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arXiv:2603.25996 · Physical Review Research

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

George Alkhalil, Hendrik Rose, Artur V. Trifonov, Polina R. Sharapova, Jan Sperling, Dmitri R. Yakovlev, Elena V. Kolobkova, Maria Kuznetsova, Marc Aßmann, M. Bayer, T. Meier, Ilya A. Akimov

Published Oct 20, 2026• 0 citations
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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 the 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 the complex energy level 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. The formation of photon echoes as well as $g^{(2)}(0) = 1$ at the echo time is reproduced by a quantized free-space multimode model. Despite the relatively low efficiency, the photon echo exhibits a high degree of coherence and minimal classical noise, consistent with Poissonian statistics.

DOI
10.1103/z126-g8bl

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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 CsPbI3_33​ nanocrystals at cryogenic temperature of 2 K using continuous-variable quantum state optical tomography based on homodyne detection. Pronounced Rabi oscillations of the 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 the complex energy level structure of excitons and non-radiative recombination channels in CsPbI3_33​ nanocrystals. We analyze the statistical characteristics of PE via the second-order correlation function g(2)(0)g^{(2)}(0)g(2)(0) and the characteristic function for different combinations of the areas of the excitation pulses. Our results show that g(2)(0)=1g^{(2)}(0) = 1g(2)(0)=1, and the characteristic function of the PE signal corresponds to classical behavior. The formation of photon echoes as well as g(2)(0)=1g^{(2)}(0) = 1g(2)(0)=1 at the echo time is reproduced by a quantized free-space multimode model. Despite the relatively low efficiency, the photon echo exhibits a high degree of coherence and minimal classical noise, consistent with Poissonian statistics.
Halide perovskites show great potential for a variety of optoelectronic applications. The presence of robust exciton resonance in these materials makes them promising for use in information photonics. In this paper, we demonstrate the possibility of writing and delayed reading of the optical coherence in halide perovskite by the spontaneous (two-pulse) photon echo in MAPbI3{\mathrm{MAPbI}}_{3}MAPbI3​ (MA+{\mathrm{MA}}^{+}MA+ = CH3NH3+{\mathrm{CH}}_{3}{\mathrm{NH}}_{3}^{+}CH3​NH3+​) lead-halide perovskite single crystal on picosecond time scales. The spectral and polarimetric measurements of the photon echo signal confirm the free excitonic origin of the excitation under study. Observed relatively long dephasing time, high exciton oscillator strength, and weakly pronounced excitation-induced dephasing make halide perovskites a promising media for applications.
We study Rabi oscillations detected in the coherent optical response from various exciton complexes in a 20-nm-thick CdTe/(Cd,Mg)Te quantum well using time-resolved photon echoes. In order to evaluate the role of exciton localization and inhomogeneous broadening we use selective excitation with spectrally narrow ps pulses. We demonstrate that the transient profile of the photon echo from the localized trion (${\mathrm{X}}^{\ensuremath{-}}$) and the donor-bound exciton (D0X{\mathrm{D}}^{0}\mathrm{X}D0X) transitions strongly depends on the strength of the first pulse. It acquires a non-Gaussian shape and experiences significant advancement for pulse areas larger than $\ensuremath{\pi}$ due to non-negligible inhomogeneity-induced dephasing of the oscillators during the optical excitation. Next, we observe that an increase of the area of either the first (excitation) or the second (rephasing) pulse leads to a significant damping of the photon echo signal, which is strongest for the neutral excitons and less pronounced for the donor-bound exciton complex (D0X{\mathrm{D}}^{0}\mathrm{X}D0X). The measurements are analyzed using a theoretical model based on the optical Bloch equations which accounts for the inhomogeneity of optical transitions in order to reproduce the complex shape of the photon echo transients. In addition, the spreading of Rabi frequencies within the ensemble due to the spatial variation of the intensity of the focused Gaussian beams and excitation-induced dephasing are incorporated in our model, which is able to explain the fading and damping of Rabi oscillations. By analyzing the results of the simulation for ${\mathrm{X}}^{\ensuremath{-}}$ and D0X{\mathrm{D}}^{0}\mathrm{X}D0X complexes we are able to establish a correlation between the degree of localization and the transition dipole moments determined as $\ensuremath{\mu}({\mathrm{X}}^{\ensuremath{-}}$)=73 D and $\ensuremath{\mu}({\mathrm{D}}^{0}\mathrm{X}$)=58 D.
An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
An ensemble of quantum dot excitons may be used for coherent information manipulation. Due to the ensemble inhomogeneity any optical information retrieval occurs in the form of a photon echo. We show that the inhomogeneity can lead to a significant deviation from the conventional echo timing sequence. Variation of the area of the initial rotation pulse, which generates excitons in a dot subensemble only, reveals this complex picture of photon echo formation. We observe a retarded echo for $\ensuremath{\pi}/2$ pulses, while for $3\ensuremath{\pi}/2$ the echo is advanced in time as evidenced through monitoring the Rabi oscillations in the time-resolved photon echo amplitude from (In,Ga)As/GaAs self-assembled quantum dot structures and confirmed by detailed calculations.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver detailed information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φφφ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a 20-nm-thick CdTe/(Cd,Mg)Te quantum well at temperature of 1.5~K. Applying narrow-band optical excitation we selectively excite different exciton complexes including the exciton, the trion, and the donor-bound exciton D0^00X. We find that polarimetry of the photon echo on the trion and D0^00X is substantially different from the exciton: The echoes of the trion and D0^00X are linearly polarized at the angle 2φ2φ2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φφφ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cos⁡φ\cosφcosφ.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver rich information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a CdTe/(Cd, Mg)Te quantum well. The echoes of the trion and donor-bound exciton are linearly polarized at the angle 2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cosφ.