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.
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.
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.
Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks. A comprehensive framework recently established that broad families of quantum states can attain the Heisenberg limit, surpassing any classical strategy. This raises a fundamental question: among all quantum-enhanced strategies, which is truly optimal? Answering this requires identifying physically meaningful resources governing each estimation task, so quantum states can be compared on equal footing. We show these resources are connected to the eigenmode basis of the generator of the relevant mode transformation. For time-shift estimation, whose generator is diagonal in the frequency domain, the pertinent resources are the mean frequency and bandwidth; analogous quantities emerge for other transformations. Our framework unifies two historically separate perspectives: the particle-number aspect and the mode-structure of quantum light, providing a coherent picture of quantum-enhanced sensing with multimode radiation. Within this unified framework, we derive a tight upper bound on the quantum Fisher information for multimode Gaussian states, expressed in terms of these natural resources, and analytically identify the optimal Gaussian states saturating it. These optimal states take a particularly transparent form in the generator eigenbasis, a structural simplicity reflecting the deep connection between the geometry of the mode transformation and the architecture of the optimal probe. We further demonstrate that multimode homodyne detection constitutes the optimal measurement, achieving this bound and completing the end-to-end characterization of optimal quantum metrology strategies for mode parameter estimation.
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and the design of optimized measurement observables. We discuss precision limits and optimal strategies in quantum metrology and sensing with a single mode of quantum continuous variables. We focus on the practically most relevant cases of estimating displacements and rotations and provide the sensitivities of the most important classes of states that includes Gaussian states and superpositions of Fock states or coherent states. Fundamental precision limits that are obtained from the quantum Fisher information are compared to the precision of a simple moment-based estimation strategy based on the data obtained from possibly sub-optimal measurement observables, including homodyne, photon number, parity and higher moments. Finally, we summarize some of the main experimental achievements and present emerging platforms for continuous-variable sensing. These results are of particular interest for experiments with quantum light, trapped ions, mechanical oscillators, and microwave resonators.
Abstract Measuring the spectral properties of an optical frequency comb is among the most fundamental tasks of precision metrology. In contrast to general single-parameter measurement schemes, we demonstrate here single shot multi-parameter estimation of an optical frequency comb at and beyond the standard quantum limit. The mean energy and the central frequency as well as the spectral bandwidth of ultrafast pulses are simultaneously determined with a multi-pixel spectrally resolved (MPSR) apparatus, without changing the photonics architecture. Moreover, using a quantum frequency comb that intrinsically consists of multiple squeezed states in a family of Hermite–Gaussian spectral/temporal modes, the signal-to-noise ratios of the multiple spectral parameters estimation can surpass the standard quantum limit. Combining our multi-pixel detection scheme and the multimode entangled resource could find applications in ultrafast quantum metrology and multimode quantum information processing.
Frequency combs enable precision measurements across timekeeping, spectroscopy, ranging and astronomy, and are now extending to integrated and field-deployable platforms. Realizing their full performance demands a comprehensive account of the quantum noise that arises when broadband optical fields are converted into finite-bandwidth electrical signals. Here we present a rigorous first-principles quantum-mechanical framework for optical frequency-comb metrology based on continuous-mode field quantization and a comb-line-resolved description of quantum fluctuations. The theory describes how quantum fluctuations of the comb field are transduced into electrical measurement noise. Formulated at the level of the comb field, the framework unifies the standard quantum limits of optical frequency division (OFD) and dual-comb spectroscopy (DCS) within a single treatment, and provides a general recipe for other comb-based measurements. On this footing, we identify practical, resource-efficient routes to quantum enhancement through engineered comb states, laying a foundation for the design of next-generation frequency combs operating at and beyond standard quantum limits.
Quantum sensing and metrology promise useful insights and alternative techniques to surpass the measurement limits of a classical framework. Significant improvement has been made in the areas of imaging, positioning, timing, interferometry, communication, and information processing through quantum detection and estimation techniques. In this Letter, we focus on the application of quantum information for spectral measurements. Specifically, we study the quantum limit to resolve two spectral modes with small frequency separation. We show that frequency superresolution can be achieved with spectrotemporal shaping of input fields before detection. Through a numerical optimization algorithm, we design the apparatus for spectrotemporal shaping based on phase modulation and dispersion engineering. This scheme can achieve performance close to the quantum limit with minimum resources, showing the robustness for experimental implementation and real-world applications.