Spectral measurements provide fundamental insights into wave systems by revealing resonances, mode hybridization, and light-matter interactions. However, intrinsic dissipation and measurement-induced spectral broadening often conceal the underlying hybridized light-matter states that give rise to measured spectra. Here, we establish a space-time Fourier correspondence that interprets spectral broadening as an effective temporal attenuation, giving rise to a temporal Fourier optics framework for recovering hidden spectral information. Implemented through a temporal point-spread-function (TPSF) reconstruction method, the framework compensates the effective temporal decay before Fourier transformation, directly reconstructing intrinsic spectral responses from experimentally measured spectra without repeated frequency synthesis or model-dependent fitting. We experimentally validate the approach in deterministic single-molecule Au nanosphere dimers and open Au@Ag nanorod- and nanotriangle-based plasmonic nanocavities coupled to J-aggregate excitons. Across these diverse platforms, TPSF consistently reconstructs hidden upper and lower polaritonic branches, thereby revealing the underlying hybridized light-matter states and strong coupling that remain unresolved in conventional scattering spectra. The reconstructed spectra agree closely with the recently developed complex-frequency formalism while offering a considerably simpler and more experimentally accessible implementation. Beyond strong light-matter coupling, temporal Fourier optics establishes a general framework for uncovering physical states hidden by dissipation, opening new opportunities for spectroscopy, imaging, sensing, and inverse wave measurements across photonics and wave physics.
Spectral measurements provide fundamental insights into wave systems by revealing resonances, mode hybridization, and light-matter interactions. However, intrinsic dissipation and measurement-induced spectral broadening often conceal the underlying hybridized light-matter states that give rise to measured spectra. Here, we establish a space-time Fourier correspondence that interprets spectral broadening as an effective temporal attenuation, giving rise to a temporal Fourier optics framework for recovering hidden spectral information. Implemented through a temporal point-spread-function (TPSF) reconstruction method, the framework compensates the effective temporal decay before Fourier transformation, directly reconstructing intrinsic spectral responses from experimentally measured spectra without repeated frequency synthesis or model-dependent fitting. We experimentally validate the approach in deterministic single-molecule Au nanosphere dimers and open Au@Ag nanorod- and nanotriangle-based plasmonic nanocavities coupled to J-aggregate excitons. Across these diverse platforms, TPSF consistently reconstructs hidden upper and lower polaritonic branches, thereby revealing the underlying hybridized light-matter states and strong coupling that remain unresolved in conventional scattering spectra. The reconstructed spectra agree closely with the recently developed complex-frequency formalism while offering a considerably simpler and more experimentally accessible implementation. Beyond strong light-matter coupling, temporal Fourier optics establishes a general framework for uncovering physical states hidden by dissipation, opening new opportunities for spectroscopy, imaging, sensing, and inverse wave measurements across photonics and wave physics.
Causality implies that by measuring an absorption spectrum, the time-dependent linear response function can be retrieved. Recent experiments suggest a link between the shape of spectral lines observed in absorption spectroscopy with the amplitude and phase of the systems response function. This has even been observed in the presence of strong, nonlinear interactions, which promote the observed system out of equilibrium, making it explicitly time dependent. Thus far, however, only the special case of a sudden modification of the response function was understood analytically, leaving the general case of the dynamical response to arbitrary interactions open to interpretation. Here, we demonstrate that even for the case of a strongly driven, time-dependent system, one can reconstruct the full temporal response information from a single spectrum if a sufficiently short signal is used to trigger the absorption process. This finding is directly applied to a time-domain observation of Rabi cycling between doubly-excited atomic states in the few-femtosecond regime. This general approach unlocks single-shot real-time-resolved signal reconstruction across time scales down to attoseconds for non-equilibrium states of matter. In contrast to available pump-probe schemes, there is no need for scanning time delays in order to access real-time information. The scientific applications of this technique range from testing fundamental quantum dynamics, to measuring and controlling ultrafast, chemical and biological reaction processes.
Ultrafast spectroscopy of molecular systems is fundamentally constrained by the Fourier uncertainty principle: high temporal resolution smears out electronic state signatures, while high spectral resolution obscures dynamic information. Here we overcome this limitation using time-resolved quantum ghost spectroscopy (tr-QGS) with entangled photon pairs, which enables independent control of temporal and spectral scales. We apply this approach to perylene bismide (PBI-1) trimers for energy transfer,by combining a quantum description of light-molecule interaction with time-dependent density matrix renormalization group (TD-DMRG) simulations. This explicitly includes five vibrational modes and nonadiabatic coupling between electronic states. Our simulations reveal that tr-QGS uniquely captures electronic coherence oscillating at 0.7 eV for >50 fs, a signature of nonadiabatic coupling that was obscured in conventional time-resolved fluorescence due to Fourier-limited broadening. Moreover, we observe a direct transfer from electronic to vibrational coherence at 200 fs, providing real-time visualization of vibronic relaxation pathways. The entangled photon correlation enables a sensitivity below the shot-noise limit and suppresses photobleaching artifacts that plague classical measurements. These results establish tr-QGS as a transformative tool for interrogating nonadiabatic dynamics in molecular aggregates, light-harvesting complexes, and photocatalysts, offering a route to reveal quantum coherence in chemistry with unprecedented time-energy precision.
