Low-Energy Free-Electron Nonclassical Lasing

Abstract

Harnessing a beam of slow free electrons in artificial photonic structures offers a powerful, tunable platform for generating nonclassical light without the need for heavy physical equipment. Here we present a theory of nonclassical lasing, demonstrating how incoherent electrons in photonic crystal cavities can coherently emit photons through collective dynamics. When photon emission rate exceeds cavity losses, nonclassical lasing with sub-Poissonian photon statistics emerges, driven by multi-photon Rabi oscillations. At specific coupling strengths, quantum state trapping effect emerges, producing high-fidelity Fock states at room temperature (e.g. nearly 90%-fidelity of four photon Fock state). Notably, the frequency of the emitted photons can be readily tuned via the velocity of the injected electrons to match cavity modes. This approach supports photonic integration and offers a scalable, energy-efficient platform for room-temperature quantum light sources and advanced studies in quantum electrodynamics.

Figures (4)

• Figure 1: (a) Sketch of the lasing process. Electrons are injected and interact with the optical mode in the FP PhC cavity with structures periodicity $\Lambda$. (b) Energy levels of a low-energy free electron when emitting the photons with the recoil of $\Delta K$. Orange arrow indicates single-photon resonance process, while purple arrows represent two-photon process. (c) Effective formulation of the electron-photon coupling dynamics for single-photon (upper) and two-photon (lower) resonance conditions.
• Figure 2: (a) Analytical (solid curves) and numerical (dots) results of the average photon number $\langle n\rangle$ in an electron-driven laser as a function of $g_{q}\tau$. (b) The normalized variance $\sigma$, quantifying photon number fluctuations, as a function of $g_{q}\tau$. (c) Steady-state photon number distributions. Insets represent Wigner functions for specific coupling strengths $g_{q}\tau=0.5/\sqrt{N_\mathrm{e}},\:(\pi/2)/\sqrt{N_\mathrm{e}},\:6/\sqrt{N_\mathrm{e}}$ and $\pi/\sqrt{10}$, which are also marked by dotted lines 'I--IV' in panels (a) and (b). Here, both numerical and analytical parameters are $v_{0}$=$0.02c$, $\lambda$=$1550$nm, $\kappa$=$2\pi \times1$GHz, $I_\mathrm{e}$=$8$nA, and $\Lambda$=$31$nm.
• Figure 3: (a) Fidelity $F_{n}$ (red dash-dot curves) and two-photon correlation $g^{(2)}$ (blue solid curves) of the Fock state $|n\rangle$ as a function of the current intensity $I_\mathrm{e}$. Numerical parameters are $\lambda$=$1550$nm, and $g_{q}\tau=\pi/\sqrt{n+1}$ for target Fock state $|n\rangle$ at temperature $300$K. (b) Maximum fidelity denoted by $\max[F_{n}(I_\mathrm{e})]$ (red dots and squares) and corresponding current requirements $I_{\mathrm{max}}$ (blue dots and squares) for different Fock states at temperatures of $3$K and $300$K, respectively. The parameters are the same as those used in panel (a).
• Figure 4: (a) The average photon number $\langle n\rangle$ as a function of the interaction length $L_{\mathrm{int}}$ under differen energy spreads of the electron beam. Partial parameters are chosen as $T_0=1\,\mathrm{keV}$, $\lambda=1550\,\mathrm{nm}$, $g_q=30\,\mathrm{GHz}$, $I_e=800\,\mathrm{pA}$, and $\kappa=2\pi\times100\,\mathrm{MHz}$. (b) Normalized variance $\sigma$ as a function of $g_{q}\tau$ corresponding to different $\Delta T$ in panel (a).