Enhancing stimulated Raman excitation and two-photon absorption using entangled states of light

We find that stimulated Raman excitation of an atom by a two-photon pulse can be enhanced by orders of magnitude if the photons are simultaneously frequency correlated and spatially anticorrelated. That is, a correlated photon pair must have an inherent time delay between its constituent photons. This counterintuitive feature is a manifestation of the uncertainty principle, which yields that frequency-correlated photons cannot be time (spatially) correlated. This is opposite to two-photon absorption by a three-level atom, for which the enhancement occurs if photons in the pulse are frequency anticorrelated and spatially correlated, that is, photons in the pair simultaneously interact with the atom. Our findings can be useful for imaging and spectroscopy of biological samples which demand low illumination intensity.

Figure 1

A three-level atom with transition frequencies ${\omega }_1$ and ${\omega }_2$ between states $|c\rangle$, $|b\rangle$, and $|a\rangle$. The state $|c\rangle$ is coupled to $|b\rangle$, and $|b\rangle$ is coupled to $|a\rangle$. In the ladder scheme (a) the ground-state atom can become excited to the state $|a\rangle$ by absorbing two photons, while in the $\mathrm{\Lambda }$ scheme (b) a photon is absorbed and reemitted with different frequency (Raman scattering).

Figure 2

Probability to find two photons with wave vectors $k_1$ and $k_2$ in the state (15) with $k_{\beta }=100{\gamma }_{-}$, $k_{\alpha }=50{\gamma }_{-}$, and either ${\gamma }_{+}=0.1{\gamma }_{-}$ (a), ${\gamma }_{+}={\gamma }_{-}$(b), or ${\gamma }_{+}=10{\gamma }_{-}$ (c). In the plots the probabilities are normalized by their maximum values.

Figure 3

The left (right) column shows the probability to find two photons in the state (15) with $k_{\beta }=100{\gamma }_{-}$, $k_{\alpha }=50{\gamma }_{-}$, and ${\mathrm{\Delta }}_{1,2}=0$ as a function of the photon wave vectors $k_1$ and $k_2$ (coordinates $x_1$ and $x_2$). For the upper and lower rows, ${\gamma }_{+}=0.1{\gamma }_{-}$ and ${\gamma }_{+}=10{\gamma }_{-}$, respectively. In the plots the probabilities are normalized by their maximum values.

Figure 4

Probability to find two photons with wave vectors $k_1$ and $k_2$ in the state (19) with $k_{\beta }=100{\gamma }_{\beta }$, $k_{\alpha }=50{\gamma }_{\beta }$, and either ${\gamma }_{\alpha }=0.1{\gamma }_{\beta }$ (a), ${\gamma }_{\alpha }={\gamma }_{\beta }$ (b), or ${\gamma }_{\alpha }=10{\gamma }_{\beta }$ (c). In the plots the probabilities are normalized by their maximum values.

Figure 5

Ground-state atoms 1 and 2 are uniformly accelerated in the right and left Rindler wedges, respectively, and become excited simultaneously.