Optical transitions from the lowest to higher exciton and biexciton Rydberg states in CuCl

We measured the optical transitions due to the internal energy levels of an exciton and biexciton in a CuCl single crystal using pump-probe spectroscopy. The transient absorption bands due to the transitions from the $1s$ to $2p$ and from the $1s$ to $3p$ exciton states were observed at 3 K, which is consistent with their reported energies. Simultaneously, the transient absorption peak due to the biexciton was observed, which corresponds to a transition from the lowest state (composed of two $1s$ excitons) to higher states (composed of $1s$ and $2p$ excitons). The value of the observed biexciton peak energy was reasonable considering the hydrogen molecule orbitals and the electron-to-hole effective mass ratio. In addition, the transient absorption peaks were broadened at 77 K, because of the increase in the homogeneous width of the $2p$ exciton state. The transient absorption spectrum was almost completely determined by this width. Our findings are of importance with regard to the optical phenomena in the infrared region related to the quantum coherence of excitons and biexcitons in semiconductors.

Figure 1

Optical system used for IRTA measurements. TS, RA, and OPA indicate a mode-locked Ti:sapphire laser, a regenerative amplifier, and an optical parametric amplifier, respectively. AGS and BBO are $\mathrm{AgGa}{\mathrm{S}}_2$ and $\beta \text{−}\mathrm{Ba}{\mathrm{B}}_2{\mathrm{O}}_4$ crystals, respectively. PD and MCT indicate a photodiode and a photovoltaic HgCdTe detector, respectively. P and LPF represent a polarizer and a low-pass filter, respectively. M, BI, and ADC are a monochromator, a boxcar integrator, and an analog-digital converter, respectively.

Figure 2

Pump-probe spectroscopy energy scheme used in this study. The wide and narrow upward arrows indicate the pump and probe lights, respectively, whereas the downward arrows indicate the biexciton and exciton relaxation. The pump-light photon energy was tuned to the resonant two-photon absorption energy of the biexcitons. The probe-light photon energy was varied to facilitate observation of the absorption from the lowest to the higher excited states.

Figure 3

Temperature dependence of PL spectra under (a) band-to-band weak excitation and (b) resonant two-photon excitation of biexcitons at $43\mu \mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ excitation density. $E_x,I_1$, and 2LO indicate the PL bands of the free exciton, the exciton trapped by the neutral accepters, and the 2LO phonon side band of the free exciton, respectively. $M_T$ and $M_L$ indicate the resonant two-photon Raman scattering associated with the transverse and longitudinal excitons, respectively. (c) Excitation density dependence of PL spectra under resonant two-photon excitation of biexcitons at 3 K. The arrows in (b,c) indicate the two-photon absorption energies of the biexcitons.

Figure 4

IRTA spectra at 3 K for the delay time of (a) 5, (b) 20, (c) 50, (d) 100, and (e) 300 ps. The thin solid curves represent the fitting results for the three Gaussian functions considering the three absorption bands due to the exciton $1s-2p$ state, $1s-3p$ state, and the biexciton ($1s,1s-1s,2p$) state transitions, respectively. The thick solid curves are the sums of the three fitting curves. (f) Absorption spectra for exciton $1s-2p$ states calculated using Eq. (4).

Figure 5

IRTA time profiles at (a) 170 and (b) 175 meV at 3 K. The experimental results were fit using Eq. (2). The dotted and solid curves are the fast- and slow-decay components, respectively, and the thick solid curves are their sums. (c) Fitting parameters $a_1,a_2,a_3$, and $g$ as a function of the delay time, which were obtained from fitting the results to the IRTA spectra, as expressed in Fig. 4.

Figure 6

(a) Transient absorption spectra for different delay times of 10, 50, 200, and 400 ps at 77 K. The downward arrows indicate the photon energies of the time profiles shown in Fig. 7. (b) Absorption spectra of exciton $1s-2p$ states calculated using Eq. (4).

Figure 7

IRTA time profiles at (a) 174- and (b) 182-meV probe photon energies at 77 K. The experimental results were fit using double exponential functions. The dotted and solid curves are the fast- and slow-decay components, respectively, and the thick solid curves are their sums.

Figure 8

(a) Two-photon PL excitation spectra of $I_1$ line from 3 to 50 K. (b) Experimental PLE spectrum at 3 K (solid circles) and fitting curves considering absorption bands of $2p,3p$, and LO-phonon sideband of the $Z_3$ excitons. (c) Temperature dependence of peak energies in PLE spectra. The $2p,3p$, and $2p+1\mathrm{LO}$ energies of the $Z_3$ exciton are associated with the left axis and the $1s$ energy of the same exciton is associated with the right axis. The $2p$ exciton energy measured in the previous report [16] is marked as $A$. In addition, the PL peak energy of the $I_1$ line is shown. (d) Temperature dependence of $2p$-band spectral width. The solid circles indicate the experimental results and the solid curve is the fitting curve obtained from Eq. (5).