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Cavity optomechanics, as a cross-discipline between nanophotonics and quantum mechanics, provides a unique platform for investigating optomechanical coupling between photons in microcavities and phonons from mechanical modes. It has a wide range of potential applications in quantum physics, and now it has become a hot topic. A theoretical scheme to enhance the sum sideband generation (SSG) via a two-level atom ensemble is proposed. The effect of the atomic ensemble’s detuning frequency on the efficiency of the SSG is considered by introducing a two-level atom medium. The results indicate that the efficiency of the generating sideband can be significantly enhanced under either red or blue detuning of the atoms, with greater dependence and more pronounced enhancement under the red detuning. In addition, we also consider the effect of pump power, which can effectively enhance the intensity of the output signal by selecting the appropriate pump power. More interestingly, the sensitivity of SSG to atomic detuning also indicates that the precise control of the atomic detuning frequency can achieve the fine-tuning of the SSG process. Furthermore, the cavity-atom coupling strength and atom decay rate are discussed for the transmission characteristics of the sum sideband signals. It is found that the efficiency of SSG can be effectively adjusted by the cavity-atom coupling strength and atom decay rate. The results show that the efficiency of SSG can be significantly improved by optimizing system parameters. The method of enhancing SSG may have potential application prospects in measuring high-precision weak forces and on-chip manipulation of light propagation.
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Keywords:
- cavity optomechanics /
- two-level atom /
- optomechanical nonlinearity /
- sum sideband effects
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图 1 含有两能级原子系综的复合光力系统模型图
Figure 1. Hybrid optomechanical system model diagram with a two-level atom ensemble.
图 2 (a)上和边带和(b)下和边带的效率(对数形式)作为原子失谐频率${\varDelta _1}$和失谐频率${\delta _1}$的函数, 其中${\delta _2} = $$ 0.05{\omega _{\text{m}}}$, 具体参数为$ G/(2\text{π)}=0.4\text{ GHz}/\text{nm} $, ${\gamma }_{\text{m}}/(2\text{π})= $$ 100\text{Hz} $, $ \varDelta ={\omega }_{\text{m}} $, $ m=10\text{ ng} $, ${\gamma }_{\text{a}}/(2\text{π)}=2.875\text{ MHz} $, $\kappa /\text{(2π})=2\text{ MHz} $, ${\omega }_{\text{m}}/\text{(2π)}=10\text{ MHz} $, ${P}_{1}={P}_{2}=0.5\text{ μW} $, ${P}_{\text{c}}=5\text{ mW} $, ${\lambda }_{\text{c}}=794.98\text{ nm} $
Figure 2. The efficiencies (in logarithmic form) of (a) upper sum sideband generation (USSG) and (b) lower sum sideband generation (LSSG) as a function of the atomic detuning frequency ${\varDelta _1}$ and the detuning frequency ${\delta _1}$, where ${\delta _2} = 0.05{\omega _{\text{m}}}$. The specific parameters are as follows: $ G/(2\text{π)}=0.4\text{ GHz}/\text{nm} $, ${\gamma }_{\text{m}}/(2\text{π})=100\text{ Hz} $, $ \varDelta ={\omega }_{\text{m}} $, $m= $$ 10\text{ ng} $, ${\gamma }_{\text{a}}/(2\text{π)}=2.875\text{ MHz} $, $\kappa /\text{(2π})=2\text{ MHz} $, ${\omega }_{\text{m}}/\text{(2π)}= $$ 10\text{ MHz} $, ${P}_{1}={P}_{2}=0.5\text{ μW} $, ${P}_{\text{c}}=5\text{ mW} $, $ {\lambda }_{\text{c}}=794.98 \text{ nm} $
图 3 ${\delta _2} = 0.05{\omega _{\text{m}}}$的USSG(上和边带)(a)和LSSG(下和边带)(b)的效率(对数形式)作为控制功率$ {p_{\text{c}}} $和失谐频率${\delta _1}$的函数, 其他参数与图2一致
Figure 3. The efficiencies (in logarithmic form) of (a) USSG and (b) LSSG as a function of the control field power $ {p_{\text{c}}} $ and the detuning frequency ${\delta _1}$ for ${\delta _2} = 0.05{\omega _{\text{m}}}$, the other parameters are the same as those in Fig. 2.
图 4 在不同的原子失谐${\varDelta _1}$下, 输出场和边带的效率$\lg \eta _{\text{s}}^{{ \pm }}$与归一化失谐$ {{{\delta _1}} {/ } {{\omega _{\text{m}}}}} $的函数关系, 其他参数同图2一致
Figure 4. The efficiency $\lg \eta _{\text{s}}^{{ \pm }}$ of the output field sum sideband as a function of the normalized detuning $ {{{\delta _1}} {/ } {{\omega _{\text{m}}}}} $ for different atom detuning ${\varDelta _1}. $ The other parameters are the same as those in Fig. 2.
图 5 (a), (b)不同${g_{{\text{ac}}}}$值和边带与${\delta _1}$的效率(对数形式), 其中$ {g_{{\text{ac}}}} = 2{\text{π}} \times 2 {\text{ kHz}} $(品红色实线), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 6 {\text{ kHz}} $(蓝色实线), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 8 {\text{ kHz}} $(黑色实线), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 10 {\text{ kHz}} $(绿色实线), $\varDelta = {\varDelta _1} = {\omega _{\text{m}}}$, 其他参数与图2相同
Figure 5. (a) , (b)Plots the efficiency (in logarithmic form) of USSG and LSSG versus ${\delta _1}$ for different values of ${g_{{\text{ac}}}}$, where $ {g_{{\text{ac}}}} = 2{\text{π}} \times 2 {\text{ kHz}} $ (magenta line), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 6 {\text{ kHz}} $ (blue line), $ {g_{{\text{ac}}}} = 2{\text{π}} \times 8 {\text{ kHz}} $ (black line), $ {g_{{\text{ac}}}} = 2{\text{π}} \times $$ 10 {\text{ kHz}} $ (green line), $\varDelta = {\varDelta _1} = {\omega _{\text{m}}}$, the other parameters are the same as those in Fig. 2.
图 6 (a), (b)不同${\gamma _a}$值和边带与${\delta _1}$的效率(对数形式), 其中$ {\gamma _a} = 2{\text{π}} \times 2 {\text{ MHz}} $(品红色实线), $ {\gamma _a} = 2{\text{π}} \times 4 {\text{ MHz}} $(绿色实线), $ {\gamma _a} = 2{\text{π}} \times 6 {\text{ MHz}} $(黑色实线), ${g_{{\text{ac}}}} = 2{\text{π}} \times 10 {\text{ kHz}}$, 其他参数与图2相同
Figure 6. (a), (b) Plots the efficiency (in logarithmic form) of USSG and LSSG versus ${\delta _1}$ for different values of ${\gamma _a}$, where $ {\gamma _a} = 2{\text{π}} \times 2 {\text{ MHz}} $ (magenta line), $ {\gamma _a} = 2{\text{π}} \times 4 {\text{ MHz}} $ (green line), $ {\gamma _a} = 2{\text{π}} \times 6 {\text{ MHz}} $ (black line), ${g_{{\text{ac}}}} = 2{\text{π}} \times $$ 10 {\text{ kHz}}$, the other parameters are the same as those in Fig. 2
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