Microscopic model for a spatial multimode generation based on Multi-pump Four Wave Mixing in hot vapours

TL;DR

The paper develops a microscopic, double-Lambda description of multimode generation in hot vapours using two-pump four-wave mixing, employing a Floquet expansion to capture multimode gain and quantum correlations. It provides a frequency-domain, gaussian-state framework to compute the covariance matrix, noise spectra, and entanglement structure, including Doppler broadening and detector losses. The approach yields detailed predictions for mode gain distributions, propagation-induced cascades, and hexapartite entanglement across numerous spatial channels, tunable by detuning, pump strength, and pump-angle. This work offers a predictive tool for designing reconfigurable multimode quantum networks and can be extended to higher-order mixing and orbital-angular-momentum modes.

Abstract

Multipartite entanglement is an important resource for quantum information processing. It has been shown that it is possible to employ alkali atoms to implement single device multipartite entanglement by using nonlinear processes with spatial modes. This work presents the first microscopic description of such multi-mode generation with two-pump four wave mixing (4WM) in dense atomic media. We implement an extension of a double $Λ$ model for a single pump 4WM in order to describe the multi-mode generation with a two-pump configuration. We propose a Floquet expansion to solve the multimode gain amplification and noise properties. The model describes the angle and the two-photon dependency of the multimode generation and the quantum correlations among the modes. We investigate the entanglement properties of the system, describing the main properties of previous experimental observations. Such a microscopic description can be used to predict the gain distribution of modes and the quantum correlation within a typical range of experimental parameters.

Figures (14)

• Figure 1: (a) Energy level diagram with the double $\Lambda$ for a 4 level system. The hiperfine splitting is not resolve due to Doppler broadening. (b) Two-pump phase scheme. (c) Multimode generation with a two-pump scheme and a generalization with four-pumps.
• Figure 2: Gain amplification two-photon spectroscopy for different angles of the pump fields. Probe (upper plot) and conjugate (lower plot) gain distribution for (a) $\theta_{\mathrm{eff}}=3$ mrads, (b) $\theta_{\mathrm{eff}}=4.5$ mrads and (c) $\theta_{\mathrm{eff}}=6$ mrads. The parameters of the calculation are: $\Omega_0/2\pi=220$ MHz, $\Delta/2\pi=0.9$ GHz, $\Gamma/2\pi=5.7$ MHz, $\gamma_d/2\pi=1$ MHz, $\omega_{\mathrm{HF}}/2\pi=3.035$ GHz and $g_a=g_b=0.28$ MHz.
• Figure 3: Gain distribution for the probe and conjugate channel. (a) and (b) for $\theta_{\mathrm{eff}}=3$ mrads, (c) and (d) for $\theta_{\mathrm{eff}}=4.8$ mrads and (e) and (f) for $\theta_{\mathrm{eff}}=6$ mrads. The parameters of the calculation are: $\Omega_0/2\pi=220$ MHz, $\Delta/2\pi=0.9$ GHz, $\Gamma/2\pi=5.7$ MHz, $\gamma_d/2\pi=1$ MHz, $\omega_{\mathrm{HF}}/2\pi=3.035$ GHz and $g_a=g_b=0.28$ MHz.
• Figure 4: Propagation of the modes for two different angles: (a) $\theta_{\mathrm{eff}}=3$ mrads and $\theta_{\mathrm{eff}}=6$ mrads. The parameters of the calculation are: $\Omega_0/2\pi=220$ MHz, $\Delta/2\pi=0.9$ GHz, $\Gamma/2\pi=5.7$ MHz, $\gamma_d/2\pi=1$ MHz, $\omega_{\mathrm{HF}}/2\pi=3.035$ GHz and $g_a=g_b=0.28$ MHz.
• Figure 5: Gain distribution for the probe and conjugate channel. (a) for $\theta_{\mathrm{eff}}=3$ mrads and (b) for $\theta_{\mathrm{eff}}=6$ mrads. The parameters of the calculation are: $\Omega_0/2\pi=220$ MHz, $\Delta/2\pi=0.9$ GHz, $\Gamma/2\pi=5.7$ MHz, $\gamma_d/2\pi=1$ MHz, $\omega_{\mathrm{HF}}/2\pi=3.035$ GHz and $g_a=g_b=0.28$ MHz.