Optical technologies based on two-photon absorption can provide high resolution and deep tissue penetration but require very high peak power intensities because of the extremely small absorption cross sections associated with this phenomenon. The use of quantum-entangled photon pairs has been reported to increase the two-photon absorption rate compared with that obtainable using classical coherent laser sources. However, the enhancement that can possibly be obtained using entangled two-photon absorption (ETPA) has thus far been realized only at low photon rates, typically ranging from 107 (on the pW level) to 1013 (on the μW level) photons/s. For this reason, ETPA has been regarded as impractical. The present work demonstrates an experimental evaluation of ETPA-excited fluorescence at both low (μW) and relatively high (mW) pump power levels, using a high-gain parametric down-conversion source. Both an increase in the absorption rate and a linear correlation between rate and power were observed within both power ranges. This work also compared quantum and coherent sources. Assessments of the crossover photon flux suggest that the larger spatial-mode diameter of the present quantum source at the focal point (relative to values used in prior research) may have contributed to the rate enhancement seen at high-power levels. The results presented herein are expected to provide a new route to the mitigation of damage often associated with two-photon imaging and photodynamic therapies.
Optical technologies based on two-photon absorption can provide high resolution and deep tissue penetration but require very high peak power intensities because of the extremely small absorption cross sections associated with this phenomenon. The use of quantum-entangled photon pairs has been reported to increase the two-photon absorption rate compared with that obtainable using classical coherent laser sources. However, the enhancement that can possibly be obtained using entangled two-photon absorption (ETPA) has thus far been realized only at low photon rates, typically ranging from 107 (on the pW level) to 1013 (on the μW level) photons/s. For this reason, ETPA has been regarded as impractical. The present work demonstrates an experimental evaluation of ETPA-excited fluorescence at both low (μW) and relatively high (mW) pump power levels, using a high-gain parametric down-conversion source. Both an increase in the absorption rate and a linear correlation between rate and power were observed within both power ranges. This work also compared quantum and coherent sources. Assessments of the crossover photon flux suggest that the larger spatial-mode diameter of the present quantum source at the focal point (relative to values used in prior research) may have contributed to the rate enhancement seen at high-power levels. The results presented herein are expected to provide a new route to the mitigation of damage often associated with two-photon imaging and photodynamic therapies.
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.
Two-photon absorption (TPA) fluorescence of biomarkers has been decisive in advancing the fields of biosensing and deep-tissue in vivo imaging of live specimens. However, due to the extremely small TPA cross section and the quadratic dependence on the input photon flux, extremely high peak-intensity pulsed lasers are imperative, which can result in significant photo- and thermal damage. Previous works on entangled TPA with spontaneous parametric downconversion light sources found a linear dependence on the input photon-pair flux, but are limited by low optical powers, along with a very broad spectrum. We report that by using a high-flux squeezed light source for TPA, a fluorescence enhancement of ∼47 is achieved in fluorescein biomarkers as compared to classical TPA. Moreover, a polynomial behavior of the TPA rate is observed in the the laser dye 4-dicyanomethylene-2-methyl-6-(p(dimethylamino)styryl)-4H-pyran in dimethyl sulphoxide.
We closely replicated and extended a recent experiment ("Spatial properties of entangled two-photon absorption," Phys. Rev. Lett. 129, 183601, 2022) that reportedly observed enhancement of two-photon absorption rates in molecular samples by using time-frequency-entangled photon pairs, and we found that in the low-flux regime, where such enhancement is theoretically predicted in-principle, the two-photon fluorescence signal is below detection threshold using current state-of-the-art methods. The results are important in the context of efforts to enable quantum-enhanced molecular spectroscopy and imaging at ultra-low optical flux. Using an optical parametric down-conversion photon-pair source that can be varied from the low-gain spontaneous regime to the high-gain squeezing regime, we observed two-photon-induced fluorescence in the high-gain regime but in the low-gain regime any fluorescence was below detection threshold. We supplemented the molecular fluorescence experiments with a study of nonlinear-optical sum-frequency generation, for which we are able to observe the low-to-high-gain crossover, thereby verifying our theoretical models and experimental techniques. The observed rates (or lack thereof) in both experiments are consistent with theoretical predictions and with our previous experiments, and indicate that time-frequency photon entanglement does not provide a practical means to enhance in-solution molecular two-photon fluorescence spectroscopy or imaging with current techniques.
Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.
