Steady-State Emission of Quantum-Correlated Light in the Telecom Band from a Single Atom

TL;DR

The paper presents a scheme to produce steady-state quantum light in the telecom band from a single atom by combining one- and two-photon resonant excitation in a diamond-like level system. A telecom cavity channels emission to the desired wavelength, and a second, independent cavity mode can boost the cycle rate and generate nonclassical two-mode correlations. Using a cesium-atom model that includes full hyperfine structure, the authors demonstrate robust, antibunched emission in the telecom channel and significant cross-cavity quantum correlations, violating Cauchy–Schwarz inequalities in steady state. The approach is designed for practical cavity QED implementations, including nanofiber-based and fiber-Bragg-grating cavities, potentially enabling integrable, long-distance quantum light sources.

Abstract

We propose and investigate a scheme for the steady-state emission of quantum-correlated, telecom-band light from a single multilevel atom. By appropriately tuning the frequency of a pair of lasers, a two-photon transition is continually driven to an atomic excited state that emits photons at the desired wavelength. We show that resonantly coupling a cavity mode to the telecom transition can enhance the rate of emission while retaining the antibunched counting statistics that are characteristic of atomic light sources. We also explore coupling a second, independent cavity mode to the atom, which increases the telecom emission rate and introduces quantum correlations between the cavity modes. A model for the hyperfine structure of a single cesium atom is then described and numerically integrated to demonstrate the viability of implementing the scheme with a modern cavity QED system.

Figures (7)

• Figure 1: Schematic of the conceptual double-diamond model, with two driving lasers, configured such that the pump laser ($\Omega_{\rm p}$) is resonant with the $\ket{g_1}\leftrightarrow \ket{e_1}$ transition ($\Delta_{\rm p} = \omega_g$). The pump and Stokes ($\Omega_{\rm S}$) laser frequencies combine to be two-photon-resonant with the $\ket{g_2}\leftrightarrow \ket{f}$ transition, i.e. $\Delta_{\rm p} +\Delta_{\rm S} =0$. Solid arrows show classical coherent driving fields, and dashed arrows indicate coupling to quantized cavity modes. Ideally, the four fields implement a cycle of transitions from the $\ket{g_2}$ state, starting with a two-photon transition through $\ket{e_1}$, followed by a sequence of cavity-enhanced relaxations via $\ket{e_2}$.
• Figure 2: Log of steady-state atomic populations with a ground-state splitting $\omega_g = 1000\gamma$, and a symmetric laser driving ($\Omega_\text{p} = \Omega_\text{S}$). (Purple) The population is distributed across all the energy levels with the choice $\Delta_\text{p}=-\omega_g$ and $\Delta_\text{S}=\omega_g$, and with an effective two-photon transition rate $\Omega_\text{eff} \approx \Omega_\text{p}\Omega_\text{S}/\Delta_\text{S}=4\gamma$. (Grey hatched) Population becomes almost entirely confined in the $\ket{g_2}$ state, when $\Delta_\text{p}=\Delta_\text{S}=0$ with an equivalent two-photon transition rate $\Omega_\text{eff} \approx \sqrt{2\Omega_\text{p}\Omega_\text{S}}=4\gamma$.
• Figure 3: Steady-state populations for the atom coupled to a telecom cavity mode, with a ground-state splitting $\omega_g = 1000\gamma$, symmetrically driven ($\Omega_\text{p} = \Omega_\text{S}$) with an effective two-photon transition rate $\Omega_\text{eff} \approx \Omega_\text{p}\Omega_\text{S}/\Delta_\text{S}=4\gamma$, and $\Delta_\text{p}=-\Delta_\text{S}=-\omega_g$. Each case has a single-atom cooperativity $C_t = 8$, with $g_t = \{1,2,4\}\gamma$ ($\kappa_t=\{0.5,2,8\}\gamma$) for the purple, grey hatched, and green hatched bars, respectively.
• Figure 4: Steady-state output fluxes from the telecom (solid black) and control (dashed black) cavities, plotted against coupling strengths, $g_t=g_c=g_i$. The atom has a ground-state splitting $\omega_g = 1000\gamma$, and is symmetrically driven ($\Omega_\text{p} = \Omega_\text{S}$) with an effective two-photon transition rate $\Omega_\text{eff} \approx \Omega_\text{p}\Omega_\text{S}/\Delta_\text{S}=4\gamma$, and $\Delta_\text{p}=-\Delta_\text{S}-\omega_g$. In dot-dashed grey, the telecom cavity flux from an otherwise equivalent system in the absence of a control cavity is also shown. The decay rate is chosen so that the telecom single-atom cooperativity is always $C_t = 8$, and, where included, $\kappa_c=\kappa_t$.
• Figure 5: Second-order correlation functions for the steady-state cavity emission, with $g_t = g_c = 4\gamma$, for $\kappa_t=\kappa_c = 8\gamma$ (left column), and $\kappa_t=\kappa_c = 16\gamma$ (right column). The atom has a ground-state splitting $\omega_g = 1000\gamma$, and is symmetrically driven ($\Omega_\text{p} = \Omega_\text{S}$) with an effective two-photon transition rate $\Omega_\text{eff} \approx \Omega_\text{p}\Omega_\text{S}/\Delta_\text{S}=4\gamma$, and $\Delta_\text{p}=-\Delta_\text{S}-\omega_g$. (Top) Cross-correlation, showing conditional likelihood of detecting a photon from the control cavity, given a detection at $\tau=0$ in the telecom cavity. (Bottom) Auto-correlations, which in this case are essentially the same for both cavity modes, with solid black (dotted grey) line showing conditional likelihood of a photon detection from the telecom (control) cavity, given an initial detection from the same mode at $\tau=0$.