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Exploring energy-time entanglement using the dynamics of two-photon absorption

Baihong Li, Holger Friedrich Hofmann

Published Aug 20, 2020• 3 citations
Publisher

Abstract

Two photon absorption processes are known to be sensitive to energy-time entanglement between the absorbed photons. It should therefore be possible to characterize the energy-time entanglement by observing the two photon absorption cross-sections in a known medium controlled by external conditions. In this paper, we analyze the correspondence between two photon absorption and projective measurements of the two photon wavefunction. It is shown that the two photon absorption process is described by a projection onto an energy-time entangled two photon state, indicating that the absorption cross-section can provide direct evidence of entanglement between the absorbed photon pairs.

DOI
10.1117/12.2567320

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Two photon absorption processes are known to be sensitive to energy-time entanglement between the absorbed photons. It should therefore be possible to characterize the energy-time entanglement by observing the two photon absorption cross-sections in a known medium controlled by external conditions. In this paper, we analyze the correspondence between two photon absorption and projective measurements of the two photon wavefunction. It is shown that the two photon absorption process is described by a projection onto an energy-time entangled two photon state, indicating that the absorption cross-section can provide direct evidence of entanglement between the absorbed photon pairs.
It is well known that energy-time entanglement can enhance two-photon absorption (TPA) by simultaneously optimizing the two-photon resonance and the coincidence rate of photons at the absorber. However, the precise relation between entanglement and the TPA rate depends on the coherences of intermediate states involved in the transition, making it a rather challenging task to identify universal features of TPA processes. In the present paper, we show that the theory can be simplified greatly by separating the two-photon resonance from the temporal dynamics of the intermediate levels. The result is a description of the role of entanglement in the TPA process by a one-dimensional coherence in the Hilbert space defined by the arrival-time difference of the two photons. Transformation into the frequency-difference basis results in Kramers-Kronig relations for the TPA process, separating off-resonant contributions of virtual levels from resonant contributions. In particular, it can be shown that off-resonant contributions are insensitive to the frequencies of the associated virtual states, indicating that virtual-state spectroscopy of levels above the final two-photon excited state is not possible.
Energy-time entanglement can enhance two photon absorption by combining a precise two photon resonance with temporal correlations between the arrival times of the two photons. In general, the optimal timing of photon arrival is determined by the dynamics of the system between the initial and the final excitations. In this presentation, we show that the optimal timing of photon arrival corresponds to a specific phase dispersion in the frequency difference of the two photons. The absorption cross-section of energy-time entangled photons can be enhanced beyond the rate observed for optimal photon coincidence by adjusting the phase dispersion of one of the photons to match the optimal characteristics. We determine the maximal enhancement factor as a function of the bandwidth of the intermediate states and their detuning relative to the average photon frequency. Significant additional enhancements can be achieved when the bandwidth of the intermediate states is very narrow.
We present an ongoing experiment to investigate the potential enhancement of the two-photon absorption (TPA) rate of an atom using time–frequency-entangled photon pairs, a process known as entangled two-photon absorption (ETPA). There has been significant debate in the literature regarding the existence and magnitude of such enhancement. Previous studies have primarily focused on ETPA in molecular fluorophores, which are relevant for biological imaging applications but typically exhibit relatively low two-photon cross sections, often not exceeding 10⁻⁵⁰ cm⁴s/photon. In this work, we sacrifice broad applicability for experimental practicality, and instead probe ETPA in rubidium vapor, which has a comparatively large two-photon cross section (∼10⁻¹⁸ cm⁴s/photon) relative to most molecular fluorophores used in prior studies. We have developed and characterized an entangled photon-pair source, and have observed two-photon absorption in rubidium vapor. We have also reproduced previous theoretical models of ETPA. Preliminary results are presented, along with a discussion of the future direction of the experiment.
Entangled two-photon absorption (ETPA) has recently become a topic of lively debate, mainly due to the apparent inconsistencies in the experimentally-reported ETPA cross sections of organic molecules. In this work, we provide a thorough experimental study of ETPA in the organic molecules Rhodamine B (RhB) and Zinc Tetraphenylporphirin (ZnTPP). The goal of this contribution is twofold: on one hand, it seeks to reproduce the results of previous experimental reports and, on the other, it aims to determine the effects of different temporal correlations -- introduced as a controllable time-delay between the photons to be absorbed -- on the strength of the ETPA signal. In our experiment, the samples are excited by entangled pairs produced by type-I SPDC, with a spectral distribution centered at 810 nm. Surprisingly, and contrary to what was expected, the time delay did not produce in our experiments any systematic change in the cross-sections when monitoring the ETPA signal using a transmission measurement scheme. As a plausible cause of this unexpected result, we argue that the photon-pair flux, typically-used in these experiments, is not sufficient to promote the two-photon absorption process in these molecules. This suggests that the actual absorption cross-section values are lower than those previously reported, and therefore do not lead to a measurable ETPA effect for the transmission method.