Vijay Bhatt

We investigate the transient dynamics of cavity-EIT-based all-optical switching in a system of trapped ions coupled to an optical cavity through numerical simulations. In contrast to steady-state analysis, the time-dependent response provides direct insight into the switching speed, transient dynamics, and achievable switching contrast. We consider three distinct switching schemes and systematically compare their performance as a function of the relevant system parameters. The switching contrast is evaluated from the time-dependent cavity output and used to characterize the performance of each scheme. For the four-level N-type system, we find distinct trade-offs between switching through suppression of the cavity-EIT signal and switching through resonance shifting, with the former exhibiting a faster temporal response. The corresponding three-level scheme can achieve near-unity switching contrast with substantially shorter switching pulses, although it does not provide an independent switching control field. These results establish the performance limits and trade-offs of different cavity-EIT-based switching schemes and provide guidelines for optimizing their operation for applications such as high-speed optical gating, frequency-selective photon routing, frequency-multiplexed quantum communication, etc.

We present a technique for measuring ion temperature using cavity-based electromagnetically induced transparency (EIT) applicable for cavity QED systems. This method enables efficient extraction of the ion's phonon occupation number following sub-Doppler cooling close to the motional ground state. The proposed method requires operation in the resolved-sideband regime, where individual motional states can be selectively addressed for all relevant transitions either by selecting appropriate energy levels for the three-level system or by employing strong confinement with high secular frequencies ($\sim 10 MHz$). It relies on monitoring the cavity probe transmission while scanning the probe laser frequency to establish cavity-induced EIT using a control beam, thereby significantly simplifying the measurement procedure. We establish a theoretical model that demonstrates the influence of the thermal state of the trapped ion vis-à-vis the EIT linewidth measured. We show through numerical simulations how the cavity-induced EIT transmission may be used as a thermometry tool to deduce the ion temperature as well as its motional state in the sub-Doppler cooling regime, even for systems that are in the weak coupling regime.