Two-Polariton Blockade via Ultrastrong Light-Matter Coupling

Abstract

We demonstrate that a two-polariton blockade (2PB) can occur under resonant single-polariton driving in an atom-cavity system operating in the ultrastrong coupling (USC) regime-a phenomenon qualitatively distinct from, and unattainable in, both the strong and weak coupling regimes. In the USC regime, where the ratio of the atom-cavity coupling strength to the cavity resonance frequency exceeds 0.1, hybrid light-matter quasiparticles known as polaritons emerge. By employing modified second- and third-order correlation functions appropriate for the USC regime, we predict the emergence of 2PB, characterized by pronounced two-polariton bunching accompanied by suppressed three-polariton coincidences. This Letter introduces a novel route to achieving 2PB, with promising implications for the realization of multiparticle quantum light sources in the USC regime.

Figures (4)

• Figure 1: (a) Schematic of the cQED system under study. A transmission-line resonator is coupled to a flux qubit, which is tunable via an external magnetic flux bias $\psi$. Here, $\pm I_p$ denote the clockwise and counterclockwise persistent currents circulating in the qubit loop. Parity is conserved when $\theta=m \pi/2$ ($\delta \psi=0$). For $\theta=0.3\pi$, the parity is non-conserved. The cavity mode is driven externally (in red) with frequency $\omega_l$ and amplitude $\Omega$ via the input capacitor, while coherent transmission is measured at the output capacitor. (b) Illustration of polariton formation via ultrastrong coupling between the qubit and the photon.
• Figure 2: Polariton statistics for the SC and USC systems. (a) Energy spectrum as a function of coupling strength $g$. Illustrations of energy-level transitions for $g/\omega_c=0.08$ and $g/\omega_c=0.6$. (b), (c) The second-order (blue dashed curves) and third-order (red solid curves) equal-time correlation functions for $g/\omega_c =0.08$ and $g/\omega_c=0.6$, respectively. The dissipation parameters are $\gamma_c=\gamma_{\sigma^{-}}=\gamma=10^{-2}\omega_c$, the drive amplitude is $\Omega=10^{-1}\gamma$, and the coupling phase $\theta=0.3\pi$.
• Figure 3: Delay-time correlation functions in the SC (a)–(c) and USC (d)–(f) regimes: (a), (d) $g^{(2)}(\tau)$ (blue solid curves), (b), (e) $g^{(3)}(\tau, \tau')$ (green solid curves), and (c), (f) $g^{(3)}(0, \tau')$ (red solid curves). The black dashed curves in (d)-(f) are the envelopes of the valleys of the correlation functions. Other parameters are the same as in Fig. \ref{['Fig2']}. These results reveal three-polariton antibunching and two-polariton bunching, which are essential for true two-polariton blockade.
• Figure 4: The physical mechanism of 2PB. (a), (b) Transition rates between the different dressed states $\Gamma_{1+,0}$ (the green solid line), $\Gamma_{1-,0}$ (the red solid line), $\Gamma_{1+,1-}$ (the red dashed line) versus the coupling strength under SC and USC regimes. (c), (d) The population of different dressed states under SC and USC regimes. $\theta = 0.3\pi$ and $\omega_l = E_{1+,0}$. (e) The equal-time correlation functions $g^{(2)}(0)$ and $g^{(3)}(0)$ as a function of the coupling strength $g$ in the SC regime. (f) Same as (e), but for the USC regime. The blue dashed and red solid curves represent the results of the second-order and third-order correlation functions, respectively. The yellow triangle point corresponds to $g/\omega_c=0.27$. Other parameters are the same as in Fig. \ref{['Fig2']}.