We present a theoretical framework for time-resolved nonlinear microspectroscopy using structured light to probe spatial coherence transfer in condensed-matter systems. Unlike traditional photon echo (PE) spectroscopy, our method employs Laguerre-Gaussian (LG) modes to encode and track quantum coherence migration spatially. By expanding the diffusion propagator in LG modes, we reveal radial mode mixing and conservation of orbital angular momentum during coherence migration. Analytical formulas for heterodyne-detected PE signals and two-dimensional spectra show distinct signatures of spatial coherence transfer in decay and line shapes. This technique allows differentiation between coherent and incoherent transfer, enabling measurement of exciton coherence diffusion constants in materials such as organic semiconductors, perovskites, and two-dimensional materials and provides new insights into coherence dynamics for quantum materials and energy transport applications.
We present a theoretical framework for time-resolved nonlinear microspectroscopy using structured light to probe spatial coherence transfer in condensed-matter systems. Unlike traditional photon echo (PE) spectroscopy, our method employs Laguerre-Gaussian (LG) modes to encode and track quantum coherence migration spatially. By expanding the diffusion propagator in LG modes, we reveal radial mode mixing and conservation of orbital angular momentum during coherence migration. Analytical formulas for heterodyne-detected PE signals and two-dimensional spectra show distinct signatures of spatial coherence transfer in decay and line shapes. This technique allows differentiation between coherent and incoherent transfer, enabling measurement of exciton coherence diffusion constants in materials such as organic semiconductors, perovskites, and two-dimensional materials and provides new insights into coherence dynamics for quantum materials and energy transport applications.
We extend our theoretical framework for time-resolved nonlinear microspectroscopy [M. Cho, J. Chem. Phys. 162, 124201 (2025)] to coherent four-wave-mixing spectroscopy using paraxial Laguerre-Gaussian (LG) beams. Unlike pump-probe or transient absorption techniques, photon echo is highly sensitive to the spatial phase structure of LG beams. This sensitivity arises because coherence evolution in inhomogeneously broadened absorbers depends on the radial and azimuthal indices of the LG modes used in the write-and-read processes within the photon echo configuration. Recent advances in spatial light modulators, metasurfaces, and ultrafast laser techniques have significantly improved spatial and temporal control over quantum materials. These innovations enable new approaches to studying heterogeneous systems, developing multidimensional microspectroscopy, and exploring alternative quantum information storage methods. In this work, we investigate photon echo signals generated by LG beams and derive analytical expressions for rephasing and non-rephasing photon echoes. Our results reveal how beam parameters influence nonlinear spatiotemporal responses, capturing spatial variations in pulse amplitudes, phases, and inhomogeneity-induced dephasing and rephasing. We show that customized ultrafast pulses and structured spatial light fields can enhance the spatial separation of photon echo signals and increase the density of stored quantum information. This work advances nonlinear molecular spectroscopy and quantum information science by leveraging structured light fields and ultrafast optics.
The three-dimensional confinement created by the ultrasmall semiconductor structures known as quantum dots greatly modifies the optical properties of the spatially localized carriers. These systems are presently of great interest to the research community, both for the improved understanding of the physics of confined structures, and for the potential applications of these systems to areas such as optoelectronics and quantum computing. Here, the techniques of transient coherent nonlinear optical spectroscopy are applied to the investigation of excitons confined within InAs/GaAs self-assembled quantum dots. These methods provide a powerful tool for the study of dynamic processes in these novel materials. The nonlinear measurements are based on the differential transmission experimental geometry, and utilize ultrafast pulsed lasers in order to temporally resolve the carrier dynamics after excitation. The experiments performed here are resonant with the ground state absorption of the quantum dots, as evidenced by comparison with the photoluminescence measurements which are used to characterize the sample. The incoherent relaxation dynamics of the population of photoexcited excitons are examined, allowing for a determination of both the lifetime of the excitons and the time scale for relaxation between the two polarization eigenstates of the system. The three-dimensional quantum confinement results in the suppression of these relaxation processes, as predicted. The use of coherent spectroscopic techniques allows for the first unambiguous demonstration of an optically-induced nonradiative Raman coherence in these quantum dots. Simultaneous excitation of both polarization states of the exciton results in a coherent superposition state, whose temporal evolution is observed through the homodyne-detection scheme. In these transient experiments, this is manifested as a beating in the nonlinear response, which allows us to directly measure the fine-structure splitting between the polarization states. Utilizing optical pulse shaping techniques, transient spectral hole burning is performed, which allows for the nonlinear response to be spectrally resolved. As expected for the strongly confined quantum dot excitons, the results show that diffusion among the localized states is not a significant effect. Temperature dependent measurements show that at elevated temperatures, extra dephasing processes, potentially related to acoustic phonon scattering, become important. Finally, this technique allows for the first direct observation of the induced absorption from the exciton to biexciton transition in these InAs quantum dots, and a measurement of the associated binding energy. These results lay the foundation for future studies in this material system, and for the possible development of quantum logic devices utilizing quantum dots.
Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.
Spatially structured photons have attracted a lot of attention in quantum photonics, where they often serve as powerful tools for investigating fundamental properties of light, and for realizing high-dimensional quantum states with beneficial properties in quantum information tasks such as cryptography or quantum simulations [1] . One way of describing any spatial structure, in the paraxial limit, is through orthogonal transverse-spatial modes e.g. Laguerre-Gaussian (LG) modes. A unique feature of higher order LG modes is their twisted phase front, to which a theoretically unbounded orbital angular momentum can be attributed.
Over the past 15 years, researchers have extended the multidimensional techniques which originated with NMR in the 1970s to infrared and visible coherent spectroscopy. These advances have dramatically enhanced the temporal resolution from the microsecond to the femtosecond regime. NMR spectroscopists have developed principles for the design of pulse sequences that enhance selected spectral features and reveal desired dynamical events. Extending these principles to the optical regime offers numerous opportunities for narrowing the line shapes in specific directions, unraveling weak cross-peaks from otherwise congested spectra, and controlling the interferences between quantum pathways. We can achieve these enhancements by shaping the spectral and temporal profiles of the pulses. Pulse polarization shaping may lead to unique probes of time-dependent chirality. In this Account, we compare two types of signals. The first, the photon echo, is generated in the direction -k(1) + k(2) + k(3), and the second, double quantum coherence, is detected at +k(1) + k(2) - k(3). Here k(1), k(2), and k(3) are the wave vectors of the three incoming pulses in chronological order. We illustrate the novel information extracted from these signals by simulations of three physical systems. In the first system, spectra of GaAs semiconductor quantum wells provide a direct look at many-body electron correlation effects. We directly observe specific projections of the many-electron wave function, which we can use to test the quality of various levels of computational techniques for electronic structure. Secondly, the spectra of photosynthetic aggregates reveal couplings between chromophores, quantum coherence signatures of chromophore entanglement, and energy-transfer pathways. Using some fundamental symmetries of pulse polarization configurations of nonlinear signals, we can construct superpositions of signals designed to better distinguish among various coherent and incoherent exciton transport pathways and amplify subtle variations among different species of the Fenna-Matthews-Olson (FMO) antenna complex. Both of the first two applications require femtosecond pulses of light in the visible range. The third application demonstrates how resonant core spectroscopy may be used to generate core excitations that are highly localized at selected atoms. Such signals can monitor the motions of valence electron wavepackets in real space with atomic spatial resolution. These future X-ray applications will require attosecond bright X-ray sources, which are currently being developed in several labs. Common principles underlie these techniques in coherent spectroscopy for spins, valence electrons, and core electronic excitations, spanning frequencies from radiowaves to hard X-rays.
Abstract We study high-resolution atomic localization in a multilevel atomic system driven simultaneously by a Gaussian and a Laguerre–Gaussian (LG) beam. The coexistence of the two fields creates a hybrid coupling landscape in which the Gaussian beam supplies radial confinement, while the LG beam contributes an orbital angular momentum (OAM)-dependent azimuthal modulation. By solving the steady-state density-matrix equations, we show that the resulting localization patterns contain mixed spatial harmonics whose structure is set by the topological charge, beam waist, and probe detuning. The OAM index determines the angular symmetry of the localized absorption features, whereas the beam waist controls their radial extent. Probe detuning provides an additional tuning mechanism that alters the contrast and geometry of the localization regions. These results highlight how structured light fields can be used to engineer controllable spatial localization in atomic media, with relevance to precision metrology, spatially resolved quantum control, and structured-light sensing.