Optimization of two-photon excitation by indistinguishable photons in a three-level atom

TL;DR

This paper analyzes how indistinguishable photon pairs can be optimized to excite a three-level atom efficiently, revealing conditions for perfect excitation and effects of photon correlations.

Contribution

It derives the optimal two-photon state for maximum atomic excitation and compares ideal and realistic photon states, guiding quantum light-matter interface design.

Findings

Perfect excitation is achievable with an infinitely long pulse.

The optimal state is the time-reversed emission in cascade decay.

Gaussian pulse states can shift spectral maxima and affect excitation efficiency.

Abstract

We investigate the excitation of a three-level ladder-type atom by a unidirectional field with a pair of indistinguishable photons. Starting from an analytical expression for the two-photon absorption probability, we determine the two-photon state that maximizes the population of the upper atomic state at a chosen time and show that, in the limit of an infinitely long pulse, perfect excitation is possible. The optimal state is identified as the time-reversed counterpart of the two-photon state emitted in spontaneous cascade decay. We then compare this ideal excitation strategy with experimentally accessible families of states, including symmetrized Gaussian product states, temporally correlated Gaussian states, and coherent pulses. We analyze how the optimal excitation conditions depend on the ratio of atomic decay rates and on the separation of the atomic transition frequencies. For indistinguishable photons described by Gaussian pulses, quantum interference may shift the maxima of the marginal spectral distribution away from the atomic resonances and qualitatively modify the optimal excitation strategy. Our results clarify the role of indistinguishability and correlations in two-photon absorption and provide guidance for designing realistic excitation schemes in quantum-optical light-matter interfaces .