Control of Fano resonances and slow light using Bose-Einstein condensates in a nanocavity

In this study, a standing wave in an optical nanocavity with Bose-Einstein condensate (BEC) constitutes a one-dimensional optical lattice potential in the presence of a finite two bodies atomic interaction. We report that the interaction of a BEC with a standing field in an optical cavity coherently evolves to exhibit Fano resonances in the output field at the probe frequency. The behavior of the reported resonance shows an excellent compatibility with the original formulation of asymmetric resonance as discovered by Fano [U. Fano, Phys. Rev. 124, 1866 (1961)]. Based on our analytical and numerical results, we find that the Fano resonances and subsequently electromagnetically induced transparency of the probe pulse can be controlled through the intensity of the cavity standing wave field and the strength of the atom-atom interaction in the BEC. In addition, enhancement of the slow light effect by the strength of the atom-atom interaction and its robustness against the condensate fluctuations are realizable using presently available technology.

Figure 1

The schematic representation of the system: an optomechanical system with BEC confined in an optical cavity with fixed mirrors. A strong driving field of frequency ${\omega }_l$ and a weak probe field of frequency ${\omega }_p$ are simultaneously injected into the cavity.

Figure 2

Fano interference and EIT for (a) $g=0.1{\omega }_b$ and (b) $g=1{\omega }_b$: Spectral tuning of the optical response of the system from asymmetric Fano resonance to EIT. When the effective cavity detuning in the BEC-cavity setup is nonresonant with the effective frequency ${\omega }_b$, i.e., $\mathrm{\Delta }\ne {\omega }_b$, the transmission exhibits asymmetric Fano resonances. At resonant detuning ($\mathrm{\Delta }={\omega }_b$), a transparency (EIT) window appears. The rest of the parameters are [67, 72]: $\kappa =0.1{\omega }_b, U_{\mathrm{eff}}={\omega }_b, {\gamma }_b/2\pi =7.5\times {10}^{-3}$ Hz, $\nu /2\pi =1000$ kHz, and ${\omega }_b/2\pi =10$ kHz.

Figure 3

Fano resonances in the absorption profiles are shown for (a) $g=5{\omega }_b, 20{\omega }_b, 50{\omega }_b$ corresponding to dot-dashed, dashed, and solid curves, respectively, and (b) $U_{\mathrm{eff}}/{\omega }_b=1$, 50, 100, solid, dashed, and dot-dashed curves, respectively. Here, $\mathrm{\Delta }=0.8{\omega }_b$, and all the other parameters are the same as in Fig. 2.

Figure 4

Spectrum of Fano resonances in the absorption profiles are shown for a range of specific detuning: (a) For $\mathrm{\Delta }/{\omega }_b=0.5\text{to}1$, i.e., $\mathrm{\Delta }<{\omega }_b$, containing the profiles as shown in Fig. 3. (b) For $\mathrm{\Delta }/{\omega }_b=1.0\text{to}1.5$, which shows that narrow and broad regions in Fano profiles can be flipped by suitably tuning the detuning at the other side (i.e., $\mathrm{\Delta }>{\omega }_b$) of the resonance $\mathrm{\Delta }\sim {\omega }_b$. (c) For $\mathrm{\Delta }/{\omega }_b=0.5\text{to}1.5$, which reflects that the Fano spectrum is symmetric around $\mathrm{\Delta }\sim {\omega }_b$. All the other parameters are the same as in Fig. 2.

Figure 5

Fano resonances in the absorption profiles are shown for different values of (a) cavity decay $\kappa$, and (b) condensate (Bogoliubov mode) fluctuations ${\gamma }_b$. In (b), we show the BEC-cavity setup can pave the way to observe original Fano-like resonances [2] with a lower minimum and a higher maximum. All the other parameters are the same as in Fig. 2.

Figure 6

The transmission $|t_p{|}^2$ of the probe field as functions of normalized probe detuning $\overline{\delta }/{\omega }_b$ for $\mathrm{\Delta }={\omega }_b$ and $g/{\omega }_b=0,1,2,3,4$, respectively. All the other parameters are the same as in Fig. 3.

Figure 7

We plot phase ${\varphi }_t$ of the probe field as function of the normalized probe detuning $\overline{\delta }/{\omega }_b$ for $\mathrm{\Delta }={\omega }_b$. The inset shows the rapid change around resonance $\overline{\delta }\sim {\omega }_b$. All the other parameters are the same as in Fig. 6.

Figure 8

The group delay ${\tau }_g$ versus the pump power $P_l$ is presented, which shows the pulse delay (subluminal behavior) of the order $5\mu \mathrm{s}$ in the probe transmission. All the other parameters are the same as in Fig. 6.

Figure 9

The group delay ${\tau }_g$ versus the pump power $P_l$ and $U_{\mathrm{eff}}$ is presented. The contour plot shows that pulse delay ${\tau }_g$ (subluminal behavior) can further be enhanced by increasing the atom-atom interaction. All the other parameters are the same as in Fig. 6.

Figure 10

The group delay ${\tau }_g$ versus the pump power $P_l$ and normalized condensate fluctuations ${\mathrm{\Gamma }}_b/{\omega }_b$ is presented, which shows that pulse delay (subluminal behavior) decreases with the increase in the fluctuations of the condensate mode. All the other parameters are the same as in Fig. 6.

Figure 11

The group delay ${\tau }_g$ versus the pump power $P_l$ and $\mathrm{\Delta }/{\omega }_b$ is presented, which is related to the Fano spectrum as shown in Fig. 4. The contour plot shows the pulse delay ${\tau }_g$ (slow light) for both the regimes, $\mathrm{\Delta }<{\omega }_b$ and $\mathrm{\Delta }>{\omega }_b$, where the former regime yields the high slow light effect. All the other parameters are the same as in Fig. 6.