Inducing Disallowed Two-Atom Transitions with Temporally Entangled Photons

Two uncoupled two-level atoms cannot be jointly excited by classical light under general circumstances, due to destructive interference of excitation pathways in two-photon absorption. However, with temporally entangled light, two-atom excitation is shown possible. Photons arising from three-level cascade decay are intrinsically ordered in time of emission. This field correlation induces a joint resonance in the two-atom excitation probability via suppression of one of the time-ordered excitation pathways. The relative gain in two-photon absorption increases with the time-frequency entanglement.

Figure 1

Two two-level atoms (ground state $g_i$ and excited state $e_i$) are driven by bichromatic light along two pathways, depending on which frequency ${\omega }_{\alpha }$ or ${\omega }_{\beta }$ is absorbed first (denoted by the solid or dashed arrows), and for two pairings, depending on which atom absorbs which frequency (exchanged in $1\leftrightarrow 2$). For each pairing, the time-ordered pathways interfere destructively to cancel classical two-photon absorption, assuming ${\omega }_{\alpha }-{\omega }_i\ne {\omega }_{\beta }-{\omega }_j$.

Figure 2

The temporal profiles of two photons emitted by a cascade source illustrate time-frequency entanglement: the solid curve represents the marginal probability $P({\tau }_{\alpha })$; the dashed curve represents the conditional probability $P({\tau }_{\beta }|{\tau }_{\alpha })$. See Eqs. (7, 8). The intrinsic time ordering of the photons, $\alpha$ first, followed by $\beta$, suppresses the dashed excitation pathway in Fig. 1, inducing joint two-atom excitation.