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Theoretical & experimental entangled two-photon absorption in cesium atoms

Michael Stiven Caracas Núñez

Published Feb 5, 2025• 0 citations
OpenAlex

Abstract

The Two-photon absorption processes (TPA) is of great interest due to its variety of technical applications. Two-photon transitions can be excited using light with different statistical properties, such as laser light (coherent light), pseudo-thermal light and entangled photons-pairs (ETPA). For a TPA process driven with entangled photons (ETPA), a linear dependence of the signal with the photon flux has been theoretically predicted and experimentally demonstrated by various groups. The main motivation for studying ETPA relies on the capability of inducing TPA with a low photon flux. This is advantageous to analyze, among other things, biological samples with a reduced probability of destroying them in the process. However, ETPA experiments developed to date raise many questions regarding the difficulty of isolating a signal in organic molecules. One of the main problems in these experiments is the difficulty to study independently all the systematic effects due to the complex structure of organic molecules. An alternative to clarify the origin of the signal is to study the ETPA process in atomic systems. In this case, the possibility to excite narrow band transitions with tunable single frequency lasers can provide a clear signature of the ETPA process. To achieve this objective, the first step consists of understanding TPA with coherent light, or classical TPA, and measuring the corresponding cross-section in atomic systems. Once the classical regime is characterized, the ETPA process can be studied considering decoherence effects and coherence between intermediate states. For this, the ETPA cross section must be calculated and measured. In this work we present a theoretical calculation of the ETPA transition probability and cross-section with the density operator formalism for the transition 62S1/2 →82S1/2. The theoretical results will be complemented with an experiment with atomic Cesium based in a coincidence detection scheme.

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Theoretical and experimental study of the 6S-8S two-photon absorption cross-section in cesium atoms

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The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.

Optics Express•Aug 14, 2023•4 citations
The Two-photon absorption processes (TPA) is of great interest due to its variety of technical applications. Two-photon transitions can be excited using light with different statistical properties, such as laser light (coherent light), pseudo-thermal light and entangled photons-pairs (ETPA). For a TPA process driven with entangled photons (ETPA), a linear dependence of the signal with the photon flux has been theoretically predicted and experimentally demonstrated by various groups. The main motivation for studying ETPA relies on the capability of inducing TPA with a low photon flux. This is advantageous to analyze, among other things, biological samples with a reduced probability of destroying them in the process. However, ETPA experiments developed to date raise many questions regarding the difficulty of isolating a signal in organic molecules. One of the main problems in these experiments is the difficulty to study independently all the systematic effects due to the complex structure of organic molecules. An alternative to clarify the origin of the signal is to study the ETPA process in atomic systems. In this case, the possibility to excite narrow band transitions with tunable single frequency lasers can provide a clear signature of the ETPA process. To achieve this objective, the first step consists of understanding TPA with coherent light, or classical TPA, and measuring the corresponding cross-section in atomic systems. Once the classical regime is characterized, the ETPA process can be studied considering decoherence effects and coherence between intermediate states. For this, the ETPA cross section must be calculated and measured. In this work we present a theoretical calculation of the ETPA transition probability and cross-section with the density operator formalism for the transition 62S1/2 →82S1/2. The theoretical results will be complemented with an experiment with atomic Cesium based in a coincidence detection scheme.
The discrepancies between theoretical and experimental results in the process of entangled two-photon absorption (ETPA) are not fully understood. Atomic systems are a promising alternative for investigating this process without the systematic effects present in molecules. We present a theoretical study of the ETPA process in cesium atoms, focusing on the 6S1/2 --> 8S1/2 transition. The ETPA cross section is evaluated both with and without the far-off-resonance (FOR) approximation, including the contributions from intermediate atomic states and decoherence effects. The quantum state of light considered is described by the joint spectral amplitude of photon-pairs produced by the spontaneous parametric down-conversion process. When the FOR approximation is applied, the enhancement factor is constant (36*pi). In contrast, without this approximation the enhancement factor oscillates with the entanglement time, and achieves a maximum value of ~500. These results show the limitations of approximations when calculating the ETPA cross section and contribute to the understanding of the discrepancies between theoretical and experimental values for the ETPA cross section in different samples. The numbers presented in this work can be a starting point for designing experiments aimed at measuring ETPA cross sections in alkali atoms.
Multiphoton absorption of entangled photons offers ways for obtaining unique information about chemical and biological processes. Measurements with entangled photons may enable sensing biological signatures with high selectivity and at very low light levels to protect against photodamage. In this paper, we present a theoretical and experimental study of the excitation wavelength dependence of the entangled two-photon absorption (ETPA) process in a molecular system, which provides insights into how entanglement affects molecular spectra. We demonstrate that the ETPA excitation spectrum can be different from that of classical TPA as well as that for one-photon resonant absorption (OPA) with photons of doubled frequency. These results are modeled by assuming the ETPA cross-section is governed by a two-photon excited state radiative linewidth rather than by electron-phonon interactions, and this leads to excitation spectra that match the observed results. Further, we find that the two-photon-allowed states with highest TPA and ETPA intensities have high electronic entanglements, with ETPA especially favoring states with the longest radiative lifetimes. These results provide concepts for the development of quantum light-based spectroscopy and microscopy that will lead to much higher efficiency of ETPA sensors and low-intensity detection schemes.
Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory and then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration, we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. This Tutorial includes a review of known theoretical methods and results as well as some extensions, especially the comparison of TPA processes that occur via far-off-resonant intermediate states only and those that involve off-resonant intermediate states by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled two-photon absorption is also given.
The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.