_M$ indicate heavy-heavy-hole and mixed heavy-light-hole biexcitons, respectively.

Figure 3

2D spectrum for rephasing pulse sequences, i.e., $\tau >0$, in a GaAs SQW at 4 K. The excitation pulses are collinearly polarized. The delay $T=0.2\mathrm{ps}$. $2X_H$ indicates the antibound two-exciton state. The arrows represent the scattering process during the pulse excitation. The delay times $\tau$ were scanned 120 points with 0.1 ps steps. The monochromator scanned 80 points with 0.1 nm steps. The measurement took 30 h. ${\omega }_1, {\omega }_2$, and ${\omega }_3$ were set to 40.000, 40.005, and 40.009 MHz, respectively. The full width at half maximum of the spectral resolution is 0.14 nm, that is, 0.27 meV at the experimental condition. The spectral resolution is comparable to the step size of the monochromator.

Figure 4

Emission spectra in a GaAs SQW for collinear and cocircular configurations due to heavy-hole exciton (${\mathrm{X}}_H$) absorption. Excitation and reference pulses are collinearly and cocircularly polarized, respectively. $B_H, B_M$, and $2X_H$ correspond to a heavy-hole biexciton, mixed heavy-light-hole biexciton, and antibound two excitons, respectively.