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 {1479} hide / / print ref: -0 tags: ETPA entangled two photon absorption Goodson date: 09-24-2019 02:25 gmt revision:6       [head] Can we image biological tissue with entangled photons? How much fluorescence can we expect, based on reasonable concentrations & published ETPA cross sections? Start with beer's law: $A = \sigma L N$ $A$ = absorbance; $L$ = sample length, 10 μm, 1e-3 cm; $N$ = concentration, 10 μmol; $\sigma$ = cross-section, for ETPA assume $2.4e-18 cm^2 / molec$ (this is based on a FMN based fluorophore; actual cross-section may be higher). Including Avogadro's number and $1 l = 1000 cm^3$ , $A = 1.45e-5$ Now, add in quantum efficiency $\phi = 0.8$ (Rhodamine); collection efficiency $\eta = 0.2$ ; and an incoming photon pair flux of $I = 1e12 photons / sec / mode$ (which roughly about the limit for quantum behavior; n = 0.1 photons / mode; will add this calculation). $F = \phi \eta \sigma L N I = 2.3e6 photons/sec$ This is very low, but within practical imaging limits. As a comparison, incoherent 2p imaging creates ~ 100 photons per pulse, of which 10 make it to the detector; for 512 x 512 pixels at 15fps, the dwell time on each pixel is 20 pulses of a 80 MHz Ti:Sapphire laser, or ~ 200 photons. Note the pair flux is per optical mode; for a typical application, we'll use a Nikon 16x objective with a 600 μm Ø FOV and 0.8 NA. At 800 nm imaging wavelength, the diffraction limit is 0.5 μm. This equates to about $7e5$ addressable modes in the FOV. Then an illumination of $1e12$ photons / sec / mode equates to $7e17$ photons over the whole field; if each photon pair has an energy of $2.75 eV, \lambda = 450 nm$ , this is equivalent to 300 mW. 100mW is a reasonable limit, hence scale incoming flux to $2.3e17$ pairs /sec. Hence, the imaging mode is power limited, and not quantum limited (if you could get such a bright entangled source). And right now that's the limit -- for a BBO crystal, circa 1998 experimenters were getting 1e4 photons / sec / mW. So, $2.3e17$ pairs / sec would require 23 GW. Yikes. More efficient entangled sources have been developed, using periodically-poled potassium titanyl phosphate (PPPTP), which (again assuming linearity) puts the power requirement at 23 MW. This is within the reason of q-switched lasers, but still incredibly inefficient. The down-conversion process is not linear in intensity, which is why Goodson pumps with SHG from a Ti:sapphire to yield ~1e7 photons; but this of induces temporal correlations which increase the frequency of incoherent TPA. Still, combining PPPTP with a Ti:sapphire laser could result in 1e13 photons / sec, which is sufficient for scanned microscopy. Since the laser is pulsed, it will still be subject to incoherent TPA; but that's OK, the point is to reduce the power going into the animal via larger ETPA cross-section. The answer to above is a tentative yes. Upon the development of brighter entangled sources (e.g. arrays of quantum structures), this can move to fully widefield imaging. {1474} hide / / print ref: -0 tags: ETPA entangled two photon absorption Goodson date: 09-19-2019 15:49 gmt revision:13       [head] Various papers put out by the Goodson group: Two-Photon Excitation of Flavins and Flavoproteins with Classical and Quantum Light Report a ETPA cross-section of 2.4e-18 cm^2 / molec; corresponded with the author, this looks legit. This is at an input flux of 2.88e6 photons / sec, of which 2e5 are absorbed (not a fluorescence measurement.) Note that figure 3 input flux is in intensity, photons/sec/cm^2. Spatial Control of Entangled Two-Photon Absorption with Organic Chromophores Optically Excited Entangled States in Organic Molecules Illuminate the Dark Entangled Photon Absorption in an Organic Porphyrin Dendrimer Quantum Optical Applications in Spectroscopy: Investigations of Entangled Two-Photon Absorption and Entangled Two-Photon Excited Fluorescence in Organic Dendritic Systems. Investigations of Thienoacene Molecules for Classical and Entangled Two-Photon Absorption Smaller ETPA cross-section, 1e-19, measured through fluorescence and absorption. Fairly extensive MO analysis of the benzodithiophene derivatives; could mine. Note that 2p absorption is quite different for centrisymmetric vs unsymmetric molecules -- e.g. one half of a quadrupole molecule can undergo (allowed) 1p absorption prior a second photon. Entangled Photon Excited Fluorescence in Organic Materials: An Ultrafast Coincidence Detector Super low fluorescence count rates - 1 / sec. And from a separate group at Northwestern: Entangled Photon Resonance Energy Transfer in Arbitrary Media Suggests three orders of magnitude improvement in cross-section relative to incoherent TPA. In SPDC, photon pairs are generated randomly and usually accompanied by undesirable multipair emissions. For solid-state artificial atomic systems with radiative cascades (singled quantum emitters like quantum dots), the quantum efficiency is near unity. Paper is highly mathematical, and deals with resonance energy transfer (which is still interesting) Regarding high fluence sources, quantum dots / quantum structures seem promising.