54
H. Oka
are achieved for high E (in other words, small σ s ), and conversely this indicates that
we cannot achieve large ζ and high S at low E even for ultrabroadband entangled
photons.
For reference, entangled photons obtained from conventional parametric downconversion exhibit E ≈ 0.55 and therefore enhancement is at most 10 if we use the
generated entangled photons directly. Our results suggest that design of entangledphoton source with high E is required in order to achieve a further strong enhancement and single vibrational-mode excitation in molecular two-photon absorption and
two-step excitation.
3.5 Conclusion
We have analyzed molecular two-photon absorption and two-step excitation using
entangled photons. By taking a cold diatomic molecule Na 2 as an example, we have
shown that photon entanglement can strongly enhance the two-photon transition
rate for both two-photon absorption (TPA) and two-step excitation (TSE) processes.
The enhancement rate reaches up to more than 1000 times compared to conventional laser light under the same conditions. In particular, the TSE excitation rate
for a single vibrational mode can be enhanced 2500 times by using ultrabroadband
frequency-entangled photons with spectral width of σ = 100 THz. In addition, the
model selectivity S of a vibrational mode nearly reaches unity for both TPA and
TSE when entangled photons with strong quantum correlation (small σ s ) are used.
However, if we achieve the strong enhancement and high selectivity concurrently,
we have to prepare entangled photons with high quantum entanglement measure E.
Entangled photons obtained from conventional parametric down-conversion exhibit
E ≈ 0.55 and our results show that the realization of strong enhancement and high
selectivity requires E ≥ 0.8. These results thus indicate that design of entangledphoton source with higher E is required in order to achieve strong enhancement and
single vibrational-mode excitation in molecular two-photon absorption and two-step
excitation. We hope our results facilitate the study of molecular two-photon excitation
by entangled photons.
Acknowledgements The present work was supported by JSPS KAKENHI Grant Number
JP17H05252, Grant-in-Aid for Scientific Research on Innovative Areas “Photosynergetics.”
References
1. Göppert-Mayer M (1931) Über Elementarakte mit zwei Quantensprüngen. Ann Phys 9:273–
294
2. Denk W, Strickler JH, Webb WW (1990) Two-photon laser scanning fluorescence microscopy.
Science 248:73–76
H. Oka
are achieved for high E (in other words, small σ s ), and conversely this indicates that
we cannot achieve large ζ and high S at low E even for ultrabroadband entangled
photons.
For reference, entangled photons obtained from conventional parametric downconversion exhibit E ≈ 0.55 and therefore enhancement is at most 10 if we use the
generated entangled photons directly. Our results suggest that design of entangledphoton source with high E is required in order to achieve a further strong enhancement and single vibrational-mode excitation in molecular two-photon absorption and
two-step excitation.
3.5 Conclusion
We have analyzed molecular two-photon absorption and two-step excitation using
entangled photons. By taking a cold diatomic molecule Na 2 as an example, we have
shown that photon entanglement can strongly enhance the two-photon transition
rate for both two-photon absorption (TPA) and two-step excitation (TSE) processes.
The enhancement rate reaches up to more than 1000 times compared to conventional laser light under the same conditions. In particular, the TSE excitation rate
for a single vibrational mode can be enhanced 2500 times by using ultrabroadband
frequency-entangled photons with spectral width of σ = 100 THz. In addition, the
model selectivity S of a vibrational mode nearly reaches unity for both TPA and
TSE when entangled photons with strong quantum correlation (small σ s ) are used.
However, if we achieve the strong enhancement and high selectivity concurrently,
we have to prepare entangled photons with high quantum entanglement measure E.
Entangled photons obtained from conventional parametric down-conversion exhibit
E ≈ 0.55 and our results show that the realization of strong enhancement and high
selectivity requires E ≥ 0.8. These results thus indicate that design of entangledphoton source with higher E is required in order to achieve strong enhancement and
single vibrational-mode excitation in molecular two-photon absorption and two-step
excitation. We hope our results facilitate the study of molecular two-photon excitation
by entangled photons.
Acknowledgements The present work was supported by JSPS KAKENHI Grant Number
JP17H05252, Grant-in-Aid for Scientific Research on Innovative Areas “Photosynergetics.”
References
1. Göppert-Mayer M (1931) Über Elementarakte mit zwei Quantensprüngen. Ann Phys 9:273–
294
2. Denk W, Strickler JH, Webb WW (1990) Two-photon laser scanning fluorescence microscopy.
Science 248:73–76