Coherent multidimensional spectroscopy probes interactions and dynamics of molecular systems through nonlinear optical signals. Quantum light excitation has been explored as a means of controlling these signals, raising the question of how excitation-light correlations affect the precision of molecular parameter estimation from the emitted signal. In this work, we show that photon-number correlations and two-photon coherence play distinct roles in encoding molecular information in the emitted rephasing signal. In the weak-emission regime and within the single Schmidt pair approximation, we derive a normally ordered information law in which the joint photon-number moment and the squared magnitude of the two-photon coherence weight the amplitude and phase sensitivities of the molecular response, respectively. For matched temporal modes and mean photon numbers in each input mode, two-mode squeezed vacuum enhances both weights relative to coherent excitation, whereas independent displaced squeezing preserves the amplitude weight but reduces the phase weight. The background population and its parameter dependence also affect the total quantum Fisher information, which therefore cannot be inferred from the coherent mean-field signal alone. We derive a leading-order bound on its enhancement over coherent excitation when the background population is nonnegative and common to the compared sources. These findings provide criteria for selecting excitation sources according to how the target molecular parameter affects the amplitude and phase of the response.
Coherent multidimensional spectroscopy probes interactions and dynamics of molecular systems through nonlinear optical signals. Quantum light excitation has been explored as a means of controlling these signals, raising the question of how excitation-light correlations affect the precision of molecular parameter estimation from the emitted signal. In this work, we show that photon-number correlations and two-photon coherence play distinct roles in encoding molecular information in the emitted rephasing signal. In the weak-emission regime and within the single Schmidt pair approximation, we derive a normally ordered information law in which the joint photon-number moment and the squared magnitude of the two-photon coherence weight the amplitude and phase sensitivities of the molecular response, respectively. For matched temporal modes and mean photon numbers in each input mode, two-mode squeezed vacuum enhances both weights relative to coherent excitation, whereas independent displaced squeezing preserves the amplitude weight but reduces the phase weight. The background population and its parameter dependence also affect the total quantum Fisher information, which therefore cannot be inferred from the coherent mean-field signal alone. We derive a leading-order bound on its enhancement over coherent excitation when the background population is nonnegative and common to the compared sources. These findings provide criteria for selecting excitation sources according to how the target molecular parameter affects the amplitude and phase of the response.
In recent years quantum metrology and quantum sensing have enabled the advancement of quantum technologies and research in fundamental physics. Through statistical analysis, in the context of parameter estimation, the amount of information about a parameter of interest encoded in a quantum state can be quantified. In this thesis we focus on the application of quantum estimation theory to imaging and spectroscopy with quantum light. We study the fundamental bound of the mean square error for an unbiased estimator in terms of the quantum Fisher information (QFI) for two problems, one in microscopy and one in spectroscopy. Firstly, we study the problem of localising multiple point sources below the diffraction limit. We show that localisation microscopy of multiple weak, incoherent point sources with possibly different intensities in one spatial dimension is equivalent to estimating the amplitudes of a classical mixture of coherent states of a simple harmonic oscillator. We obtain the QFI matrix elements analytically. In the regime of arbitrarily small separations we find it to be no more than rank two – implying that no more than two independent parameters can be estimated irrespective of the number of point sources. We use the eigenvalues of the classical and quantum Fisher information matrices to compare the performance of spatial-mode demultiplexing and direct imaging in localisation microscopy with respect to the quantum limits. Secondly, we study the estimation of the electric dipole moment (EDM) of a two-level atom through its interaction with quantum pulses of light in free space. We derive analytical expressions for the states of one-photon wavepackets and entangled photon pairs (EPP). We numerically calculate the QFI for different states of light, including coherent and squeezed pulses, and compare their performance in estimating the EDM. We find that the one-photon wavepacket and the EPP have similar performances, while the performance of the entangled photon pair is not improved by increasing the entanglement of the EPP. Our results indicate that using Fock states to estimate the EDM of a two-level atom is preferable to using entangled light.
We find the optimal initial states of a linearized cavity-optomechanical system for estimating the single-photon coupling by quantum Fisher information. In the red-detuned (beam-splitter) regime the interaction exchanges excitations between the two modes, and for pure inputs the Fisher information is four times the variance of the excitation-exchange operator, reducing the optimization to variance maximization with a closed-form solution. With the mechanical mode in a Fock state the probe is degenerate: any state saturating the photon-number constraint is optimal, and a Fock reference with many phonons enhances the per-photon sensitivity linearly. For an arbitrary fixed mechanical reference it becomes a phase-matched squeezed vacuum, from an exact bound on that coherence obtained by a Lagrange-dual argument. Jointly optimizing both modes at fixed total excitation number, the quantum Fisher information obeys a Heisenberg bound quadratic in the energy, saturated by equal superpositions of the two extremal eigenstates of the generator, equivalently a two-mode NOON state after a balanced beam splitter; balanced product Fock states reach only a linear enhancement. Exact diagonalization in truncated Fock spaces confirms all the results, the familiar single-photon input being the simplest saturating case. Three extensions are worked out: the blue sideband has an unbounded two-mode-squeezing spectrum, so the entangled optimum becomes impossible and the balanced product Fock state is exactly optimal at definite energy; under cavity loss the information accumulation turns linear on the cavity-lifetime timescale, at a renewal-optimal duration of about two and a half lifetimes; and for a state-of-the-art quantum-coherent coupling experiment the per-hour relative precision lies between one part in a million and ten parts in a million, number and thermal references being the most robust.
