Optimal photon antibunching in a quantum-dot–bimodal-cavity system

We theoretically investigate the photon statistics in a cavity quantum electrodynamics system of a single quantum dot coupled to a bimodal nanocavity. It is shown in a recent work [A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, Phys. Rev. Lett. 108, 183601 (2012)] that the system can generate strongly sub-Poissonian light when one of the cavity modes is driven coherently and resonantly. We study the two-mode coherent driving regime of the coupled system. The effect of additional cavity mode driving on statistical characteristics of photon emission is presented by evaluating the zero-delay second-order correlation function $g^2$(0). The antibunching character can be optimized by regulating the ratio between driving strengths of two cavity modes to achieve optimal combination of superbunched and coherent light. As a result $g^2$(0) can be reduced up to several orders of magnitude [$g^2$(0)$\sim$10${}^{-7}$] with proper system parameters, compared with the one-mode driving system [$g^2$(0)$\sim$0.1].

Figure 1

The second-order correlation $g^2$(0) of (a) $a$ mode and (b) $b$ mode as functions of the laser detuning Δ for different $E_b$. Intracavity photon numbers of (c) $a$ mode and (d) $b$ mode as functions of the laser detuning Δ for different $E_b$. Parameters used for calculations are QD–cavity coupling strength $g$/2π = 20 GHz for both modes, cavity decay rate κ/2π = 20 GHz for both modes, QD dipole decay rate γ/2π = 1 GHz, and $E_a$/2π = 1 GHz.

Figure 2

(a) The second-order correlation $g^2$(0) and (b) intracavity photon numbers of modes $a$ and $b$ as functions of the driving laser strength ratio $r$ in resonant driving case. Parameters used for calculations are the same as in Fig. 1 but the laser detuning Δ = 0.

Figure 3

The second-order correlation $g^2$(0) of (a) mode $a$ and (b) mode $b$ as functions of the ratio $r$ for different $E_a$ in resonant driving case. (c) The minimum value of $g^2$(0) of modes $a$ and $b$ as functions of $E_a$. Additionally, $g^2$(0) in absence of driving of mode $b$ ($r$ = 0) is plotted for comparison. (d) The optimal ratio $r$ of modes $a$ and $b$ as functions of $E_a$. Parameters used for calculations are the same as in Fig. 2.

Figure 4

(a) The minimum value of $g^2$(0) of modes $a$ and $b$, as well as $g^2$(0) in absence of driving of mode $b$ ($r$ = 0) as functions of coupling strength $g$. (b) The optimal ratio $r$ of modes $a$ and $b$ as functions of $g$. Parameters used for calculations are the same as in Fig. 2.

Figure 5

(a) The minimum value of $g^2$(0) of modes $a$ and $b$ and $g^2$(0) in absence of driving of mode $b$ ($r$ = 0) as functions of cavity decay rate κ. (b) The optimal ratio $r$ of modes $a$ and $b$ as functions of κ. Parameters used for calculations are the same as in Fig. 2 but $g$/2π = 10 GHz.

Figure 6

(a) The minimum value of $g^2$(0) of modes $a$ and $b$ and $g^2$(0) in absence of driving of mode $b$ ($r$ = 0) as functions of QD–cavity-mode coupling strength ratio $g_b$/$g_a$. (b) The optimal ratio $r$ of modes $a$ and $b$ as functions of $g_b$/$g_a$. Parameters used for calculations are the same as in Fig. 2 except $g_b$.