Quantifying the enhancement of two-photon absorption due to spectral-temporal entanglement

Abstract

When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a twophoton transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We present 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.

How to optimize the absorption of two entangled photons

“…As discussed in Sec. 2.4, the matter response function (15) is symmetric in the two photon frequencies, which implies that its Schmidt modes ϕ k , ψ k in (35) are equal for each k, possibly up to a phase. For ∆ 1, as in Fig.…”

“…Substituting (35) (on the left-hand side, via (32)) and ( 41) (on the right-hand side) in the identity (40) we obtain…”

“…In addition, quantum correlations may help to further manipulate optical signals [28][29][30]. Yet, a key problem in the practical application, currently, is the low absorption cross section of many samples [31][32][33][34], unless the two-photon transition can proceed through near-resonant intermediate states [35]. In this case [36], the shaping of entangled photonic wave functions [37][38][39] can enhance the absorption probability.…”

“…All results here displayed are based on the Schmidt decomposition(35) of the two-photon wave function Φ(ω 1 , ω 2 ) discretized in frequency space, i.e., we used a linear algebra package (Wolfram Mathematica) to calculate the singular values of a matrix. Frequencies were discretized on a grid of size ±200γ f and resolution γ e /5.…”

Is Heralded Two-Photon Excited Fluorescence with Single Absorbers Possible with Current Technology?

“…The photon statistics of a light field is important for nonlinear processes [16] and enhanced TPA was experimentally achieved with "classical" light by utilizing thermal light instead of coherent light [19,20]. The utilization of entangled photons for TPA was proposed by Gea-Banacloche [17], as well as Javaninen and Gould [18], and later experimentally demonstrated with atoms [21] as well as molecules [22][23][24][25][26][27][28]. Teich and Saleh proposed to exploit entangled photons for TPM in 1997 [29] with an ideal two-photon or biphoton source.…”