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Quantum Communications and Quantum Imaging

Phase matching between energy-time entanglement and two photon absorption processes

Holger Friedrich Hofmann, Baihong Li

Published Jul 30, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2593479

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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.
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.
Broadband energy-time entanglement can be used to enhance the rate of two-photon absorption (TPA) by combining a precise two-photon resonance with a very short coincidence time. Because of this short coincidence time, broadband TPA is not sensitive to the spectrum of intermediate levels, making it the optimal choice when the intermediate transitions are entirely virtual. In the case of distinct intermediate resonances, it is possible to enhance TPA by introducing a phase dispersion that matches the intermediate resonances. Here, we consider the effects of a phase flip in the single photon spectrum, where the phases of all frequencies above a certain frequency are shifted by half a wavelength relative to the frequencies below this frequency. The frequency at which the phase is flipped can then be scanned to reveal the position of intermediate resonances. We find that a resonant phase flip maximizes the contributions of the asymmetric imaginary part of the dispersion that characterizes a typical resonance, resulting in a considerable enhancement of the TPA rate. Due to the bosonic symmetry of TPA, the enhancement is strongest when the resonance occurs when the frequency difference of the two photons is much higher than the linewidth of the resonance. Our results indicate that broadband entangled TPA with spectral phase flips may be suitable for phase-sensitive spectroscopy at the lower end of the spectrum where direct photon detection is difficult.
When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We use a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrations, and conventional TPA cross sections than are achieved in typical experiments.
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.
Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled photons to enable measurements with enhanced sensitivity and selectivity. Here, we investigate the spectroscopic measurement utilizing entangled three photons. In this measurement, time-resolved entangled photon spectroscopy with monochromatic pumping [A. Ishizaki, J. Chem. Phys. 153, 051102 (2020)] is integrated with the frequency-dispersed two-photon counting technique, which suppresses undesired accidental photon counts in the detector and thus allows one to separate the weak desired signal. This time-resolved frequency-dispersed two-photon counting signal, which is a function of two frequencies, is shown to provide the same information as that of coherent two-dimensional optical spectra. The spectral distribution of the phase-matching function works as a frequency filter to selectively resolve a specific region of the two-dimensional spectra, whereas the excited-state dynamics under investigation are temporally resolved in the time region longer than the entanglement time. The signal is not subject to Fourier limitations on the joint temporal and spectral resolution, and therefore, it is expected to be useful for investigating complex molecular systems in which multiple electronic states are present within a narrow energy range.
Inspired by the unique nonclassical character of two-photon interactions induced by entangled photons, we develop a new comprehensive Förster-type formulation for entangled-two-photon resonance energy transfer (E2P-RET) mediated by inhomogeneous, dispersive, and absorptive media with any space-dependent and frequency-dependent dielectric function and with any size of donor/acceptor. In our theoretical framework, two uncoupled particles are jointly excited by the temporally entangled field associated with two virtual photons that are produced by three-level radiative cascade decay in a donor particle. The temporal entanglement leads to frequency anticorrelation in the virtual photon’s field, and vanishing of one of the time-ordered excitation pathways. The underlying mechanism leads to more than 3 orders of magnitude enhancement in the E2P-RET rate compared with the uncorrelated photon case. With the power of our new formulation, we propose a way to characterize E2P-RET through an effective rate coefficient K E2P, introduced here. This coefficient shows how energy transfer can be enhanced or suppressed depending on rate parameters in the radiative cascade, and by varying the donor–acceptor frequency differences.