Multielectron Ground State Electroluminescence

The ground state of a cavity-electron system in the ultrastrong coupling regime is characterized by the presence of virtual photons. If an electric current flows through this system, the modulation of the light-matter coupling induced by this nonequilibrium effect can induce an extracavity photon emission signal, even when electrons entering the cavity do not have enough energy to populate the excited states. We show that this ground state electroluminescence, previously identified in a single-qubit system [Phys. Rev. Lett. 116, 113601 (2016)] can arise in a many-electron system. The collective enhancement of the light-matter coupling makes this effect, described beyond the rotating wave approximation, robust in the thermodynamic limit, allowing its observation in a broad range of physical systems, from a semiconductor heterostructure with flatband dispersion to various implementations of the Dicke model.

Figure 1

A right lead ($R$) is connected to a left lead ($L$) via a middle region, the two elements kept at chemical potentials ${\mu }_R$ and ${\mu }_L$, respectively, by applying an electrical bias, which induces an electron current quantified by a rate ${\mathrm{\Gamma }}_{\mathrm{el}}$ for the free electrons (blue spheres) flowing out of the device. Sandwiched between the leads, a solid-state cavity (dark purple disks), enhances the electronic coupling to the photonic vacuum field (light purple disk cross section), at a strength quantified by $\chi$ for each electron. The bare frequency difference between the two electronic flatbands, ${\omega }_0={\omega }_2-{\omega }_1$, separates the lower states (blue) and upper states (red). The presence of virtual photons inside the cavity induces an extracavity photon emission (green blobs) from the polaritonic ground state, at a rate ${\mathrm{\Gamma }}_{\mathrm{cav}}$.

Figure 2

(a),(c) Polariton emission rates ${\mathrm{\Gamma }}_{\mathrm{em}}^{B^{\prime }}$ and fluxes ${\omega }^{B^{\prime }}{\mathrm{\Gamma }}_{\mathrm{em}}^{B^{\prime }}$, in units of the total electron-transport rate ${\mathrm{\Gamma }}_{\mathrm{el}}$ for the upper polariton ($B^{\prime }=+$, blue curves) and lower polariton ($B^{\prime }=-$, green curves), and sum of the two signals (black curves) versus the normalized detuning for $g_N/{\omega }_0=0.05$. (b),(d) Total photon emission rates, from Eq. (6), and fluxes. Solid curves correspond to the bosonic RWA quantities, dashed curves to the full bosonic model developed in the SM [75].

Figure 3

(a) Polariton emission rate ${\mathrm{\Gamma }}_{\mathrm{em}}={\mathrm{\Gamma }}_{\mathrm{em}}^{-}+{\mathrm{\Gamma }}_{\mathrm{em}}^{+}$ and (b) flux as a function of the frequency detuning and coupling strength, setting $\chi =3\times {10}^{-3}{\omega }_0$ fixed and varying $N$, and thus $g_N=\sqrt{N}\chi$. The vertical solid black lines correspond to the cut shown in Fig. 2. The resonance condition is marked by dashed horizontal lines (and vertical lines in Fig. 2).