The 'entangled photon' hypothesis of enhanced two-photon absorption collapses under a rigorous experiment

Abstract

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