Entangled photon pairs have been used for molecular spectroscopy in the form of entangled two-photon absorption and in quantum interferometry for precise measurements of light source properties and time delays. We present an experiment that combines molecular spectroscopy and quantum interferometry by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer to study molecular properties. We find that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer, and the resulting signal contains information pertaining to the light-matter interaction. We can extract the dephasing time of the coherent response induced by the excitation on a femtosecond time scale. A dephasing time of 102 fs is obtained, which is relatively short compared to times found with similar methods and considering line width broadening and the instrument entanglement time As the measurement is done with coincidence counts as opposed to simply intensity, it is unaffected by even-order dispersion effects, and because interactions with the molecular state affect the photon correlation, the observed measurement contains only these effects and no other classical losses. The experiments are accompanied by theory that predicts the observed temporal shift and captures the entangled photon joint spectral amplitude and the molecule's transmission in the coincidence counting rate. Thus, we present a proof-of-concept experimental method based of entangled photon interferometry that can be used to characterize optical properties in organic molecules and can in the future be expanded on for more complex spectroscopic studies of nonlinear optical properties.
A structural pattern emerges across five recent results in optical quantum information: the classical-field approximation—the assumption that a bosonic mode with large occupation or a coherent-state input suffices to replace quantum light—fails precisely at the boundaries where quantum-optical resources are most useful. This synthesis, drawing primarily from the **physics.optics** and **quant-ph** categories of the arXiv corpus, argues as a heuristic reading (not a derivation) that photon statistics are not merely a background parameter but are actively imprinted onto observable spectra, metrological sensitivity, and network-level certification. Five specific findings anchor the argument: (1) quantum-light RABBIT spectroscopy maps photon autocorrelation and cross-correlation functions directly onto photoelectron sideband amplitudes and phases [corpus:arxiv:2606.13447]; (2) hot-state displacement sensing shows that thermal mixedness can be compatible with enhanced quantum Fisher information via parity selection or coherence between displaced components, invalidating the assumption that ground-state cooling is a prerequisite [corpus:arxiv:2606.13650]; (3) time-frequency grid states provide a mode-selective, model-free correction framework that improves Gaussian-shape fidelity from 76.2% to 90.0% (hypothesized, as stated in the abstract) without requiring a prior physical distortion model [corpus:arxiv:2606.12216]; (4) nonreciprocal quantum rotation sensing encodes angular velocity into virtual-excitation energy denominators via the Sagnac effect, producing intrinsically direction-dependent quantum Fisher information [corpus:arxiv:2606.10984]; and (5) certified network sensing via bilateral Pauli-twirling forces an effective Bell-diagonal channel structure that simultaneously preserves metrological sensitivity and certifies privacy [corpus:arxiv:2606.10700]. Together, these results suggest a candidate organizing principle: the degree to which photon statistics and mode structure are explicitly tracked—rather than averaged over—determines both the achievable precision and the security of optical quantum information protocols. A concrete falsification path is identified for each claim. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.09759, 2606.09765, 2606.10055, 2606.10700, 2606.10865, 2606.10984, 2606.11882, 2606.12168, 2606.12216, 2606.12313, 2606.13375, 2606.13412, 2606.13447, 2606.13650
It is shown that the maximal phase sensitivity of a two-path interferometer with high-intensity coherent light and squeezed vacuum in the input ports can be achieved by photon-number-resolving detection of only a small number of photons in a dark output port. It is then possible to achieve the quantum Cram\'er-Rao bound of the two-path interferometer using only the field displacement dependence of the photon number statistics in the single mode output of the dark port represented by a field-displaced squeezed vacuum state. We find that, at small field displacements, it is not sufficient to use the average photon number as the estimator, indicating that an optimal phase estimation depends critically on measurements of the precise photon number. We therefore analyze the effect of detection efficiency on the Fisher information and show that there is a transition from low robustness against photon losses associated with quantum interference effects at low field displacements to high robustness against photon losses at high field displacements. The transition between the two regimes occurs at field shifts proportional to the third power of the squeezing factor, indicating that squeezing greatly enhances the phase interval in which quantum effects are relevant in optimal phase estimations using photon resolving detectors. The case under study could thus be understood as a ``missing link'' between genuine multiphoton interference and the straightforward suppression of noise usually associated with squeezed light.
A recurring structural pattern across recent quantum optics and quantum information preprints is that **photon statistics and mode correlations function not merely as resources to be consumed, but as diagnostic channels that encode, transduce, and amplify physical information**. This paper synthesizes six findings from the corpus—spanning phase-estimation probe-state optimization, twin-beam LiDAR under correlated noise, coherence-to-entanglement transduction in high-dimensional systems, frequency upconversion via molecular cavity optomechanics with gain, quantum-optical RABBIT spectroscopy, and bath-memory-enhanced transport precision—into a candidate heuristic framework (explicitly not a unified derivation) in which the photon-statistical structure of a probe or environment determines the achievable sensing precision, the noise resilience, and the information-extraction pathway. Each source is drawn from the quant-ph and physics.optics primary categories of arXiv, selected over the past 30 days for direct relevance to quantum-optical sensing and transduction. The thesis is: **the hierarchy of quantum sensing advantages—from shot-noise to Heisenberg scaling, from local squeezing to entanglement advantage, from Gaussian to non-Gaussian regimes—is controlled by matching the photon-statistical structure of the probe to the correlation structure of the noise and the target signal**. This is a heuristic reading supported by mechanistic parallels across the cited works, not a single shared formalism. The central falsification path is: construct a sensing scenario in which the optimal probe state predicted by the photon-statistics-matching principle conflicts with the independently computed quantum Cramér-Rao bound; if such a conflict is found, the framework requires revision or abandonment. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.12383, 2606.13447, 2606.16548, 2606.16695, 2606.16712, 2606.16854, 2606.16916, 2606.17026, 2606.17877, 2606.17899, 2606.17907, 2606.17908, 2606.17956, 2606.18035, 2606.18133, 2606.18145, 2606.18167, 2606.18169, 2606.18240