Entangled Polariton States in the Visible and Mid-Infrared Spectral Ranges

Abstract

Entanglement generation in polariton systems is fundamentally constrained by high losses and decoherence, which typically outweigh polariton nonlinearities. Here, we propose a conceptually different approach that uses optomechanical interactions, rather than polariton-polariton interactions, to generate entangled polaritons. Our double-resonant scheme relies on strong exciton-phonon coupling, found in both inorganic and molecular semiconductors, enabling room-temperature generation of spectrally disparate photon pairs. The quantum coherent and delocalized nature of polariton states inside optical cavities ensures efficient single-mode outcoupling and allows for unconditional quantum state preparation - not relying on any post-selection or projective measurements. When conditioned on exciton-polariton emission, single phonon-polariton states can be prepared that subsequently yield bright, heralded single-photon emission in the mid-IR/THz. We introduce a double-resonant optomechanical platform that enables scalable, room-temperature quantum polaritonics without relying on conventional excitonic nonlinearities.

Figures (12)

• Figure 1: Double resonant polariton optomechanical system. Double-resonant polariton system hosting optomechanically interacting exciton-polaritons and phonon-polaritons that generates entangled polariton states and emits entangled photons under coherent pumping.
• Figure 2: Dispersion relations. (a) Dispersions of upper (purple line) and lower (blue line) exciton-polarotons and upper (pink line) and lower (red line) phonon-polaritons. Gray line in (a) shows the resonant frequency of excitons. (b) Generation of exciton- and phonon-polariton pairs. (c) Generation of entangled exciton- and phonon-polariton Bell pairs. Operators in (b) and (c) are introduced in Eq. (\ref{['H_optomech_f']}). Parameters are typical for room-temperature polariton systems; for concreteness, we use those of molecular polariton cavities with strong sideband-resolved optomechanical interaction zasedatelev2019roomzasedatelev2021single.
• Figure 3: Entangled polaritons. Logarithmic negativity, $E_N$, for lower exciton-polaritons with the wave vector ${\bf k}_f$ and (a) upper, (b) lower phonon-polaritons with the wave vector ${\bf k}_i-{\bf k}_f$ under CW excitation, $n_{s_{\rm U}|{\bf k}_i} = 1630$. Green regions indicate $E_N=0$. Parameters are specified in Appendix \ref{['appendix: Hamiltonian']}.
• Figure 4: Entangled light emitted by the double resonant system. (a) Logarithmic negativity, $E_N$, for visible light with in-plane wave vector ${\bf k}_f$ and IR light in-plane wave vector ${\bf k}_i-{\bf k}_f$. Green regions indicate areas where $E_N=0$. (b) $g^{(2)}_{\rm Vis-IR}(0)$ for visible and mid-IR light. Green regions indicate areas $g^{(2)}_{\rm Vis-IR}(0)\leq 2$. (c) $g^{(2)}_\text{IR(her)}(0)$ for visible and mid-IR light. Green regions indicate areas $g^{(2)}_\text{IR(her)}(0) \geq 0.5$. The parameters are the same as in Fig. \ref{['fig: LogNegMat']}, with ${\rm SNR_{Vis}} = \langle \hat{n}_{s_{\rm L}|{\bf k}_f} \rangle/N^{(\rm bg)}_{\rm Vis}$, $N^{(\rm bg)}_{\rm Vis}=10^{-6}$ and ${\rm SNR_{IR}} = \langle \hat{n}_{{\rm IR}|{\bf k}_i-{\bf k}_f} \rangle/N^{(\rm bg)}_{\rm IR}$, $N^{(\rm bg)}_{\rm IR} = 10^{-3}$.
• Figure 5: Quantum interference. $g^{(2)}_{\rm Vis-IR}(\tau)$as a function of time delay and wave vector ${\bf k}_i$ with IR light coming from (a) upper, (b) lower, and (c) both phonon-polariton states. Insets in (a-c): The dispersion of phonon-polaritons, with the vertical purple and green lines mark the phonon-polariton states assisting the transition of energy, corresponding to the green and purple dashed lines in (a-c). (d-f) $g^{(2)}_{\rm Vis-IR}(\tau)$ for fixed ${\bf k}_i$ corresponding to the green and purple dashed lines in (a-c). The parameters are the same as in Fig. \ref{['fig:correlations_CW']}.