Controllable optical bistability of an asymmetric cavity containing a single two-level atom

Optical bistability of a single-mode cavity containing a two-level atom in the Purcell regime has been analyzed. Compared with the case of a symmetric cavity, we find that the bistable regime of input power in an asymmetric cavity can be controlled by adjusting the cavity-loss rates of the asymmetric walls. Such results provide an optimal window of input power to realize giant optical nonreciprocity, which has promising application as the smallest all-optical diode unit with low operation power and high transmitted contrast.

Figure 1

Scheme of the atom-cavity coupling system under external input. Here, the cavity-loss rate $k_1$ $\left(k_2\right)$ represents the decay of cavity mode into port 1 (2) through ${\mathrm{M}}_1$ $\left({\mathrm{M}}_2\right)$.

Figure 2

Single-atom optical bistability in the forward input case. (a) $n_t$ vs $n_{\mathrm{in}}$ in a symmetric cavity with $k_1=k_2=500$. Two vertical green dotted lines refer to the threshold intensities of bistable states $n_l$ and $n_u$. (b) $n_t$ vs $n_{\mathrm{in}}$ in two kinds of asymmetric cavities with $k_1\ne k_2$. Common parameters are ${\gamma }_{\mathrm{at}}=1,\Delta =\delta ={\gamma }_{\mathrm{cav}}=0,\Omega =50$, and $k=500$.

Figure 3

Optical bistable threshold intensities $n_l$ and $n_u$ vs detuning Δ in the symmetric and asymmetric cavities. ${\gamma }_{\mathrm{at}}=1,\delta ={\gamma }_{\mathrm{cav}}=0,\Omega =50$, and $k=500$.

Figure 4

Optical bistable threshold intensities $n_l$ and $n_u$ as functions of the left side cavity-loss rate $k_1$ in an asymmetric cavity. Common parameters are ${\gamma }_{\mathrm{at}}=1,\Delta =\delta ={\gamma }_{\mathrm{cav}}=0,\Omega =50,k=500$, and $k_2=2k-k_1$. Curves $n_u$ and $n_l$ bound the regime of optical bistability (gray area).

Figure 5

Transmittivity $T$ as a function of input power $n_{\mathrm{in}}$ with $k_1=600$ and $k_2=400$. (a) Input power ranges from 0 to 2.0. (b) Input power falls in the optimal operation power window [0.78, 1.11]. Solid blue curves refer to the backward input case, while the dashed red curves refer to the forward input case. Common parameters are ${\gamma }_{\mathrm{at}}=1,\Delta =\delta ={\gamma }_{\mathrm{cav}}=0,\Omega =50$, and $k=500$.