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The Journal of Chemical Physics

Quantum metrology of pump–probe spectroscopy

Frank Schlawin

Published May 4, 2026• 0 citations
Publisher

Abstract

Pump-probe spectroscopies form an irreplaceable tool for the investigation of ultrafast dynamics and energy relaxation. The extent to which they can benefit from new quantum technologies is an open question and a very active field of research. To provide a solid theoretical foundation for this research, here we formulate the measurement of a molecular relaxation rate with a two-pulse experiment as a parameter estimation problem. We derive a quantum map for the light fields and use it to investigate possible enhancement by the use of squeezed quantum states of light and pump-probe entanglement in the impulsive limit.

DOI
10.1063/5.0323961

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Pump-probe spectroscopies form an irreplaceable tool for the investigation of ultrafast dynamics and energy relaxation. The extent to which they can benefit from new quantum technologies is an open question and a very active field of research. To provide a solid theoretical foundation for this research, here we formulate the measurement of a molecular relaxation rate with a two-pulse experiment as a parameter estimation problem. We derive a quantum map for the light fields and use it to investigate possible enhancement by the use of squeezed quantum states of light and pump-probe entanglement in the impulsive limit.
A two level model of a single molecule undergoing spectral diffusion dynamics and interacting with a sequence of two short laser pulses is investigated. Analytical solution for the probability of n=0,1,2 photon emission events for the telegraph and Gaussian processes is obtained. We examine under what circumstances the photon statistics emerging from such pump-probe setup provides new information on the stochastic process parameters and what are the measurement limitations of this technique. The impulsive and selective limits, the semiclassical approximation, and the fast modulation limit exhibit general behaviors of this new type of spectroscopy. We show that in the fast modulation limit, where one has to use impulsive pulses in order to obtain meaningful results, the information on the photon statistics is contained in the molecule's dipole correlation function, equivalently to continuous wave experiments. In contrast, the photon statistics obtained within the selective limit depends on the both spectral shifts and rates and exhibits oscillations, which are not found in the corresponding line shape.
Squeezed light is expected to enable new quantum metrology and quantum computation applications, but the very high degree of experimental control required in practice places severe demands on the physical devices used to generate it. As ultrafast squeezed light sources are reaching an unprecedented degree of brightness and modal control, there is a strong interest in developing methods for their experimental characterization and theoretical understanding. In this thesis, we demonstrate both a new application and a new characterization technique for pulsed squeezed light. In the first part of the thesis, we present a new metrological application of pulsed squeezed light: quantum-enhanced label-free nonlinear microscopy. Stimulated emission microscopy (SEM) is a state-of-the-art pump-probe microscopy technique whose sensitivity is ultimately limited by shot noise in the probe beam. We propose to overcome this fundamental limitation by using a sub-Poissonian probe generated via optical parametric amplification. We demonstrate an intensity-squeezed sub-picosecond pulsed probe, and a simple stimulated emission microscope. Using this squeezed probe, sub-Poissonian statistics are observed in the SEM signal. After this proof-of-principle experiment, we aim to provide an improved design for a source of intensity-squeezed light. First, we develop a theoretical framework to simulate the photon statistics of a general sub-Poissonian source, considering pulsed and focused pump and seed fields in a unified spatio-temporal description. Next, we use this framework to suggest possible improvements to our previous squeezed probe. In the second part of this thesis, we provide new theoretical and experimental tools to analyze the high gain regime of pulsed spontaneous parametric down-conversion (SPDC). We study a waveguided source capable of generating twin-beams with tens of photons in a single spatio-temporal mode. We develop a framework to efficiently simulate SPDC for an arbitrary nonlinear gain, including the effect of parasitic nonlinearities such as self-phase modulation (SPM) of the pump and cross-phase modulation (XPM) between pump and twin-beams. We experimentally characterize our source using a new technique based on stimulated difference-frequency generation (DFG). In a type-II down-conversion process, we measure the frequency generation produced not only in the orthogonal polarization to the seeding beam, but also in its same polarization, which we interpret as cascaded difference-frequency generation. We argue that the additional information obtained in this measurement allows for a self-referenced estimation of the squeezing gain. Using these measurements, we accurately fit our theoretical model, revealing that, in the high gain regime, parasitic nonlinearities strongly affect the spectral structure of the twin-beams. We propose a simple strategy to reduce the impact of these nonlinearities on the modal structure of SPDC.
Revealing possible long-living coherence in ultrafast processes allows detecting genuine quantum mechanical effects in molecules. To investigate such effects from a quantum chemistry perspective, we have developed a method for simulating the time evolution of molecular systems based on ab initio calculations, which includes relaxation and environment-induced dephasing of the molecular wave function whose rates are external parameters. The proposed approach combines a quantum chemistry description of the molecular target with a real-time propagation scheme within the time-dependent stochastic Schrödinger equation. Moreover, it allows a quantitative characterization of the state and dynamics coherence through the l1-norm of coherence and the linear entropy, respectively. To test the approach, we have simulated femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well-studied fluorophore in single-molecule spectroscopy. Our approach is able to reproduce the experimental findings [R. Hildner et al., Nat. Phys. 7, 172 (2011)], confirming the usefulness of the approach and the correctness of the implementation.
We present a fully quantum theory of time-resolved transient absorption spectroscopy, providing a general framework for describing the linear response of a nonequilibrium target to quantum probe fields beyond the semiclassical approximation. We elucidate how quantum correlations between probe-field frequency modes couple to coherences in the target and derive a simple expression for computing the resulting spectroscopic signals. We identify conditions under which quantum light can modify transient absorption spectra beyond the limits achievable with classical fields. Our work establishes a theoretical foundation for exploiting quantum light in ultrafast spectroscopy and suggests new routes for resolving dynamics in matter on timescales shorter than the duration of the probe pulse.
Squeezed photons, which provide a quantum-correlated light with reduced noise, have emerged as a powerful resource for sensing the structures of matter. Here, we study the pump-probe scheme using squeezed photons whose spectral correlation of amplitudes can be tailored. A microscopic theory reveals a highly time-energy-resolved signal that is not attainable by classical pump-probe scheme. The results show high selectivity of accessing the molecular correlation functions, e.g., suppression of ground-state bleaching signal, and can significantly enhance signal intensity that surpasses the bottleneck by entangled twin photons. An application to a monolayer semiconductor model reveals a real-time monitoring of valley excitons and their dynamics, i.e., conversion between dark and bright excitons. We further show the intermediate squeezing regime-not strong squeezing-where time-resolved spectroscopy is favorable. Our work offers a paradigm for studying nonequilibrium dynamics of matter, in photocatalysis and optoelectronics.