Efficient Modeling of Organic Chromophores for Entangled Two-Photon Absorption

Abstract

The use of a nonclassical light source for studying molecular electronic structure has been of great interest in many applications. Here we report a theoretical study of entangled two-photon absorption (ETPA) in organic chromophores, and we provide new insight into the quantitative relation between ETPA and the corresponding unentangled TPA based on the significantly different line widths associated with entangled and unentangled processes. A sumover-states approach is used to obtain classical TPA and ETPA cross sections and to explore the contribution of each electronic state to the ETPA process. The transition moments and energies needed for this calculation were obtained from a second linear-response (SLR) TDDFT method [J. Chem. Phys., 2016, 144, 204105], which enables the treatment of relatively large polythiophene dendrimers that serve as two-photon absorbers. In addition, the SLR calculations provide estimates of the excited state radiative line width, which we relate to the entangled two-photon density of states using a quantum electrodynamic analysis. This analysis shows that for the dendrimers being studied, the line width for ETPA is orders of magnitude narrower than for TPA, corresponding to highly entangled photons with a large Schmidt number. The calculated cross sections are in good agreement with the experimentally reported values. We also carried out a state-resolved analysis to unveil pathways for the ETPA process, and these demonstrate significant interference behavior. We emphasize that the use of entangled photons in TPA process plays a critical role in probing the detailed electronic structure of a molecule by probing light-matter interference nature in the quantum limit.

How to optimize the absorption of two entangled photons

“…According to (36), strong entanglement S requires L 1 and thus small r 1 , which implies strong quantum enhancement E q , by (38). We test this mutual relationship in Fig.…”

“…5 As shown in [40], the optimal separable state can be obtained with the same optimization procedure of Sec. 3.1, and it is simply given by the modes pertaining to the largest Schmidt coefficient r 1 in (36),…”

“…Yet, a key problem in the practical application, currently, is the low absorption cross section of many samples [31][32][33][34], unless the two-photon transition can proceed through near-resonant intermediate states [35]. In this case [36], the shaping of entangled photonic wave functions [37][38][39] can enhance the absorption probability. This strategy was explored in a number of recent theoretical papers, where the crucial role of quantum correlations between different travelling modes [40][41][42], or of the quantum statistics of a cavity mode [43], was highlighted.…”

“…Figure2: Entanglement entropy S as defined in(36), and quantum enhancement E q given in(38), of the excited state population p f (t)(25) achieved by the optimal two photon state(32) for (a) fixed detuning ∆ = 5 with variable deviation δ ∈ (−2; 2] (note the colour code, and specific values indicated by labels), and (b) fixed deviation δ = −1.9 with variable detuning ∆ ∈ [0.1; 100] (colour coded and labeled). The dashed lines indicate the maximally achievable entanglement and quantum enhancement, respectively, in the limit ∆ → ∞.…”

Designing high-power, octave spanning entangled photon sources for quantum spectroscopy

“…As a result, two entangled photons leave the same side of a beamsplitter 3 and diffract from a grating at the wavelength of the pump photon [4][5][6] . Entangled photon pairs also linearize multiphoton and nonlinear spectroscopy, as has been well-studied in two photon absorption and fluorescence [7][8][9][10][11][12][13] . Entangled photons also have non-Fourier reciprocal spectral-temporal resolutions and are able to yield spatial resolutions which scale inversely with the number of correlated entangled photons N [14][15][16][17][18] .…”