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arXiv:2412.12402 · Physical Review A

Perturbation-theory approach for predicting vibronic selectivity by entangled-photon-pair absorption

Christian David Rodríguez-Camargo, Hallmann Óskar Gestsson, Charlie Nation, Alex R. Jones, Alexandra Olaya-Castro

Published Jun 2, 2025• 5 citations
arXivHTMLPDF

Abstract

Using second-order perturbation theory in the light-matter interaction, we derive an analytical approximation for the vibronic populations of a diatomic system excited by ultrabroadband frequency-entangled photons and evaluate the population dynamics for different degrees of entanglement between photon pairs. Our analytical approach makes the same predictions as previously derived via numerical solutions of the complete Schrödinger equation [H. Oka, ], with the added advantage of providing clear physical insights into the vibronic selectivity as a function of the degree of photon correlations while requiring significantly reduced computational effort. Specifically, our analytical expression for the probability of vibronic excitation includes a factor which predicts the enhancement of vibrational selectivity as a function of the degree correlation between the entangled photon pairs, the targeted vibrational energy level, and the vibrational molecular structure encoded in the Franck-Condon factors. Our results illustrate the importance of going beyond the usual approximations in second-order perturbation theory to capture the relevance of the vibrational structure of the molecular system of interest in order to gain a deeper understanding of the possible quantum-enhancement provided by the interaction between quantum light and matter.

DOI
10.1103/physreva.111.063101

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Using second-order perturbation theory in the light-matter interaction, we derive an analytical approximation for the vibronic populations of a diatomic system excited by ultrabroadband frequency-entangled photons and evaluate the population dynamics for different degrees of entanglement between photon pairs. Our analytical approach makes the same predictions as previously derived via numerical solutions of the complete Schrödinger equation [H. Oka, ], with the added advantage of providing clear physical insights into the vibronic selectivity as a function of the degree of photon correlations while requiring significantly reduced computational effort. Specifically, our analytical expression for the probability of vibronic excitation includes a factor which predicts the enhancement of vibrational selectivity as a function of the degree correlation between the entangled photon pairs, the targeted vibrational energy level, and the vibrational molecular structure encoded in the Franck-Condon factors. Our results illustrate the importance of going beyond the usual approximations in second-order perturbation theory to capture the relevance of the vibrational structure of the molecular system of interest in order to gain a deeper understanding of the possible quantum-enhancement provided by the interaction between quantum light and matter.
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A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.
We propose an alternative formulation of the sensor method presented in Phys. Rev. Lett. 109, 183601 (2012) for the calculation of frequency-filtered and time-resolved photon correlations. Our approach is based on an algebraic expansion of the joint steady state of quantum emitter and sensors with respect to the emitter-sensor coupling parameter $\ensuremath{\epsilon}$. This allows us to express photon correlations in terms of the open quantum dynamics of the emitting system only and ensures that computation of correlations are independent on the choice of a small value of $\ensuremath{\epsilon}$. Moreover, using time-dependent perturbation theory, we are able to express the frequency- and time-resolved second-order photon correlation as the addition of three components, each of which gives insight into the physical processes dominating the correlation at different time scales. We consider a bioinspired vibronic dimer model to illustrate the agreement between the original formulation and our approach.
The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.
Quantum entanglement offers an incredible resource for enhancing the sensing and spectroscopic probes. Here we develop a microscopic theory for the stimulated Raman scattering (SRS) using entangled photons. We demonstrate that the time-energy correlation of the photon pairs can optimize the signal for polyatomic molecules. Our results show that the spectral-line intensity of the entangled-photon SRS (ESRS) is of the same order of magnitude as the one for the entangled two-photon absorption (ETPA); the parameter window is thus identified to do so. Moreover, the vibrational coherence is found to play an important role for enhancing the ESRS against the ETPA intensity. Our work paves a firm road for extending the schemes of molecular spectroscopy with quantum light, based on the observation of the ETPA in experiments.
Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials and for modeling next-generation nonlinear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.