Assessing the classicality of photon echo from excitons in lead halide perovskite nanocrystals

Abstract

Photon echo (PE) spectroscopy is a powerful technique for probing decoherence mechanisms and charge carrier dynamics in semiconductor systems. Beyond traditional coherence measurements, characterizing the photon statistics of the echo signal is important for assessing its potential in quantum information applications and understanding the underlying quantum mechanical processes. Here, we study the photon statistics of PE signals generated by excitons in ensembles of lead halide perovskite CsPbI$_3$ nanocrystals at cryogenic temperature of 2 K using continuous-variable quantum state optical tomography based on homodyne detection. Pronounced Rabi oscillations of PE amplitude allow us to evaluate the statistics for various pulse areas in the excitation sequence. The damping of the oscillations with increasing pulse area is attributed to spatial excitation inhomogeneity and excitation-induced dephasing. Despite the large ensemble of optically addressed excitons, the efficiency of generated PE signals is low which is attributed to complex energy structure of excitons and non-radiative recombination channels in CsPbI$_3$ nanocrystals. We analyze the statistical characteristics of PE via the second-order correlation function $g^{(2)}(0)$ and the characteristic function for different combinations of the areas of the excitation pulses. Our results show that $g^{(2)}(0) = 1$, and the characteristic function of the PE signal corresponds to classical behavior. Despite the relatively low efficiency, the photon echo exhibits a high degree of coherence and minimal classical noise, consistent with Poissonian statistics.

Figures (10)

• Figure 1: Photoluminescence (PL, dashed blue line) and absorption coeficient $\alpha(h\nu) L$ (solid red line) spectra of a CsPbI$_3$ nanocrystals measured at $T=2$ K. The PL spectrum was measured in back reflection geometry under excitation with photon energy of 2.33 eV. The laser spectrum used in the PE measurements is shown with dotted magenta line. Inset shows CsPbI$_3$ perovskite crystal structure.
• Figure 2: Schematic presentation of the experimental setup for measuring and characterizing the photon echo. Notations: BS -- beam-splitter; PBS -- polarizing beamsplitter; DL -- delay line, HWP -- half waveplate, QWP -- quarter waveplate. PE -- photon echo, ref -- reference. The inset shows a close-up of the sample in the cryostat with the excitation and four-wave mixing beam geometry.
• Figure 3: (a) The blue curve represents a cross-correlation measurement between the reference and attenuated second excitation pulse (about 20 photons per pulse). The green curve is the corresponding deviation angle of the oscillating glass plate around the incidence angle $\gamma_0=0.27$ rad. Each segment (b) represents about $7\times10^4$ quadrature points collected at the center of the glass plate’s linear ramp. The blue curve shows the experimental data and the red curve is the sinusoidal fitting curve used to determine the phase for each quadrature point. (c) The segment shape for the PE signal, illustrating the double-frequency modulation compared to single frequency modulation for the excitation laser pulse shown in (b). (d) A histogram shows the initial unequal distribution of the number of quadrature, and the red dashed line illustrates the level of the distribution of quadrature samples after truncation.
• Figure 4: The histogram of phase-resolved quadratures for a highly attenuated second excitation laser pulse. The figure is based on $3\times 10^7$ acquired data points.
• Figure 5: The PE temporal profile (a) and PE amplitude decay (b) measured for $h\nu= 1.697$ eV, $T=2$ K, $\tau_{12}= 36.7$ ps, $A_1=4.5$ pJ$^{1/2}$, $A_2=9.0$ pJ$^1/2$. Dots correspond to experimental data and lines to the fit with Gaussian (a) and exponential (b) functions.