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arXiv:2602.22635

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

Wenjun Shao, Jian Li

quant-phSubmitted Feb 26, 2026• Announced Feb 27, 2026• 0 citations
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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.

Comments
7 pages,6 figures

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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.
We study the spectra of collective low excitations of two atomic ensembles which couple with a single-mode cavity field. When the left ensemble is driven with an external optical field, its corresponding response spectrum to the incident optical light shows an electromagnetically-induced-transparency--like (EIT-like) phenomenon when the layers are arranged in the sequence of node antinode but not in the sequence of antinode node. In the case of antinode-antinode sequence, the response spectrum shows an EIT-like phenomenon with two transparent windows. We also investigate the fluctuation spectra of the atomic collective excitation modes and show similar EIT-like phenomena.
Abstract In this work, the absorption spectrum of a two-level ion in a linear Paul trap is investigated, the ion is supposed to be driven by two orthogonal laser beams, the one along the axial of the trap acts as the control light beam, the other as probe beam. When the frequency of the control laser is tuned to the first red sideband of the ionic transition, the coupling between the internal states of the ion and vibrational mode turns out to be a Jaynes–Cummings (JC) Hamiltonian, which together with the coupling between the probe beam and the two-level ion constructs a Λ -type three-level structure. In this case the transparency window may appear in the absorption spectrum of the probe light, which is induced by the ionic vibration and is very similar to the cavity induced transparency (Rice and Brecha 1996 Opt. Commun . 126 230–5). On the other hand, when the frequency of the control laser is tuned to the first blue sideband of the ionic transition, the two-level ion and vibrational mode are governed by an anti-Jaynes–Cummings (anti-JC) Hamiltonian, the total system including the probe beam forms a V -type three-level structure. And the Autler–Townes splitting in the absorption spectrum is found.
We study the optical properties of a two-level atomic ensemble controlled by a high-finesse cavity. Even though the cavity is initially in the vacuum state in the absence of external driving, the probe response of the atomic ensemble can be dramatically modified. When the collectively enhanced atom–cavity coupling is strong enough and the cavity decay rate is much smaller than the atomic damping rate, an electromagnetically induced transparency-like coherent phenomenon emerges with a dip absorption for the response of the two-level atoms in the cavity without driving, and thus is called vacuum induced transparency. We also show the slow light with very low group velocity in such an atomic ensemble.
We study the optical properties of a two-level atomic ensemble controlled by a high-finesse cavity. Even though the cavity is initially in the vacuum state in the absence of external driving, the probe response of the atomic ensemble can be dramatically modified. When the collectively enhanced atom–cavity coupling is strong enough and the cavity decay rate is much smaller than the atomic damping rate, an electromagnetically induced transparency-like coherent phenomenon emerges with a dip absorption for the response of the two-level atoms in the cavity without driving, and thus is called vacuum induced transparency. We also show the slow light with very low group velocity in such an atomic ensemble.
Summary form only given. The preparation of quantum systems in pure states is a prerequisite for coherent control. In this context laser cooling of trapped particles to the ground state of the confining potential is a powerful tool for preparing e.g. ions for quantum logic. In particular sideband cooling has been demonstrated to be the most efficient technique, allowing to achieve more than 99% of occupation of the ground state of the trap. This cooling technique relies on two conditions: the Lamb-Dicke regime, and the strong confinement regime. This latter condition, which allows the spectral resolution of individual sidebands of the motion, is however a limitation on the cooling time. We propose a model for cooling single ions inside a trap as an alternative to sideband cooling. The scheme uses electromagnetically induced transparency (EIT) in a /spl Lambda/-level scheme, where one of the transitions is dressed by a strong laser field. For detuning of the dressing laser, the absorption spectrum for the transition shows EIT when the cooling (probe) laser has detuning. Then, by tuning the cooling laser on the dark resonance (or EIT), for a suitable set of parameters and in the Lamb-Dicke regime the atoms are cooled to the ground state by the sideband transitions which are resonantly excited. The scheme achieves efficient ground state cooling and fast cooling rates using a continuous driving, instead of a pulsed one as in Raman sideband cooling schemes. An example is illustrated, where the average vibrational number is plotted as a function of the cooling time, and the final probability of occupation is plotted as a function of the vibrational state. This method may also be applied to reduce phase errors in coherent manipulations of trapped ions for quantum logic.