Vibration induced transparency and absorption with two ion ensembles in a linear trap

Abstract

We study the spectra of collective low excitations of two atomic ion ensembles which are confined in a liner trap by addressing lases. When the left ensemble is driven by an external optical field, its corresponding response spectrum to the incident optical light shows a vibration-induced transparency phenomenon when the detuning of the laser addressing the ion is tuned to the first red sideband. In the case of the detuning tuned to the first blue sideband, the response spectrum shows a conversion from the absorption peak to the transparency window. Furthermore, we investigate the fluctuation spectra of the collective excitation modes of ion ensemble and show the similar phenomena.

Figures (6)

• Figure 1: The response intensities of ion ensembles $\vert A_s/\chi \vert^2$ (red solid curve) and $\vert B_s/\chi \vert^2$ (blue dashed curve) in arbitrary units as a function of the detuning $\Delta$ according to Eqs. \ref{['A_s']} and \ref{['B_s']} with $g_A=g_B=10$ but with different decay rates: (a) $\gamma_A =3$, $\gamma_B =3$; (b) $\gamma_A =30$, $\gamma_B =30$; (c) $\gamma_A =30$, $\gamma_B =3$; (d) $\gamma_A =3$, $\gamma_B =30$. All the frequencies are in units of $\kappa$.
• Figure 2: The response intensities of ion ensemble $\vert A_s/\chi \vert^2$ as a function of the detuning $\Delta$ for (a) $g_B=1$, (b,c) $g_B= 10$ with different coupling strengths $g_A$, or for (d) $g_A= 1$, (e,f) $g_A= 10$ with different coupling strengths $g_B$. Here $\gamma_A = \gamma_B = 5$ (in units of $\kappa$).
• Figure 3: The response intensities of ion ensemble $\vert A_s/\chi \vert^2$ as a function of the detuning $\Delta$ for (a) $g_B=1$, (b,c) $g_B= 10$ with different coupling strengths $g_A$, or for (d,e) $g_A= 1$, (f) $g_A= 10$ with different coupling strengths $g_B$. Here $\gamma_A = \gamma_B = 5$.
• Figure 4: The fluctuation spectra of driven ion ensemble, $S_A(\omega)$ in Eq. \ref{['SY']}, as a function of (a) $\omega/\kappa$ and $g_A/\kappa$ for $g_B = 10$, (b) $\omega/\kappa$ and $g_B/\kappa$ for $g_A = 10$. Here $\Delta=0$ and $\gamma_A = \gamma_B = 5$ (in units of $\kappa$).
• Figure 5: The fluctuation spectra of driven ion ensemble, $S_A(\omega)$ in Eq. \ref{["SY'"]}, as a function of $\omega/\kappa$ for (a) different coupling strengths $g_A$ with fixed $g_B = 1$ or (b) different coupling strengths $g_B$ with fixed $g_A = 10$. For the other parameters, see Fig. \ref{['fluct']}.