Optimized Multi-Ion Cavity Coupling

Recent technological advances in cavity quantum electrodynamics (CQED) are paving the way to utilize multiple quantum emitters confined in a single optical cavity. In such systems, it is crucially important to control the quantum mechanical coupling of individual emitters to the cavity mode. In this regard, combining ion trap technologies with CQED provides a particularly promising approach due to the well-established motional control over trapped ions. Here, we experimentally demonstrate coupling of up to five trapped ions in a string to a high-finesse optical cavity. By changing the axial position and spacing of the ions in a fully deterministic manner, we systematically characterize their coupling to the cavity mode through visibility measurements of the cavity emission. In good agreement with the theoretical model, the results demonstrate that the geometrical configuration of multiple trapped ions can be manipulated to obtain optimal cavity coupling. Our system presents a new ground for exploring CQED with multiple quantum emitters, enabled by the highly controllable collective light-matter interaction.

Figure 1

(a) Experimental setup. Pump and repump laser beams are overlapped and sent obliquely to the trap axis. The cavity emission at 866 nm is detected with an avalanche photodiode (APD). A reference laser at 894 nm is used for locking the cavity frequency. A combination of filters are used to remove background light from the cavity emission. Dichroic mirror (DM), focusing lens (FL), polarization beam splitter (PBS), photodiode (PD), quarter wave plate (QWP). (b) Level scheme of ${}^{40}{\mathrm{Ca}}^{+}$ indicating wavelengths relevant for the experiment.

Figure 2

Cavity emission rate $R_{\mathrm{em}}$ as the cavity is translated relative to the position of a single ion ($\lambda =866\mathrm{nm}$). The axial secular frequency is 620 kHz. A visibility of 39% is obtained from a sinusoidal fit. This corresponds to a temperature of $\approx 1.2T_D$ where $T_D$ is the Doppler temperature. Note that the far-detuned cooling beam is not used in this measurement.

Figure 3

Visibility measurements for (a) a single ion and (b) two ions as a function of the c.m. secular frequency. Error bars are derived from the fitting errors. The blue curves are fits based on our theoretical model (see Supplemental Material [34]). The temperatures extracted from the fits are $\sim 1.5T_D$ in both cases. The increase in temperature compared to Fig. 2 is due to the presence of the far detuned laser. The inset figures in (b) illustrate the relationships between the ions’ positions and the spatial variation of $g^2(z)$ at a local maximum and minimum of the visibility. (c) The inter-ion spacing between two ions. The dotted vertical lines indicate the c.m. secular frequencies at which the spacing becomes an integer multiple of $\lambda /2$.

Figure 4

Visibility measurements for (a) three, (b) four, and (c) five ion strings. The fits assume that the temperatures of all normal modes are identical. The extracted temperatures are (a) 1.56 $T_D$, (b) 1.57 $T_D$, (c) 1.72 $T_D$, showing a slight increase with the number of ions. The insets illustrate the configurations of ion strings. In particular, with four and five ions, the inter-ion spacing is not uniform, i.e., $d_1\ne d_2$.