Two-Photon Resonance Fluorescence in a Three-Level Ladder-Type Atom

TL;DR

This work analyzes a three-level ladder-type atom driven on two-photon resonance, revealing a seven-peak fluorescence spectrum arising from transitions between three dressed states. By developing an effective two-level description via adiabatic elimination and performing a secular-dressed-state analysis, the authors derive analytic expressions for second-order photon correlations, capturing both auto- and cross-correlations of the dressed-state transitions. The results highlight how the spectral structure and photon statistics depend on driving strength, anharmonicity, and the dipole-moment ratio $oldsymbol{ extxi}$, including Stark shifts and a shifted two-photon resonance. The study extends prior work on two-level and three-level resonance fluorescence, providing a detailed theoretical framework and open-source computational tools for exploring cascaded emission and frequency-filtered correlations in strongly driven ladder-type atoms.

Abstract

In this work, we consider a three-level ladder-type atom driven by a coherent field, inspired by the experimental work of Gasparinetti et al. [Phys. Rev. A 100, 033802 (2019)]. When driven on two-photon resonance, the atom is excited into its highest energy state $| f \rangle$ by absorbing two photons simultaneously. The atom then de-excites via a cascaded decay $| f \rangle \rightarrow | e \rangle \rightarrow | g \rangle$. Here we present a theoretical study of the atomic fluorescence spectrum where, upon strong coherent driving, the spectrum exhibits seven distinct frequencies corresponding to transitions amongst the atomic dressed states. We characterize the quantum statistics of the emitted photons by investigating the second-order correlation functions of the emitted field. We do so by considering the total field emitted by the atom and focusing on each of the dressed-state components, taking in particular a secular-approximation and deriving straightforward, transparent analytic expressions for the second-order auto- and cross-correlations.

Figures (10)

• Figure 1: Energy level diagram of the three-level ladder-type atom: $\delta$ is the detuning of the drive frequency $\omega_{d}$ from the two-photon resonance frequency, $\omega_{fg} / 2$; $\alpha$ is the detuning of the driving field from the two single-photon resonance frequencies, $\omega_{eg}$ and $\omega_{fe}$; and $\Omega$ and $\xi \Omega$ are Rabi frequencies for the lower and upper dipole transitions, respectively.
• Figure 2: Steady-state populations from Eq. (\ref{['eq:2_atomic_master_equation']}) of the $\ket{g}$ (left), $\ket{e}$ (center), and $\ket{f}$ (right) atomic states as a function of the drive detuning $\delta$ and drive amplitude $\Omega$ for three values of the dipole moment ratio: (a) $\xi = 1 / \sqrt{2}$, (b) $\xi = 1$, and (c) $\xi = \sqrt{2}$. Also shown is the Stark-shifted two-photon resonance frequency (black, dotted), Eq. (\ref{['eq:2_shifted_resonance']}). The atomic anharmonicity is $\alpha = -120 \Gamma$.
• Figure 3: (a) Energy level diagram of the dressed states of the three-level ladder-type atom at two-photon resonance ($\delta = 0$), with all possible de-excitation paths shown. As the driving amplitude increases, the degeneracy of the dressed states is lifted, allowing for a total of twelve de-excitation paths. (b) Incoherent power spectrum in the weak driving, $\Omega = 5 \Gamma$, and (c) strong driving, $\Omega = 40 \Gamma$, regimes. Each peak is labeled with the appropriate transition frequencies, Eq. (\ref{['eq:3_dressed_state_frequencies']}). The other parameters are $\alpha = -120 \Gamma, \delta = 0$, and $\xi = 1$.
• Figure 4: Normalized incoherent power spectrum as a function of driving amplitude $\Omega$ at two-photon resonance $\left( \delta = 0 \right)$. The other parameters are $\alpha = -120 \Gamma$ and $\xi = 1$.
• Figure 5: Normalized incoherent power spectrum at two-photon resonance $\left( \delta = 0 \right)$ for three different values of the dipole moment ratio: (a) $\xi = 1 / \sqrt{2}$, (b) $\xi = 1$, and (c) $\xi = \sqrt{2}$. The other parameters are $\Omega = 40 \Gamma$ and $\alpha = -120 \Gamma$.