Strong photon blockade in an all-fiber emitter-cavity quantum electrodynamics system

We present an all-fiber emitter-cavity quantum electrodynamics (QED) scheme which makes it possible to realize the strong photon blockade phenomenon in the strong coupling regime. To begin with, we study the emitter-cavity system where the two-level emitter and cavity are driven by a laser field under different driving strengths, respectively. Then, we theoretically derive that through driving the single-mode nanofiber cavity and a single two-level emitter simultaneously with two classical fields, the photon antibunching effect and the intracavity mean photon number will be tremendously enhanced. Compared with the systems driving an emitter or the cavity, respectively, the second-order correlation function at zero time decay $g^{\left(2\right)}\left(0\right)$ in our system can reach the minimum value as 0.0003, which is much smaller than a single-emitter-cavity QED system of emitter drive or cavity drive. In particular, under the condition of quantum interference model, the strong phenomenon of photon antibunching can be flexibly reached by controlling of the intensity relationship between the dual-pumping fields in the strong coupling regime. Our proposal can be achieved in the near future and has great potential applications in high-quality single-photon sources and quantum communication processing.

Figure 1

Simple schematic of the system, where two FBG mirrors with a nanofiber waist form a Fabry-Perot nanofiber cavity, and a single two-level emitter with resonant frequency ${\omega }_a$ trapped in the nanofiber cavity with frequency ${\omega }_c$. The red (blue) arrow represents the emitter (cavity) driving strength $\eta$ ($\varepsilon$) with frequency ${\omega }_p$ (${\omega }_d$). $\left|g\right.〉$ ($\left|e\right.〉$) is the ground (excited) state of the emitter. $\gamma$ and $\kappa$ are the decay rats of the emitter and the cavity, respectively.

Figure 2

(a) Shows energy-level diagram of the dressed states in a cavity drive emitter-cavity system (only section field is applied). (b) Shows the transition paths for cavity drive case under Jaynes-Cummings model. Here, the green arrows are the emitter-cavity coupling strength $g$. $\left|j,n\right.〉$ is the dressed state of emitter state $\left|j\right.〉$ and photon number state $\left|i\right.〉$. Our system parameters are taken as ${\kappa }_1/\left(2\pi \right)={\kappa }_2/\left(2\pi \right)=1.233\text{MHz}, {\kappa }_{b,\mathrm{loss}}/\left(2\pi \right)=0.166\text{MHz}, \gamma /2\pi =2.65\text{MHz}$ according to Ref. [62].

Figure 3

In the case of cavity drive system, the plots of second-order correlation function $g^{\left(2\right)}\left(0\right)$ (blue dashed-dotted curve), third-order correlation function $g^{\left(3\right)}\left(0\right)$ (green dotted curves), and mean photon number $〈a^{†}a〉$ (red solid curve) as a function of detuning $\mathrm{\Delta }/2\pi$ for (a) $\varepsilon /2\pi =0.1\text{MHz}$ and (b) $\varepsilon /2\pi =2.6\text{MHz}$. The red dashed lines indicate $g^{\left(2\right)}\left(0\right)=1$ for Poissonian statistics, and the pink dashed lines indicate the detuning regime to realize the three-photon blockade. We also use the black arrows to show the one-photon excitation in (a) and two-photon excitation in (b). Here, the coupling strength $g/2\pi =20\text{MHz}$ is taken in both panels.

Figure 4

(a) Energy-level diagram of the dressed states in coupled emitter-driven system. (b) The transition pathway of emitter drive system for different photon states.

