Generation of pseudo-sunlight via quantum entangled photons and the interaction with molecules

Light incident upon molecules triggers fundamental processes in diverse systems present in nature. However, under natural conditions such as sunlight illumination, it is impossible to assign known times for photon arrival due to continuous pumping, and therefore the photoinduced processes cannot be easily investigated. In this work, we demonstrate theoretically that the characteristics of sunlight photons, such as photon number statistics and spectral distribution, can be emulated through a quantum entangled photon pair generated with parametric down-conversion (PDC). We show that the average photon number of sunlight in a specific frequency spectrum, e.g., the visible light, can be reconstructed by adjusting the PDC crystal length and pump frequency, and thereby the molecular dynamics induced by the pseudo-sunlight can be investigated. The entanglement time, which is the hallmark of quantum entangled photons, can serve as a control knob to resolve the photon arrival times, enabling investigations on real-time dynamics triggered by pseudo-sunlight photons.

Figure 1

Average photon number in the signal beam generated through the PDC process with the CW pumping, $\overline{n}\left(\omega \right)$ in Eq. (2) (red solid line) and the thermal distribution, ${\overline{n}}_{\mathrm{th}}\left(\omega \right)={(e^{\hslash \omega /k_{\mathrm{B}}T}-1)}^{-1}$ at temperature $T=5777\mathrm{K}$ (blue dashed line). To evaluate Eq. (2), the parameters of ${\omega }_{\mathrm{p}}=25000{\mathrm{cm}}^{-1}$, ${\overline{\omega }}_{\mathrm{s}}=12000{\mathrm{cm}}^{-1}$, $T_{\mathrm{e}}=2.5\mathrm{fs}$, and $B=0.15$ are employed. The two vertical lines indicate electronic transition energies that will be discussed later, ${\omega }_{1g}=18000{\mathrm{cm}}^{-1}$ and ${\omega }_{2g}=18500{\mathrm{cm}}^{-1}$.

Figure 2

Time evolution of the normalized density matrix elements describing molecular electronic excitations, Eq. (3), under illumination of the signal photons generated through the PDC process (red solid lines) and the black-body radiation of temperature 5777 K (blue dashed line). The average photon number and the electronic transition energies shown in Fig. 1 were used in the calculations. The normalization is such that the maximum value of the real part of the off-diagonal element, ${\rho }_{12}\left(t\right)=\langle e_1|{\widehat{\rho }}_{\mathrm{el}}\left(t\right)|e_2\rangle$, for the PDC case is unity; therefore, it is of no consequence that the normalized population exceeds unity.

Figure 3

Time evolution of the normalized density matrix elements describing the electronic excitations triggered by interaction with the signal photons, provided that idler photons are detected at time $t=t_{\mathrm{i}}$, Eq. (5). (a) The entanglement time $T_{\mathrm{e}}=2.5\mathrm{fs}$ and the other parameters are the same as in Figs. 1 and 2. (b) The entanglement time is set to $T_{\mathrm{e}}=50\mathrm{fs}$, and the other parameters are ${\overline{\omega }}_{\mathrm{s}}=18001{\mathrm{cm}}^{-1}$ and $B=0.11$. The normalization is such that the maximum value of the diagonal element, ${\rho }_{11}(t;t_{\mathrm{i}})=\langle e_1|{\widehat{\rho }}_{\mathrm{el}}(t;t_{\mathrm{i}})|e_1\rangle$, is unity.

Figure 4

Illustration of the two-photon coincidence counting measurement. The signal and idler beams generated through the PDC in the birefringent crystal are split on a beam splitter (BS). Only the signal photons interact with molecules, and the idler photons propagate freely. The idler photons and photons spontaneously emitted from the molecule excited by the signal photons are detected in coincidence.