Spatial Properties of Entangled Two-Photon Absorption

We experimentally study entangled two-photon absorption in rhodamine 6G as a function of the spatial properties of a high flux of broadband entangled photon pairs. We first demonstrate a key signature dependence of the entangled two-photon absorption rate on the type of entangled pair flux attenuation: linear, when the laser pump power is attenuated, and quadratic, when the pair flux itself experiences linear loss. We then perform a fluorescence-based $Z$-scan measurement to study the influence of beam waist size on the entangled two-photon absorption process and compare this to classical single- and two-photon absorption processes. We demonstrate that the entangled two-photon absorption shares a beam waist dependence similar to that of classical two-photon absorption. This result presents an additional argument for the wide range of contrasting values of quoted entangled two-photon absorption cross sections of dyes in literature.

Figure 1

Epifluorescence setup schematic: PPLN—periodically poled lithium niobate crystal, pumped by 532 nm laser; ${\mathrm{IF}}_L$—set of long-pass interference filters; L1—pair collimating lens; Dichroic—dichroic mirror, transparent to IR and reflective to visible light; L2—pair focusing and fluorescence collecting lens; Sample—cell with liquid Rh6G solution; $Z$—translation stage; ${\mathrm{IF}}_{\mathrm{S}}$—short-pass interference filter; L3—fluorescence focusing lens; SPAD—single-photon avalanche diode.

Figure 2

ETPA-induced fluorescence counts as a function of laser pump power attenuation (red circles) and SPDC flux attenuation (blue squares), concentration of Rh6G in ethanol is 5 mM. Each point is an integration of detector counts over $2\times {10}^4\mathrm{s}$, $4.3\times {10}^6$ accumulated dark counts subtracted. Error bars are standard deviations over the set of measurements. The red dashed line corresponds to a linear fit and the blue dash-dotted line to a quadratic fit of the experimental data.

Figure 3

Normalized fluorescence detection rate from a liquid 5 mM Rh6G ethanol solution as a function of translation stage displacement from the focus in the epifluorescence scheme. The fluorescence is induced by 532 nm laser photons (green circles); SPDC pairs (blue squares), and 1064 nm laser photons (red triangles). The SPDC-induced fluorescence data points are an average of 100 measurements of 1 s each and the laser induced are an average of 5 measurements of 1 s each, measured at $10\mu \mathrm{m}$ displacement intervals. The red dashed line is the model of the TPA for a Gaussian 1064 nm laser beam (6). The green dash-dotted line is the model of SPA for a 532 nm beam (5). Error bars are Monte Carlo propagated standard deviations. The sizes of error bars for SPA and TPA data points are smaller than the data points.

Figure 4

Normalized fluorescence detection rate from a liquid 5 mM Rh6G ethanol solution as a function of translation stage displacement from the focus in the epifluorescence scheme under the SPDC excitation (blue squares), and models of fluorescence rate under single- (red dashed line) and two-photon excitation (green dash-dot line), described in Eqs. (5) and (6).