Efficient Two Photon Generation from an Emitter in a Cavity

TL;DR

This work analyzes efficient two-photon generation from an incoherently pumped emitter in a doubly resonant cavity using a Lindblad master equation framework. By developing a manifold approximation and validating it with numerical simulations, it identifies optimal outcoupling and decay rates, showing that maximizing two-photon emission occurs near $\kappa_2 \approx g_1$ while minimizing $\kappa_1+\gamma$, enabling practical efficiencies around $η \approx 0.35$ and biphoton rates of tens to hundreds of kHz. The study reveals strong photon-bunching with $g^2(0)$ in the hundreds and Mandel $Q \approx 0.5$, and a three-peak emission spectrum arising from transitions between dressed states. In the high-pump regime, efficiency decreases as the system populates higher manifolds, but a rapid cascade mechanism underlies the two-photon process, offering a compact, bright biphoton source that can surpass SPDC in efficiency with appropriate cavity engineering.

Abstract

Two-photon states are essential for quantum technologies such as metrology, lithography, and communication. One of the primary methods of two-photon generation is based on parametric down-conversion, but this suffers from low efficiency and a large footprint. This work presents a detailed theoretical investigation of an alternative approach: two-photon generation from an emitter in a doubly resonant cavity. The system is modeled by the Lindblad master Equation, and an approximate analytical solution is derived to determine the experimentally achievable limits on efficiency and brightness. Additionally, the optimal cavity parameters for achieving these limits are also identified. For experimentally feasible parameters, the maximum efficiency is approximately 35%, which is significantly higher than that of parametric down-conversion-based methods. The optimal rate and efficiency for two-photon generation are achieved when the outcoupling rate of the cavity mode at the two-photon emission frequency matches the single-photon atom-field coupling strength. Moreover, the outcoupling rate of the cavity mode at the one-photon emission frequency for single photons should be minimized. The cavity field properties are also examined by studying the second-order correlation function at zero time delay and the Mandel Q parameter, revealing highly bunched two-photon emission and super-Poissonian statistics. The quantum-jump framework, combined with Monte Carlo simulations, is used to characterize the mechanism of two-photon emission and the emission spectra of the cavity. Two-photon emission is demonstrated to be a rapid cascade process of quantum jumps, and its spectrum consists of three prominent peaks corresponding to transitions between the dressed states of the system.

Figures (13)

• Figure 1: Diagram of the two-level system's energy levels and the transitions. The atom consists of ground and excited states denoted by $\ket{g}$ and $\ket{e}$ respectively, interacting with the $\omega_0$ (annihilation operator $\hat{a}$) and $\omega_0/2$ (annihilation operator $\hat{b}$) modes of the cavity which drive one and two-photon transitions respectively, denoted by bidirectional arrows. The unidirectional arrows represent incoherent excitation at rate $P$ and decay of the excited state at rate $\gamma$. The outcoupling rates of the $\omega_0,\omega_0/2$ modes are $\kappa_1,\kappa_2$ respectively.
• Figure 2: Dependence of the steady state statistics on $P$, at $\kappa_1=0.02g_1,\kappa_2=g_1,\gamma=0.016g_1$. Sub-figure (a) depicts $\eta$ ,Sub-figure (b) depicts $T$. Sub-figure (c) depicts $O$ and $L$
• Figure 3: Dependence of the steady state statistics on $\kappa_2$, at $\kappa_1=0.02g_1,P=0.005g_1,\gamma=0.016g_1$. Sub-figure (a) depicts $\eta$, Sub-figure (b) depicts $T$. Sub-figure (c) depicts $O$ and $L$
• Figure 4: Dependence of the steady state statistics on $\kappa_1$, at $\kappa_2=g_1,P=0.005g_1,\gamma=0.016g_1$. Sub-figure (a) depicts $\eta$, Sub-figure (b) depicts $T$. Sub-figure (c) depicts $O$ and $L$
• Figure 5: Efficiency and Emission Rates at low values of $\kappa_1$, for $\kappa_2=g_1,P=0.005g_1,\gamma=0.016g_1$. The range of $\kappa_1$ is from $2 \times10^{-5}g_1$ to $2 \times 10^{-3}g_1$. Sub-figure (a) depicts $\eta$, Sub-figure (b) depicts $T$. Sub-figure (c) depicts $O$ and $L$