This thesis explores how spectral-temporal structure in quantum optical fields can be used for state reconstruction and metrology. We utilize continuous-frequency modes as a framework for describing quantum correlations and parameter encoding. In the first part, we develop compressive stimulated emission tomography (CSET) to reconstruct the joint spectral amplitude (JSA) of biphoton states generated through spontaneous parametric downconversion. We perform stimulated emission measurements together with compressive sensing methods to recover high-dimensional quantum states from a reduced dataset. Spectral phase is incorporated using frequency-resolved optical gating, which experimentally characterizes the spectral amplitude and phase of the seed pulses and allows them to be directly integrated into the reconstruction model. The resulting inverse problem is formulated as a constrained convex optimization task, enabling recovery of the full complex JSA. Informational completeness certification is used to evaluate the adequacy of the measurement set, and the method is validated using both simulated and experimental data, showing accurate and robust reconstruction under noise and limited sampling. In the second part, we study quantum metrology in structured optical fields, focusing on frequency-comb ranging in dispersive media. We use quantum Fisher information to relate parameter sensitivity to spectral mode geometry. Our results suggest that bandwidth and modal structure play a significant role in determining precision, while squeezing offers limited benefit under loss. Overall, spectral-temporal modes appear to play a central role in both quantum state reconstruction and metrology tasks considered in this work.
Continuously monitored quantum systems are emerging as promising platforms for quantum metrology, where a central challenge is to identify measurement strategies that optimally extract information about unknown parameters encoded in the complex quantum state of emitted radiation. Different measurement strategies effectively access distinct temporal modes of the emitted field, and the resulting choice of mode can strongly impact the information available for parameter estimation. While a ubiquitous approach in quantum optics is to select frequency modes through spectral filtering, the metrological potential of this technique has not yet been systematically quantified. We develop a theoretical framework to assess this potential by modeling spectral detection as a cascaded quantum system, allowing us to reconstruct the full density matrix of frequency-filtered photonic modes and to compute their associated Fisher information. This framework provides a minimal yet general method to benchmark the performance of spectral measurements in quantum optics, allowing to identify optimal filtering strategies in terms of frequency selection, detector linewidth, and metrological gain accessible through higher-order frequency-resolved correlations and mean-field engineering. These results lay the groundwork for identifying and designing optimal sensing strategies in practical quantum-optical platforms.
Drawing on formal parallels between scalar diffraction theory and quantum mechanics, it is demonstrated that quantum wavefunction propagation requires a holographic model of time. Measurable time manifests between interactions as a duration which is encoded in the frequency domain. It is thus a unified entity, and attempts to subdivide these intervals introduce oscillatory artifacts or spectral broadening, altering the system’s physical characteristics. Analogous to spatial holograms, where information is distributed across interference patterns, temporal intervals encode information as a discrete whole. This framework challenges the concept of continuous time evolution, suggesting instead that discrete trajectories define a frequency spectrum which holographically constructs the associated time interval, giving rise to the experimentally observed energy spread of particles in applications such as time-bin entanglement, ultra-fast light pulses, and the temporal double slit. A generalized model of quantum wavefunction propagation based on recursive Fourier transforms is discussed, and novel applications are proposed, including starlight analysis and quantum cryptography.
Broadband optical response governs light-matter interactions across photonics, plasmonics, thermal radiation, and quantum fluctuation electrodynamics, yet determining a continuous dielectric function over many decades in frequency typically requires combining multiple spectroscopies, extrapolations, and material models. Here we show that quantum-fluctuation forces provide a route to broadband optical characterization. Casimir interactions depend on the dielectric response of materials across the electromagnetic spectrum, but this information is encoded through Lifshitz theory in a spectrally weighted and nontrivial way. By training physics-constrained supervised learning models on synthetic dielectric spectra and their corresponding Casimir force curves, we invert this relationship and constrain the complex permittivity of materials over more than seven orders of magnitude in frequency and provide an estimate of their values from force-distance data. The reconstruction reveals a direct separation-frequency correspondence: large separations constrain the free-carrier response, whereas shorter separations encode higher-frequency resonant structure. Applying the method to measured force gradients identifies the current experimental limits imposed by measurement noise, restricted separation range, and model complexity. These results establish fluctuation-induced forces as a spectrally weighted route to broadband optical characterization and define the experimental and physical limits that govern what spectral information is accessible from near-field quantum electromagnetic measurements.