Figure 5

In the case of emitter drive system, plots of field correlation function $g^{\left(2\right)}\left(0\right)$ (blue dashed-dotted curves), $g^{\left(3\right)}\left(0\right)$ (green dotted curves), and mean photon number $〈a^{†}a〉$ (red solid curves) versus the normalized detuning $\mathrm{\Delta }/2\pi$ for (a) $\varepsilon /2\pi =0.1\text{MHz}$ and (b) $\varepsilon /2\pi =2.6\text{MHz}$. The red dashed lines indicate $g^{\left(2\right)}\left(0\right)=1$ for Poissonian statistics and the black arrows for the one-photon excitation in (a) and two-photon excitation in (b). We show the one-photon transition in (a) and two-photon transition in (b). Two pink dashed lines indicate the detuning area of two-photon blockade. The coupling strength $g/2\pi =20\text{MHz}$ is taken in both panels.

Figure 6

(a) Energy-level diagram of the dressed states in a two-field drive coupled emitter-cavity system. (b) Transition path of both emitter drive and cavity drive under quantum interference model.

Figure 7

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ and the mean photon number $〈a^{†}a〉$ as a function of the normalized detuning $\mathrm{\Delta }/2\pi$ in the weak driving limitation. The blue and red solid lines denote $g^{\left(2\right)}\left(0\right)$ for the analytical expression given by Eq. (14) and the dotted lines show numerical simulation by numerically solving the master equation (2) using the quantum optics toolbox [75]. The red dashed-dotted line indicates $g^{\left(2\right)}\left(0\right)=1$ for Poissonian statistics, and the black dashed lines indicate the detunings at the position of the relatively minimum value of the $g^{\left(2\right)}\left(0\right)$ as well as the relatively maximum value of $〈a^{†}a〉$. The black arrows in (a) and (b) show the minimum value of $g^{\left(2\right)}\left(0\right)=1$ at the location of $\mathrm{\Delta }=-g$. Here, we choose $g/2\pi =15\text{MHz}$ and $g/2\pi =20\text{MHz}$ for (a) and (b), respectively. The other parameters are taken as $\varepsilon /2\pi =0.25\text{MHz},\eta /2\pi =0.75\text{MHz}$.

Figure 8

Plots of mean photon number $〈a^{†}a〉$ (a) and the second-order correlation function $g^{\left(2\right)}\left(0\right)$ (b) as functions of the detuning $\mathrm{\Delta }/2\pi$ in the cases of cavity drive system with driving strength $\varepsilon /2\pi =0.25\text{MHz}$, emitter drive system with driving strength $\eta /2\pi =0.75\text{MHz}$, and both the cavity and emitter are driven by two fields with strength $\varepsilon /2\pi =0.25\text{MHz},\eta /2\pi =0.75\text{MHz}$. The three system parameters are the same as those used in Fig. 6.

Figure 9

Plots of second-order correlation function ${log}_{10}{g}^{\left(2\right)}\left(0\right)$ as the function of the two field strengths $\eta$ and $\varepsilon$. Here, we choose $g/2\pi =15\text{MHz}$ and $g/2\pi =20\text{MHz}$ for (a) and (b), respectively. The white dashed line demonstrates the relationship of emitter driving strength and cavity driving strength. The other parameters are taken as $\kappa /2\pi =\gamma /2\pi =2.6\text{MHz}$.

Figure 10

Plots of second-order correlation function ${log}_{10}{g}^{\left(2\right)}\left(0\right)$ as the function of coupling strength $g/2\pi$ and detuning $\mathrm{\Delta }/2\pi$ in (a). The dark white dashed line indicates strong photon blockade effect at the detuning with $\mathrm{\Delta }=-g$, the light white dashed line indicates the relatively strong photon blockade behavior at the detuning with $\mathrm{\Delta }=g$. In (b), considering the case of ${\mathrm{\Delta }}_a\ne {\mathrm{\Delta }}_c$, we plot $g^{\left(2\right)}\left(0\right)$ as the function of ${\mathrm{\Delta }}_a$ and ${\mathrm{\Delta }}_c$. The coupling strength $g/2\pi =20\text{MHz}$ and other parameters are $\kappa /2\pi =\gamma /2\pi =2.6\text{MHz},\eta /2\pi =0.75\text{MHz},\varepsilon /2\pi =0.25\text{MHz}$.