Setting Experimental Bounds on Entangled Two-Photon Absorption Cross Sections

Two-photon absorption (2PA) is widely used in microscopy for deep, sub-cellular imaging.
However, the efficiency of 2PA is limited by the properties of both the absorber and the excitation
light. Entangled photon pairs produced via spontaneous parametric down-conversion (SPDC) exhibit
correlations in energy, time and space that may improve the excitation efficiency relative to
a classical laser. The most significant improvement is expected at low photon flux where isolated
pairs interact with the absorber. In this regime, the rate of the entangled two-photon absorption
(E2PA) process scales linearly with photon flux and the E2PA cross section (σ_E).

Despite over a decade of publications claiming to measure huge σ_E that suggest a quantum
advantage exists of up to 10 orders of magnitude, in this thesis I will show strong evidence that
σ_E are several orders of magnitude lower than previously reported. First, we provide relevant
background information on nonlinear and quantum optics. Next, we discuss theoretical descriptions
of σ_E and review the large body of experimental work in the field. Afterwards, we discuss the four
experiments we designed to measure E2PA.

In the first and third experiments, we measure SPDC transmittance through samples of two-photon
absorbers in room-temperature liquids. In our second experiment, we collect fluorescence
from samples excited with SPDC. Despite the high sensitivity of the techniques, we could not
resolve a signal in any of the measurements. We set upper bounds on the σ_E of eight independent
absorbers that are up to five orders of magnitude lower than previously published σ_E.

The third experiment also served as a classical 2PA (C2PA) measurement system. We made
one-to-one comparisons between E2PA and C2PA to bound the quantum advantage. We derived
absolute C2PA cross sections that closely agreed with values already reported in literature. In the
fourth experiment, we designed a toluene-filled hollow-core-fiber platform for 2PA measurements. We measured C2PA down to 20 nanowatts, and expect to make further improvements. This
platform is at least 4-fold more sensitive than a standard cuvette-based technique and thus is ideal
for the next generation of E2PA measurements.