Researchers at the University of Colorado Boulder and the National Institute of Standards and Technology (NIST) built a single apparatus that illuminates a sample alternately with a classical laser and with entangled photon pairs from SPDC, and used it to test two-photon absorption efficiency in six fluorophores. Entangled pair excitation produced no fluorescence signal above the noise floor in any of the samples, and the resulting upper bounds on the entangled two-photon absorption (E2PA) cross section fall as much as five orders of magnitude below previously reported values. The team argues that the claims of a ten-order-of-magnitude quantum advantage in the literature may rest on reading a simple linear dependence on photon flux as proof while leaving the spatio-temporal correlations of the source unspecified, and their evidence indicates that E2PA efficiency lies far below current detection limits. [Quantum Biology Society] Two-photon absorption (2PA) microscopy is a central tool for looking deep inside living tissue. The classical pulsed-laser approach carries a serious cost, however: concentrating an enormous number of photons into a small spot generates heating and other forms of damage. As an alternative, the idea that spatially and temporally correlated entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) could maximize 2PA efficiency even at extremely low light levels, the process known as E2PA, has attracted considerable attention. A series of recent experimental studies reported that E2PA delivers a quantum advantage over classical 2PA of as much as ten orders of magnitude, and expectations across the field rose accordingly. A collaboration between the University of Colorado Boulder and NIST, with Ralph Jimenez as corresponding author, challenged those enormous numbers head-on in a paper published in Physical Review Applied in 2021. The group built a precision apparatus capable of comparing a classical laser and entangled photon pairs under essentially identical optical conditions, and used it to test the inflated claims experimentally. ■ Mismatched yardsticks: what goes wrong when entangled cross sections are compared The classical 2PA cross section (σC) is an intrinsic property of a molecule. The E2PA cross section (σE), by contrast, depends strongly on how tight a time window (the entanglement time, Te) and how small a spatial region (the entanglement area, Ae) the two photons of a pair arrive in together. The team points out that earlier reports either did not specify Te and Ae, or estimated Te at the output of the nonlinear crystal while neglecting the group delay dispersion (GDD) accumulated in the optics along the way, so that the value at the sample can be smaller by orders of magnitude. They also note that the linear dependence of signal on photon flux, offered in previous work as evidence of entangled absorption, appears equally in ordinary one-photon processes such as scattering, one-photon absorption, or fluorescence from the coating of an optic in the beam path. Working backwards, they find a physical contradiction: to justify the large cross sections previously reported, the light would have to be confined to a region 10⁻⁶ to 10⁻¹⁰ times the diffraction-limited spot size. ■ Cross-checking in one controlled apparatus: a signal below the noise floor The apparatus splits an 810 nm pulsed laser into two paths, one used directly for classical excitation, the other frequency-doubled to 405 nm and sent into a type-0 ppKTP crystal to generate entangled photon pairs by SPDC. The two beams are combined on a polarizing beam splitter and sent along essentially the same path to a focus inside a single cuvette, with an optical chopper providing on-the-fly background subtraction. Across six fluorophores including AF455, quantum dot 605 and fluorescein, classical laser excitation produced a clear 2PA signal scaling with the square of the photon flux, with fitted exponents between 1.95 and 2.05, and the derived classical cross sections agreed closely with published values, confirming the integrity of the instrument. Under SPDC excitation, however, all six samples stayed at the noise floor, below the instrument's detection limit of 0.22 counts per second, despite an incident SPDC rate of 8.9 × 10⁹ photons per second, which is part of what makes the resulting sensitivity so high. ■ An upper bound a hundred thousand times lower With no signal to measure, the team substituted its measurable fluorescence lower bound to calculate upper bounds on σE. These run from 1.0 ± 0.2 × 10⁻²⁵ cm² per fluorophore for fluorescein to 4.8 × 10⁻²³ cm² for quantum dot 605. For 9R-S and rhodamine 6G (Rh6G) in particular, two molecules previously reported to show strong E2PA, the bounds established here fall five orders of magnitude and four orders of magnitude respectively below the published values. Converted into a quantum advantage of E2PA over classical 2PA, the upper bounds come out at 410 to 7000, against prior claims approaching 10¹⁰. ■ Significance and outlook The paper does not prove that E2PA does not exist. When the team fed its measured σC together with its estimates of Te and Ae into the simple probabilistic model, the theoretically expected σE landed three to five orders of magnitude below this experiment's detection limit. Their Te at the sample was about 1620 fs, against roughly 17 fs for a transform-limited pulse, and Ae could only be constrained to somewhere between 2.1 and 13,700 µm². In other words, entangled two-photon absorption may simply be too faint to capture with present sensitivity, and the enormous quantum advantages in the existing literature are, on this evidence, likely to be experimental artefacts or overstated interpretation. The authors are careful to add that they do not expect this simple model to give an exact answer. They also set out a methodological standard: any report of E2PA results should quantify Te and Ae at the sample position. The vision of low-light biological imaging built on quantum optics remains attractive, but opening that door will require stepping back from expectations inflated by several orders of magnitude and taking a cool second look at the limits of the instruments and the correlations of the source. #QuantumBiology #EntangledTwoPhotonAbsorption #E2PA #TwoPhotonMicroscopy #SpontaneousParametricDownConversion #SPDC #QuantumAdvantage #UpperBounds #Fluorophores #Rhodamine6G #EntanglementTime #EntanglementArea #Reproducibility #NIST #PhysRevApplied https://arxiv.org/abs/2008.02664
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.