Towards High-Brightness Perfect Photon Blockade

Abstract

Single-photon sources with high single-photon purity and high brightness are key elements of many future quantum technologies. While photon blockade (PB) is widely exploited in the development of such sources, achieving the coexistence of high purity and high brightness remains a long-standing challenge. Here, we identify a novel mechanism for high-brightness PB and demonstrate that near-ideal purity and near-ideal brightness can be simultaneously achieved in an extended nondegenerate two-photon Jaynes-Cummings model with two-body and three-body interactions. This mechanism is underpinned by a distinctive energy-level structure arising from the combined action of the two interactions. The energy levels in the multi-excitation manifold essentially retain a harmonic ladder of degenerate doublets, whereas in the single-excitation subspace the doublet degeneracy is lifted, with a finite splitting between the two levels. Consequently, when one bosonic mode is driven by a coherent continuous-wave pump, the former degeneracy enables the other bosonic mode to exhibit near-perfect PB even in the strong driving regime, while the latter splitting allows the mean photon number of that mode to approach unity. Our proposed scheme overcomes the outstanding challenge and offers a promising pathway toward realizing ideal single-photon sources.

Figures (6)

• Figure 1: (a) Setup of the extended nondegenerate two-photon Jaynes-Cummings model. (b) Energy spectrum of the system Hamiltonian at $\omega_a=2\omega_c$ in the subspaces containing zero, one, two, and three excitations, shown in the uncoupled basis (left) and the diagonal basis (right). The up arrows illustrate photon transition processes of the driven cavity mode induced by the pump field (cyan arrow), and blue lines highlight the core energy levels of the system.
• Figure 2: Equal-time second-order correlations $g^{(2)}_{\bf k}(0)$ of (a) the driven and (b) the undriven cavity modes versus the coupling strength $\raisebox{0.28ex}{$\mathrm{g}$}/\kappa_1$ for $J=\{0.1,1,2.5\}\kappa_1$ and $\Delta=0$. The dashed black line shows the biquadratic scaling law. (c) Dependence of $g_{2}^{(2)}(0)$ on the pump detuning $\Delta/\kappa_1$ for $\raisebox{0.28ex}{$\mathrm{g}$}=\{0.1,1,10\}\kappa_1$ and $J=0.1\kappa_1$, with the inset showing the variations of $\delta\Delta$ versus the coupling strength $\raisebox{0.28ex}{$\mathrm{g}$}/\kappa_1$ for $\zeta=2,4,8$. Notice that the discrete data points in panels (a)--(b) are numerical solutions to the FME in the weak driving amplitude $\Omega=10^{-4}\kappa_1$, and the solid curves are obtained from the analytic expression (\ref{['Eq5']}). The remaining parameters are $\kappa_2=\kappa_1$ and $\gamma=0.01\kappa_1$.
• Figure 3: Panels (a) and (c) show the correlation $g^{(2)}_{2}(0)$ and the mean photon number $\expval{\hat{n}_2}$ versus the coupling strength $\raisebox{0.28ex}{$\mathrm{g}$}/\kappa_1$ for different values of $\kappa_2/\kappa_1$ (encoded by color), respectively. Panel (b) presents the fitting coefficients $\beta_0$ and $\beta_1$, extracted from the power-law fit shown by the dashed lines in panel (a). (d) Validation of the RME against the FME at $\raisebox{0.28ex}{$\mathrm{g}$}=20\kappa_1$ for computation of the mean photon number $\expval{\hat{n}_2}$ as a function of $\kappa_2/\kappa_1$, with the difference $|\!\expval{\hat{n}_2}-\langle\hat{\tilde{n}}_2\rangle|$ shown in the inset. Other parameters are $\Omega=0.5\kappa_1$, $J=0.1\kappa_1$, and $\gamma=0.01\kappa_1$.
• Figure 4: (a) Schematic illustration of the effective dynamics in the regime $J/\raisebox{0.28ex}{$\mathrm{g}$}\ll1$ and $\aleph/\raisebox{0.28ex}{$\mathrm{g}$}\ll1$ (or for $J=0$), including the driving, dissipation, and interaction processes. These colored dots represent the basis states that span the yellow regions. (b) Single-photon state infidelity $1-\langle\hat{\tilde{n}}_2\rangle_{\rm opt}$ versus the decay rate $\kappa_2/\kappa_1$ under the optimal parameters $J_{\rm opt}$ and $\Omega_{\rm opt}$ shown in panels (c) and (d). Notice that in panel (b), three discrete data points (crosses) are obtained from the FME at $\raisebox{0.28ex}{$\mathrm{g}$}=20\kappa_1$ and $\gamma=0.01\kappa_1$ under the same optimal parameters, with the inset showing their values of $\expval{\hat{n}_2}$ and $P$. The solid black lines in panels (b)--(d) display the analytical asymptotic behaviors.
• Figure 5: Panel (a) shows the infidelity dynamics of the projection approximation for different 3BI strengths, while panel (b) displays its steady-state infidelity dependence on the 3BI strength. Panels (c) and (d) show the mean photon numbers $\expval{\hat{n}_2}$ and $\langle\hat{\tilde{n}}_2\rangle$ (for $N_{\rm max}^{\rm ph}=1\sim9$), and single-photon purity $P$ as functions of the driving amplitude $\Omega/\kappa_1$, respectively. Note that we have used $\Omega=0.5\kappa_1$ in panels (a)--(b) and $\raisebox{0.28ex}{$\mathrm{g}$}=10\kappa_1$ in panels (c)--(d). The remaining parameters are $\gamma=0.01\kappa_1$, $\kappa_2=0.01\kappa_1$, and $J=J_{\rm opt}$ [see Eq. (\ref{['Eq18']})].